MICROCHANNEL HEAT EXCHANGER

CLAIM OF PRIORITY

Benefit of priority is hereby claimed to U.S. Provisional Patent

Application Serial Number 61/281,022, entitled, "Integrated Bubble Generation, Transport and Removal for Enhanced Liquid Cooling in a MicroChannel Heat Sink," filed November 12, 2009, Attorney Docket Number 2413.114PRV, which is hereby incorporated by reference herein in its entirety, including its description of integrated bubble generation, transport and extraction for enhanced liquid cooling in a microchannel heat exchanger. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR

DEVELOPMENT

This invention is made with government support under CAREER award number 0449269 from NSF. The government has certain rights in this invention. BACKGROUND

Heat exchange is an important design consideration. Heat exchangers such as heat sinks or heat emitters benefit many systems and methods by transferring heat away from, or to, a heat source. Improved heat sinks provide several benefits, such as reduced size, mass, cost, improved performance or increased reliability, among others.

OVERVIEW

In an example, computer processing units emit high heat and benefit from efficient heat exchangers, such as to aid in faster computation. In an example, heat exchanger performance is a function of the materials used, the geometry of the heat exchanger, and the heat exchanger's heat transfer coefficient. In an example, the more efficient a heat exchanger is, the greater its Nusselt number is. In an example, microchannel heat exchangers, possessing a manifold of channels through which either a liquid (single-phase) or a gas and a liquid (two-phase) are flown transfer more heat than single-phase heat exchangers, as measured by their higher Nusselt number, but can be difficult to manage. Some examples disclosed here represent a manageable and efficient two-phase flow heat exchanger, with a Nusselt number double that of single- phase flow heat exchangers. An example uses segmented flow, a type of two- phase flow where bubbles segment the flow of water through the channels. In an example, segmented flow is more readily controlled than a boiling two-phase flow approach, where the water boils to produce the second phase while flowing. In an example, segmented flow increases convection, thereby increasing the Nusselt number. In an example, gas is removed from a channel such as a microchannel using a hydrophobic porous membrane. In an example, dynamic bubble traps and diffusion-based gas separators remove gas.

In an example, one or more heat exchangers are configured to cool electronic equipment, such as CPUs. Soldering irons can reach temperatures greater than 400°C. In an example, a heat exchanger is configured to reduce damage to transistors by absorbing heat. In an example, one or more laser diodes, such as in continuous and pulsed mode lasers, benefit from cooling. In an example, twenty- five or more diodes are fixed to a small bar, generating heat fluxes of up to 107 W/m ² , are cooled using subject matter disclosed herein.

In an example, deaerating liquids are used in the operation of equipment such as analytical equipment. In an example, during a process such as a liquid chromatography exam, gas such as air is removed from a supply influent to a pump to prevent bubble formation. In an example, a gas such as air can cause reactions in samples used in clinical testing if not properly removed from a circulating loop. In an example, deaeration is a part of an industrial purification of water to produce deionized water or water for nuclear power plants.

Example 1 can include a heat exchange system for heat exchange with a heat source and a cold source. In Example 1, the system can include a circulation loop. In Example 1, the circulation loop can include a heat emission portion configured to exchange heat with the cold source and a heat absorption portion configured to exchange heat with the heat source, the heat absorption portion comprising a channel. Example 1 can include a liquid pump configured to circulate a liquid through the circulation loop, from an inlet of the channel to an outlet of the channel and a bubble injector coupled to the circulation loop proximal to the inlet of the channel and configured to flow a gas to form a plurality of gas bubbles in the channel, with each of the plurality of gas bubbles monodispersed across the channel, with segments of liquid separating successive gas bubbles of the plurality of gas bubbles.

In Example 2 the subject matter of Example 1 can optionally include a gas circulation loop coupled to the bubble injector and can include a gas separator coupled to the circulation loop proximal to the outlet of the channel, the gas separator configured to remove the gas from the liquid.

In Example 3 the subject matter of any one of Examples 1-2 can include a gas circulation loop coupled to the gas separator, with the bubble injector configured to draw the gas from the gas separator, through the gas circulation loop.

In Example 4 the subject matter of any one of Examples 1-3 can optionally be configured such that the gas separator includes a hydrophobic membrane.

In Example 5 the subject matter of any one of Examples 1-4 can optionally be configured such that the channel is sized such that at least one of the plurality of gas bubbles has a bond number below around 3.6.

In Example 6 the subject matter of any one of Examples 1-5 can optionally be configured such that at least one of the plurality of bubbles has an aspect ratio of length to width less than or equal to 4:1.

In Example 7 the subject matter of any one of Examples 1-6 can optionally be configured such that the channel is sized to maintain a wetted channel between successive segments of liquid.

In Example 8 the subject matter of Example 7 can optionally be configured such that the bubble injector is configured to disperse the segments of liquid over regular intervals.

In Example 9 the subject matter of any one of Examples 1-8 can optionally be configured such that the bubble injector includes a jet pump. In Example 10 the subject matter of Example 9 can optionally be configured such that the liquid pump is peristaltic pump.

In Example 11 the subject matter of any one of Examples 1-1 1 can optionally be configured such that the bubble injector is configured to flow the plurality of gas bubbles, substantially free of bubbly flow.

Example 12 includes a method for heat exchange between a heat source and a heat sink. Example 12 can includes affixing the heat sink to the heat source, with the heat sink thermally communicative with the heat source, flowing a liquid through a channel in the heat sink, at a determined flow rate and liquid pressure, flowing a gas into the liquid and forming a plurality of gas bubbles in the liquid, with each of the plurality of gas bubbles monodispersed in the liquid, in the channel, with segments of liquid separating successive gas bubbles of the plurality of gas bubbles and exchanging heat between the heat sink and the heat source.

In Example 13 the subject matter of Example 12 can optionally include separating the gas from the liquid after exchanging heat between the heat sink and the heat source.

In Example 14 the subject matter of any one of Examples 13-14 can optionally be configured such that flowing the gas includes flowing gas separated from the liquid and circulated to a gas pump.

In Example 15 the subject matter of any one of Examples 12-14 can optionally include extracting the gas from the liquid after exchanging heat between the heat sink and the heat source.

In Example 16 the subject matter of any one of Examples 12-15 can optionally be configured such that segmenting the bubbles includes controlling the segmenting by adjusting at least one of a gas pressure of the gas, a gas-flow rate of the gas, a wetting angle of the liquid, a liquid flow rate of the liquid and a liquid pressure of the liquid.

In Example 17 the subject matter of any one of Example 12-16 can optionally include circulating liquid through a circulation loop, and cooling the liquid along a heat emission portion of the circulation loop, can optionally be configured such that exchanging heat between the heat sink and the heat source includes heating the liquid along a heat absorption portion of the circulation loop.

Example 18 can include a heat exchange system for heat exchange with an integrated circuit. Example 18 can include a heat sink comprising a close circulation loop. The heat sink of Example 18 can include a heat emission portion configured to exchange heat with a cold source and at least one heat absorption portion configured to exchange heat with the integrated circuit, the heat absorption portion including a microchannel. Example 18 can include a liquid pump configured to circulate a liquid through the circulation loop, from an inlet of the microchannel to an outlet of the microchannel, a bubble injector coupled to the microchannel and configured to flow a gas to form a plurality of gas bubbles in the microchannel, with each of the plurality of gas bubbles monodispersed across the microchannel, with segments of liquid separating successive gas bubbles of the plurality of gas bubbles and a closed gas circulation loop, with a hydrophilic membrane coupled to the circulation loop proximal to the outlet of the microchannel and between the circulation loop and the gas circulation loop, the hydrophilic membrane configured to remove the gas from the liquid, the bubble injector configured to draw the gas from the hydrophilic membrane to the bubble injector.

In Example 19 the subject matter of Example 18 can optionally be configured such that the heat sink defines a plurality of microchannels, each coupled to the circulation loop in parallel.

In Example 20 the subject matter of any one of Examples 18-20 can optionally be configured such that the integrated circuit forms a part of a computer comprising a random access memory coupled to the integrated circuit.

This overview is intended to provide an overview of subject matter of the present patent application. It is not intended to provide an exclusive or exhaustive explanation of the invention. The detailed description is included to provide further information about the present patent application. BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file can contain at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

Figure 1 illustrates a heat sink such as a microchannel heat sink in direct contact with a heated substrate (such as an integrated circuit chip), according to some examples.

Figure 2 illustrates a thermal resistances and temperature profile along the flow path for constant heat flux conditions, according to some examples.

Figure 3 A illustrates LB &ndL _s i _ug , according to some examples.

Figure 3B illustrates a definition of LB, L _s i _ug , and L _ce n, according to some examples.

Figure 4 illustrates a cross-sectional view of a bubble in a square channel at low Ca, with partitions, according to some examples.

Figure 5 illustrates a thermal resistance plotted for a heat sink with 7 parallel 500 μιη channels, 25 mm in length, according to some examples.

Figure 6 illustrates thermal resistances plotted for a heat sink with 70 parallel 50μιτι channels, 25 mm in length, according to some examples.

Figure 7 illustrates thermal resistances plotted for a mini channel heat sink with 3 parallel 2mm channels, 25 mm in length, according to some examples.

Figure 8A illustrates a heat sink and an o-ring, according to some examples.

Figure 8B illustrates an example with heated substrate showing thermocouple locations, with a heat sink on top, with units in mm, according to some examples.

Figure 8C illustrates a cross-sectional view of an example section.

Figure 9 illustrates a set up for energy balance verification, with corresponding Equations, according to some examples.

Figure 10A illustrates a graphical representation of experimental setup, according to some examples. Figure 10B illustrates a flow visualization, according to some examples.

Figure IOC illustrates a flow visualization, according to some examples.

Figure 10D illustrates a flow visualization, according to some examples.

Figure 1 OE illustrates a flow visualization, according to some examples.

Figure 11 illustrates theoretical and measured values of Nusselt number for single phase and segmented flow versus the Reynolds number based on the mass velocity of water, according to some examples.

Figure 12 illustrates theoretical and measured values of pressure drop for single phase and segmented flow versus the Reynolds number based on the mass velocity of water, according to some examples.

Figure 13 illustrates a Nusselt number expressed as a function of the pressure drop for single phase and segmented flow, according to some examples.

Figure 14 illustrates surface temperatures, Ts, along the flow direction, for a water flow rate of 75 mL/min, in the single-phase and segmented flow cases, according to some examples.

Figure 15A illustrates an assembly of a gas separator, according to some examples.

Figure 15B illustrates a micrograph of a porous hydrophobic membranes with a 0.2 μπι pore size, according to some examples.

Figure 15C illustrates a micrograph of a porous hydrophobic membranes with a 1.2 μιη pore size, according to some examples.

Figure 15D illustrates a micrograph of a porous hydrophobic membranes with a 10 μηι pore size, according to some examples.

Figure 16 illustrates bubble dynamics during a extraction process, according to several examples.

Figure 17 illustrates shapes of vanishing bubbles at different Weber numbers, according to several examples.

Figure 18 illustrates pressure drop across the membrane as a function of the volume flux of the gas-flow through the membrane, according to some examples.

Figure 19 illustrates a comparison between some examples and examples using Equation 18 for criteria 2, according to several examples. Figure 20 illustrates bubble travel distance and theoretical film thickness as functions of bubble travel speed, according to several examples.

Figure 21 illustrates a gas-liquid meniscus that is held at an entrance of a pore as the surface tension holds the pressure difference across the meniscus and discourages or prevents water from leaking through the pore.

Figure 22 illustrates a method, according to some examples.

DETAILED DESCRIPTION

The apparatus, systems and methods described here are for enhancing heat exchange between a heat source and a liquid. Various examples include a heat sink including liquid flowing through or more channels such as one or more microchannels. Bubbles are created in the liquid, such as to produce a segmented or slug flow pattern. Segmented flow increases the heat transfer coefficient in some instances, even in instances where the bubbles have a lower thermal conductivity than the liquid in which the bubbles are formed. In some examples, the heat transfer coefficient is increased by more than 100% over a single-phase liquid flow. Some examples remove the bubbles after heat transfer.

In certain instances, bubbles are extracted from liquid in a channel using a separator such as a gas separator. In examples, a separator includes a hydrophobic porous membrane. According to some examples, in the channel, bubbles travel along a hydrophobic porous membrane where they are extracted through the membrane, with liquid remaining in the channel. Removing bubbles from the channel is useful, such as for preventing the bubbles from reaching some elements of a closed-loop system, such as a pump, where they can cause undesirable effects, such as pump damage or bubbly flow.

SEGMENTED FLOW EXAMPLES

Liquid cooling is an efficient way to remove heat fluxes, such as those with magnitudes of up to 10,000 W/cm ² . One limitation of heat sinks including a single-phase fluid flow through a channel such as a microchannel is their relatively low Nusselt number, due in some instances to laminar flow. Examples discussed here enhance the Nusselt number, such as by introducing segmented flow. In some examples, a segmented flow pattern is created by periodic or regular injection of bubbles such as gas bubbles into one or more liquid filled channels, such as by injecting gas through a T-junction, such as into one or more water-filled channels. Various injection methods can be used, such as the opening of a valve that constrains a pressurized gas, jet pump injection, and other injection forms.

Some examples include a polycarbonate heat sink. Some heat sinks include an array of parallel channels such as an array of parallel microchannels. In some instances, each channel has a square cross-section that is around 500 μηι wide. Some examples increase the Nusselt number of laminar flow by more than a hundred percent, such as in instances when the mass velocity of the liquid is within the range 330 - 2000 kg/m ² s.

Nomenclature:

A = area (m ² )

B = hydraulic coefficient

Ca = capillary number (μΙΙ/σ)

c = specific heat (J/kgK)

C = gas constant

d = hydraulic diameter (m)

f = volumetric flow rate (m Is)

f _r = friction factor

G = mass velocity (kg/m s)

h = convection coefficient (W/m K)

H = height (m)

k = thermal conductivity (W/mK)

K = minor loss term

L = length (m)

n = number of bubbles

N= number of channels

p = pressure (Pa)

P = perimeter (m) Pr = Prandtl Number (v/a) Nu = Nusselt Number (hd/k) Re = Reynolds Number (pUd/μ) Q = heat flow (W)

q"= heat flux (W/m ² )

T= temperature (°C)

U = velocity (m/s)

V = volume (m ³ )

w = width (m)

Greek Letters:

a = fin enhancement factor a* = aspect ratio

j3= temperature difference (°C) δ= film thickness (m) e= liquid fraction

η= fin efficiency

Θ = thermal resistance (K/W) μ= viscosity (Pa s)

p= density (kg/m )

a = surface tension (N/m)

Subscripts:

B = bubble

c = channel

G= gas

L = liquid

S = surface

seg = segmented flow sin = single phase flow slug = liquid slug

sub = substrate w= wall

Various approaches include a heat sink for the purpose of cooling, such as cooling electronics. As the example of Figure 1 illustrates, a heat sink that removes heat, Q , such as by flowing fluid such as liquid or liquid-gas mixes in channels over a heated substrate (e.g. a computer chip). Some approaches improve or optimize the dimensions of one or more channels in terms of width and height for single-phase flow of water under the constraint of maximum allowable pressure drop and substrate surface temperature. One approach demonstrates that single-phase water-cooling removes up to 790 W/cm .

According to this approach, a heat flux required a mass velocity, G, of 5700 kg/m ² s and a pressure drop of 220 kPa.

In another approach, an optimization process is done to minimize the pressure drop under the constraints of a given heat flux and maximum substrate temperature. In this approach, it is found that a water pressure drop below 10 kPa is sufficient to remove 100 W/cm ² with optimum channel geometry. One problem with single-phase flow heat transfer in one or more channels such as one or more microchannels is the low Nusselt number obtained in laminar flow, on the order of 4. Methods for increasing the Nusselt number include: surface area enhancement by geometric obtrusions, tree-like bifurcating channels, large aspect ratio channels, serpentine channels to promote mixing and turbulence, short channels where the entrance region dominates, nano-fluids, and two-phase flow, among others.

In various examples, two-phase flow is desirable, due at least in part to a very high heat of vaporization. According to some examples, flow boiling can dissipate up to 10,000 W/cm ² , which in some cases is 10 times more heat than single-phase flow. While flow boiling is beneficial in some instances because it delivers high heat flux at the constant temperature of the phase change, it is difficult to control due to backflow and instabilities. Some approaches have attempted to control the instabilities and backflow, such as by manufacturing artificial nucleation sites and inlet restrictions. A drawback of boiling flow, where water is the working liquid, is that the saturation temperature is higher than the operating temperature of most electronics. As such, various examples use refrigerants as working fluids, since the boiling temperature is lower than water. Refrigerants, however, offer lower cooling capabilities due to a lower specific heat and heat of vaporization.

Various examples discussed here use segmented flow as a way to enhance single-phase heat transfer with water in channels such as microchannels. According to various examples, segmented flow is a periodic pattern of non- condensable bubbles and liquid slugs. According to some examples, the bubbles are created at a T-junction by the injection of a gas such as air or nitrogen. In some examples, bubbles are injected into liquid-filled channels such as microchannels. In some examples, the bubbles are longer than the channel diameter. Some examples use segmented flow in chemical engineering applications where it increases mass transfer. In some examples, segmented flow increases heat transfer, due to the same phenomenon of enhanced convection by recirculating wakes in the liquid slugs. In some examples, the presence of recirculating wakes requires surface tension to dominate over gravity, which occurs when the Eotvos or Bond number pgd ² /o < 3.6. In some examples, the Bond number pgd ² /a < 3.368.

In one approach, a finite-element simulation is used to determine the liquid to solid mass transfer, for the case of catalyst removal from a monolith wall. The approach determined that the rate of mass transfer in the liquid slugs is 10 times the rate of laminar flow. According to various examples, the presence of bubbles increases the pressure drop in the channel due to the Laplace pressure at the liquid gas interface, but the present subject matter is not so limited.

Some examples, including some industrial applications, have a closed loop system, where water from the outlet is circulated through a pump and a heat sink to an inlet of a channel. In some examples, bubbles are extracted before the pump and re-injected after the pump. In some examples, bubbles are extracted from segmented flow by the addition of smaller capillary vessels or tubes downstream which remove the bubbles due to the difference in interfacial tension. Some examples use a hydrophobic porous membrane forming part of a circulation loop or flow channel to remove bubbles.

Figure 1 illustrates a heat sink 102 couplable to a heated substrate 104. Examples of heated substrates include, but are not limited to integrated circuits, power supplies, radiators, reactors and other heat sources. The heated substrate 104 is one type of heat source that the heat sink 102 is coupleable to, as the heat sink 102 is also couplable to a cold source such as a finned heat sink.

The heat sink 102 and the heat source are adjacent, in some examples, and are not necessarily touching one another. In some examples they abut. In some examples, the heat sink 102 defines a plurality of channels 106 extending through the heat sink 102.

In some examples, the ID equivalent resistances method used in some approaches is used to calculate the performance of a micro heat sink, such as the heat sink 102 illustrated in Figure 1. In Figure 2, the total thermal resistance Θ Mai is the ratio of ΔΤ= Ts, _max -TL,i _n , the difference between the maximum heated substrate temperature and the fluid temperature at the inlet, over the power dissipated, Q , according to some examples. In some examples, the total thermal resistance, θ, ₀ , _α ι = & _hea & S _conv , is the sum of a heat resistance and a convective resistance, according to some examples. In some instances, the heat resistance in Equation 1 is due to the heating of the fluid as it passes through the heat sink; it depends on volumetric flow rate/ΐ and specific heat capacity of the fluid (c . earV(Clfl) (1)

Equation 2 gives θ _∞ην , which is the resistance of the coolant fluid to heat convection, according to some examples. According to one approach, the expression for 0 _co „ _v is derived by treating the rectangular walls of a heat sink as fins with adiabatic boundary conditions at their end, the fin efficiency η is found by η = tanh(mH _c )/mH _c ,where m = (NukL/(k _s w _c w _w ) ) ^{1 2} . In Equation 2, according to one approach, L _c is the channel length, w is the heat sink width, w _c is the channel width, w _w is the width between one or more channels, H _c is the channel height and = 2H _c /(w _w +w _c ) is the fin enhancement factor.

From that example, the outlet temperature of the fluid and the maximum temperature of the substrate surface are found, according to one approach, based on the power dissipated Q and the inlet temperature of the fluid, as shown in Equation 3 and 4.

s. _m = (Qe _amf ) + T _L _ _oal (4)

Several correlations are available for the Nusselt number and pressure drop, as presented below. They are used to correlate examples for the respective single-phase and segmented flow case.

In one approach, single-phase, laminar, fully developed flow in rectangular channels with constant heat flux boundary conditions, Nu is calculated according to the correlation in Equation 5:

Nu _sin = 8.235(1 - 2.042 l(a*) + 3.0853(a*) ² - 2.4765(a*) ³ + 1.0578(a*) ⁴ - 0.186 l(a*) ⁵ ) (5) The aspect ratio is characterized by a parameter a*=min (H, w)/max (H, w), in one approach. In an approach including square channels where a* = 1, this correlation yields Nu = 3.61. The Nusselt number of single phase flow is expected to increase at higher Re due to the increasing thermal entry length, in some examples. According to one approach, when the thermal entry length is less negligible or no longer negligible, Nu is found using a first correlation approach. According to the approach, this correlation is valid for rectangular channels of any aspect ratio, constant heat flux boundary conditions, and laminar, hydrodynamically developed flow. According to an approach, when the hydrodynamic entry region is no longer negligible, one or more correlations according to a second correlation approach are used to find Nu. This approach is valid for Pr > 0.1, uniform heat flux and constant surface temperature, and any channel cross-section.

The pressure drop for single-phase flow, in one approach, is found valid for both laminar and turbulent flow, given in Equation 6, where d is the hydraulic diameter, K is the minor loss term and UL is the liquid velocity.

Ap = p (4f _r L _c /d+K) U _L ² /2 (6)

In one approach, for segmented flow, Nu at constant heat flux is estimated with a correlation established from detailed multiphase flow simulations in cylindrical pipes.

Nu = Nu . + 0.022Pr ⁰⁴ Re ^{4 5} ( ⁷ )

In Equation 7, Nu _s i _n is the Nusselt number for single-phase fully developed liquid flow, found with Equation 5, Pr is based on the properties of the liquid phase, and Re _seg = d PLUB/H'(LB/(LB+L _S I _U ^)), where ½ is the bubble velocity and the definitions of LB and L _s i _ug are the respective length of the bubble 302 and liquid slug 304, as shown in Figures 3A-B. According to some examples, a channel 306 is illustrated with a bubble 302 monodispersed in the channel 306. Figures 3A-B show examples with values for segmented flow at GL = 670 kg/m ² s. This is equivalent or substantially equivalent to the Reynolds number developed in some approaches. In some examples, Equation 7 is valid for well-defined bubbles when d is on the order of mm, Pr > 1 , Re _seg is on the order of 1000, and 300 K < (7L) _mea n < 340 K. In some examples, multiphase flow simulations revealed two mechanisms that increase Nu: the generation of the bubbles and the circulation in the liquid slugs. As mentioned herein, according to several examples, a segmented flow with recirculating wakes are generated provided the Bond number pgd ² /o < 3.6 and the capillary number Ca < 0.04. As disclosed here, other correlations for determining the Nusselt number of segmented flow are possible. As mentioned above, one approach provides an expression for Nu from numerical simulation in square channels. This approach is valid when there is full circulation in the slugs, as verified for Re < 300. One approach including heat transfer of gas-liquid flow in heat sinks, establishes correlations for the Nusselt number in triangular channels, for negligible entry length and Re < 100. As some of the examples disclosed here show, the correlation associated with Equation 7 reflects conditions in terms of Re and Ca range, flow patterns and entry length.

According to some examples, the pressure drop in segmented flow is described with Equation 8, where a pressure drop term across the bubbles is added to the single-phase pressure drop for the liquid slugs. In some examples, the pressure drop depends on two measurable quantities: the number of bubbles in a channel, n, and slug length, L _s i _ug , as per the example of Equation 8.

For some examples including square channels, the hydraulic coefficients are B = 56.91 and C - 2.39. The capillary number, Ca, is determined by the bubble velocity, in several approaches.

Ca= υ _Β μι σ (9)

Parameters in Equation 7 through 9, such as L _s i _ug , LB and L¾, are available from high-speed visualizations, as set forth herein. Values of pressure drop and Nu compare with the correlations, in some examples.

Equation 7 through 9 are used to design a heat sink, in some examples.

Bubble velocity L¾ is determined from an assumed water mass velocity Gi in some examples. Some examples determine a liquid volume fraction e = 0.5, and slug length L _S - 0.001 m, which are values representative of the information in

Figure 3. In some examples, a cross-section of the bubble is constant along its length, and according to some approaches, the bubble velocity is expressed by mass conservation.

U _B /U _slug =A _c /A _B (10) In some approaches, the slug velocity defined as U _s i _ug = Gi epL, used in

Equation 1 1.

For Equation 1 1 the cross-sectional area of the bubble, AB, is found using several examples, including the following. Figure 4 illustrates a cross-sectional shape of the bubble 402 monodispersed in a channel 404 for Ca < 0.04. A cross- section shape as disclosed in Figure 4, with a thin, constant film thickness δ along the walls and a thicker film at the edges with radius of curvature, r = (w _c - 2δ)/4, shows bubble area by dividing the cross-section of the bubble into several contiguous subsections or partitions 406, as shown in Figure 4, where 4 A i = v(w _c -2S) ² /l6, 4A ₂ = (w _c -2S) ² /2 and A ₃ = (w _c -2S) ² /4 and the total bubble area is AB =4Ai+ 4A ₂ + As. The film thickness δ is a function of the capillary number, Equation 9, and is expressed by Equations 12 and 13 using a correlation based on simulations according to some approaches. δ = 0.00332w _c (12) For 0.001 < Ca < 0.04 δ = -0.0423e ⁽ - ^c ^ ^5'3092) -0.1018e ^W3343) + 0.1761 (13) For Ca > 0.04

Several examples include a heat sink. In the example of Figure 2, heat transfer enhancement is noticeable under two conditions: first, _conv dominates over dheai , and second, the flow regime is such that there is a large difference between θ _εοην for segmented and Q _conv for single-phase flow. Equation 1 and 2 are plotted in Figure 5-7, and show how the thermal resistances vary in some examples with liquid flow rate for several channel diameters, with the same base area, L= 0.025 m and w=0.0075 m and w _w = w _c . According to several examples, the Ca transition represents a point where Ca = 0.04, when the bubble cross- section changes from the non-axisymmetric shape or monodispersed shape shown in Figure 4 to a more circular cross-section. In some instances, this results in a decrease of circulation in the slug. According to several examples, the Re transition represents the change from laminar to turbulent flow for the liquid flow rate. For an example including 500 μτη wide channels, Figure 5 illustrates that the Reynolds number of the liquid flow is greater than 60 in a regime where θ _εοην dominates over dheat- Figure 6 and Figure 7 show examples including the thermal resistances plotted for different channel widths, with the length remaining unchanged. In some examples, for smaller geometries, such as 50 μπι, shown in Figure 6, Θ heat hs the dominant resistance so that changes in Nu would not significantly modify the surface temperature, which is used to experimentally determine the Nusselt number. In some examples, for larger widths, such as 2 mm, shown in Figure 7, values of B _conv are higher than in the 500 μιτι channel case, resulting in a less efficient heat sink. Various examples are contemplated in which at least one of a plurality of bubbles has an aspect ratio of length to width of 4: 1 or smaller.

Examples of a heat sink and a heated substrate are shown in Figures 8A- C. A heat sink 802 including channels such as microchannels is coupled or affixed to a heat source such as a heated substrate 804. In some examples, the heated substrate includes an aluminum block. A layer such as a

polydimethylsiloxane (PDMS) seal is disposed over the heat sink 802, with a glass cover 808 disposed over the PDMS seal, held in place by one or more fasteners 810. The heated substrate, made from aluminum in some instances, is configured to provide uniform heat flow from the cartridge heater 814. Foam such as melamine foam 816 insulates the heated substrate, and Teflon 812 provides insulation between the heated substrate 804 and the fasteners 810. An o-ring 818 provides a seal to discourage flow leakage. Some examples quantify the heat loss of the heated substrate 804 through the insulation 816. In some examples, the surface temperature of the heated substrate 804 is found using a linear interpolation of thermocouple

measurements. In some examples, a heat sink 802 is extracted, and the top surface of the aluminum block 804 is exposed to an gaseous atmosphere such as air. In some examples, a remainder of the heated substrate 804 is insulated with melamine foam 816, in some examples approximately 2 cm thick, as shown in Figure 9. Some examples include a base such as an acrylic base 850. In some examples, an infrared pyrometer is to measure the heated substrate 804 temperature. Since the emissivity of aluminum is very low, in some examples 0.05, the surface of aluminum is painted black so that the emissivity is in the range of the pyrometer (in some examples 0.95). The natural convection heat transfer h is obtained by a correlation specific to small geometries and dependent on surface temperature, ranging from 15-25 W/m K, according to some approaches. In some examples, five rows of three K-type thermocouples, as shown in Figure 8B, are used to determine the surface temperature and temperature gradient using linear extrapolation. In some examples, the procedure is run at 5 substrate temperatures: 50, 75, 90, 115, 150°C. According to some examples, the maximum heat loss through the insulation Q _loss is found to be less than 1W. In some cases, this is negligible in instances where a 40 W heat flux is applied during measurements involving fluid flow. An example describing Figure 9 includes one or more of the following calculations:

Q heater Q conv ~^~ Q rad ^ Q loss

Q _conv = hA _s (T _s - T Q _rad = A _s sa - T^)

In some examples, a surface temperature is recorded with a pyrometer and corresponds within 0.5°C to the surface temperatures extrapolated from a set of 5 thermocouple measurements perpendicular to the surface. The standard deviation of the extrapolated values along the surface is less than 0.5°C, in some examples. In some examples, the heat sink 802 is milled from a polycarbonate slab. In some examples, the heat sink 802 has a glass transition temperature of 150°C. In some examples, the heat sink 802 includes seven parallel square channels 820, although examples with another number are contemplated. In some examples, one or more channels 820 of the heat sink 802 have a respective length and width of 25 mm and 500 μιη. Benefits of polycarbonate include that it is transparent and that it is easy to manufacture; some examples include other materials. In several examples, the heat sink 802 is pressed on top of the heated substrate 804 and sealed with the O-ring 818. In various examples, the heat sink 802 is heated with a constant power of 40W and the water flow rate is varied from 238 - 3095 kg/m ² s.

According to several examples, the heated substrate 804 and heat sink 802 are insulated with melamine foam, as shown in Figure 8C. Some examples demonstrate a typical loss of less than 1W. In various examples, a liquid such as water is pumped with a pump, such as a peristaltic pump, and the liquid mass velocity G _L is found by measuring the fluid volume at the outlet over time. In certain examples, bubbles are generated by introducing, such as through injecting, gas through an opening such as a slit, in various examples. In some examples, introducing bubbles in the liquid includes shearing the gas. In some examples, a bubble injector includes a jet pump. In some examples, a bubble injector is configured to introduce a plurality of bubbles at a gas pressure of from around 2 kilopascals to 10 kilopascals. In some examples, a bubble injector is configured to pressurize gas to a determined pressure and wherein the bubble injector is configured to flow the gas at a determined flow rate. In some examples, bubbles are introduced at constant pressure using a pressure regulator, such as a DRUCK DPI 530 pressure regulator. In certain examples, the pressure is varied depending on G _L to produce a liquid fraction close to 0.5. In certain examples, a pressure drop along the channel 820 is measured with a pressure transducer (e.g. a HONEYWELL, 15 psi/105.53 kPa, ± 0.087 psi / 0.61 kPa uncertainty, 100 /xs response time). In certain examples, thermocouples (e.g., type K, 0.5 mm diameter, OMEGA, 100ms response time, ± 0.5°C uncertainty) record inlet and outlet temperatures of the fluid, along with 15 measurements on the substrate, as shown in the example of Figure 8B. In some examples, a bubble injector is configured to disperse the segments of liquid over regular intervals, that is, at repeating rates. Successive bubbles flow one after another, in some examples.

In some examples, convective heat transfer recordings are made using the heat sink described in the previous section at constant heating power of 40W, and with water flow rates between 35-300 mL/min, corresponding to water mass velocities Gi of 300-3000 kg/m ² s and ReL from 160-1580, where ReL is defined as Gid/\iL for both single phase and segmented flow. Neglecting the low thermal losses through the insulation, as discussed in relation to Figure 8, enthalpy change of the fluid is replaced by the power supplied by the heater, according to some examples. An energy balance surrounding the channel provides the convection coefficient, h:

Q _heilter = {2 H _{c +} w _c )Nh [ dx ⁽¹⁴⁾ where β, r\ and N are the temperature difference between the substrate and the fluid, the fin efficiency and the number of channels, respectively, according to one approach. In some examples, the first and last row of the thermocouples on the heated substrate correspond to the fluid inlet and outlet, the integral is discretized along the fluid flow direction into four sections using the trapezoidal rule.

[β dx + -)] where ^{( 15)}

Ax=0.00625m

In some examples, a linear interpolation of the fluid is used in some examples to find the fluid temperature at the three interior points between the inlet and outlet temperatures, justified by the constant heat flux boundary conditions. Equation 14 is rearranged to solve for h as a function of the 5 surface temperatures and the inlet and outlet temperature of the fluid, according to some examples.

In some examples, the Nusselt number is found from the heat transfer coefficient by Nu = hd/ki, where ki = 0.64 W/Km is the fluid thermal conductivity. In some examples, a determined or maximum uncertainty of the Nusselt number is ± 4 % due to the propagation of uncertainties in the temperature, geometry and thermal losses through the insulation. A summary of uncertainties and their sources is found in Table 1 , according to several examples.

Table 1. Measured uncertainties

Various contributors to the uncertainty include, in some examples, the thermocouple measurements and the heat flow measurement. For example, at GL ~ \ 140 kg/m ² s, the average temperature difference β is 20°C with an uncertainty of ± 0.5°C, or ± 2.5 %. Also, as set forth in the portion of the specification discussing Figure 8, the uncertainty of Q _HEATER due to heat losses is less than 1 W, i.e. 2.5 %. In certain examples, Figure 1 1 illustrates that segmented flow increases the dimensionless heat transfer coefficient Nu up to 140% over single phase flow, for values of GL < 2000 kg/m ² s, in agreement with the numerically obtained correlation of at least one approach. For flow rates higher than 2000 kg/m ² s (or Re^-lOOO), the heat transfer enhancement due to the segmented bubble flow decreases quickly, and at GL > 2500 kg/m ² s (Re=1200), the bubbles have no more influence on the heat transfer process, according to some examples. In some examples, transition starts at flow rates where the capillary number reaches the transition value of 0.04 (shown by a vertical bar), and the flow visualizations in Table 2, which illustrates an example transition to churn flow. Table 2 includes example visualization of four cases spanning three flow regimes with corresponding liquid mass velocity GL, according to some examples. The liquid fraction, e, is calculated precisely for slug flow using the method described in section 2, according to some examples.

Table 2

According to some examples, segmented flow with a wetted channel, that is a liquid film between the bubble and the channel, enhances heat transfer provided the film between bubbles and wall does not become too thick, which can weaken the recirculation wakes, as explained in the discussion of Figure 2, and according to some additional approaches. Some examples produce segmented flow for values of GL between 330 and 2850 kg/m s. According to some examples, at lower GL values, segmented flow is replaced by bubbly flow (i.e. bubbles with diameters smaller than the channel diameter), and at higher GL values a churn flow appears (fast bubbles with thick films, Ca reaching 0.04 and above, no heat transfer enhancement), in agreement with some approaches. Visualization of these flow regimes is seen in Figures 10B-E, according to several examples. In various examples, a bubble injector is configured to flow a plurality of gas bubbles, substantially free of bubbly flow.

Figure 10 illustrates one configuration for single-phase and segmented flow apparatus, according to some examples. A pump 1002 such as a peristaltic pump is coupled in fluid communication to a pressure sensor 1020 and a water reservoir 1018 such as a DI water reservoir, in some examples. The pressure sensor 1020 is electronically coupled with a DAQ board 1010, which is electronically coupled to a PC 1008, in some examples. A CMOS camera 1006 is to record images of flow in a heat sink 1004, to which the pressure sensor 1020 is coupled in fluid communication, in some examples. The heat sink 1004 is in fluid communication with a water outlet 1012, which is some examples that circulate fluid, is coupled in fluid communication with the pump 1002, in some examples. A heater controller 1014 is configured to heat liquid in the heat sink 1004, in some examples. A bubble injector 1016 is coupled in fluid

communication with the heat sink 1004 and is configured to generate bubbles in a liquid in the heat sink, such as through injection via pressurizing a gas and regulating such as by throttling the introduction of gas into the heat sink 1004, in some examples. A reservoir 1018 is coupled in fluid communication with pump 1002 to provide water to the pump 1002, in some examples. In some examples, the water outlet 1012 is in fluid communication with the reservoir 1018 as part of a closed-loop circulation system including a circulation loop. Some examples include a gas separator 1028, as discussed herein in relation to bubble extraction. Figures 10B-10E show four operational modes for segmented flow, each showing a bubble 1022, a liquid slug 1024 and a channel 1026.

In some instances, the increasing values of the Nusselt numbers for single phase flow at larger flow rates are due to the non-negligible thermal and hydrodynamic entry lengths. As mentioned in the portion of the specification discussing Figure 2, the first correlations approach is used to calculate Nu for thermally developing flow. In several examples, the thermal entry region accounts for 10% of the channel length at Re = 30. In some examples, this correlation is valid until Re -100, when the hydrodynamic entry becomes non- negligible. For cases where both thermal and hydrodynamic entry length are significant, the second correlation approach discussed in relation to Figure 2 is used. Predictions from this correlation agree with physical examples set forth herein, with Re > 100.

As penalty in pressure drop associated with segmented flow is evaluated in the example illustrated in Figure 12, which illustrates that segmented flow exhibits pressure drops higher than single phase flow at the same prescribed liquid mass velocity, as predicted by the correlations associated with Eq. 8. The segmented flow heat transfer enhancement set forth herein provides a higher Nusselt number than single phase flow, for the same pressure drop, in several examples. This is expressed in the example of Figure 13 for pressure drop values ranging from 5 to 30 kPa, where the Nusselt number enhancement is about 50% using segmented flow rather than single phase flow, for the same amount of pressure drop. In various examples, a heat transfer enhancement is also seen with the lower measured substrate temperature as shown in Figure 14. Figure 14 confirms that the temperature variation along the substrate increases linearly: this is expected since the fluid experiences a constant heat flux.

In Table 3, in several examples, the pressure drop and Nusselt number are compared to single phase and evaporative flow measurements with similar flow rate and heat flux. According to some approaches, values are produced by an aluminum heat sink with 21 channels and a hydraulic diameter of 348.8 μν . Table 3 illustrates examples in which segmented flow provides Nusselt number values in a range that is between single-phase and evaporative cooling.

Table 3. Comparison of three modes of convective heat transfer.

Certain examples demonstrate that segmented flow enhances heat transfer by up to 140% in a heat sink, in comparison with single-phase flow at the same liquid flow rate. The Nusselt number demonstrates the improvement in heat transfer, in some examples. In some examples, the pressure drop penalty in

implementing segmented flow is acceptable, as for selected values of pressure drop, segmented flow delivers a higher Nusselt number than single phase flow. According to various examples, segmented flow provides an intermediate step between single-phase and boiling flow for the purpose of electronic cooling. Also, according to certain examples, the heat transfer enhancement occurs for a specific range of flow rates and capillary numbers. According to various examples, at lower or higher capillary numbers, no significant heat transfer enhancement is observed because segmented flow is replaced by bubbly or churn flow respectively.

BUBBLE EXTRACTION EXAMPLES

Various examples provide a simple and efficient way to remove gas bubbles from liquid-filled channels such as microchannels. Various examples integrate or combine a gas separator such as a membrane or a portion including one or more capillary vessels or tubes, with channels such that liquid in one or more channels passes over the separator. Several examples include a hydrophobic porous membrane. In some examples, a chip is manufactured in hard, transparent polymer filters gas plugs out of a segmented flow at rates up to 7.4 μΕ/s per mm ² of gas separator area. Several examples include a bubble generation section and a gas separation section. In certain examples, the bubble generation section includes a T-junction is used to generate a train of gas plugs into a water stream. In various examples, these gas plugs are transported towards a gas separation section, and slide along a hydrophobic membrane until extraction is sufficient or complete.

In various examples, a gas separation process occurs provided four criteria are met, in some cases simultaneously. In various examples, the first criterion is that the bubble diameter is larger than the channel diameter. In examples where the channel is rectangular, the first criterion is that the bubble cross sectional width is larger than the channel width. According to several examples, the second criterion is that the gas plug remain on the gas separator for a time sufficient to transport a determined, e.g., 100%, of the gas through the separator. In some examples, the third criterion is that the gas plug travel speed remain lower than a determined or critical value. In some examples, if the speed rises above the critical value, a stable liquid film between the bubble and the membrane reduces or prevents mass transfer. In some examples, the fourth criterion is that the pressure difference across the membrane remain below the Laplace pressure to prevent water from leaking through the membrane. Bubbles are generated in systems such as fluidic systems such as fluidic systems such as microfluidic systems, in some approaches, such as continuously by flow-focusing and T-junction configurations, among others, or on-demand by thermal heating and piezo actuation, among others. Unwanted gas pockets, in some examples, form accidentally due to priming or cavitation. In some examples, these bubbles are sometimes useful, e.g. for enhancing heat and mass transfer according to some approaches, creating streaming or microstreaming according to one approach, providing a platform for biochemical synthesis according to one approach, or enhancing mixing for chemical reaction and cell lysis according to some approaches. In some instances, however, bubbles are associated with disturbances in fluidic device such as microfluidic devices. For instance, they clog channels or reduce the dynamic performance of a fluidic device such as microfluidic device. Therefore a gas separation process, such as one integrated on a chip, is of interest in fluidics such as microfluidics.

Various approaches have been explored for trapping and removing bubbles from a channel such as a microchannel, such as dynamic bubble traps, and diffusion/capillarity based devices. In some examples, dynamic bubble traps are often used in extracorporeal blood flow circuits: they use 3D spiral channels to accelerate the flow radially and focus the bubbles towards one location, where extraction proceeds. However, in some examples, a significant amount of liquid is extracted together with the gas. Diffusion-based bubble extraction uses a gas- permeable membrane, such as a thin PDMS layer, according to some approaches. However, in these approaches, gas separation rates are relatively low, e.g. lxlO ^"4 μΐ,/s per mm ² . Thus, for some approaches in application, at least several minutes of extraction time are needed. Alternatively, in some examples a porous membrane is used to separate immiscible fluids: some approaches complete separation of organic-aqueous and fluorous-aqueous liquid/liquid systems in a fluidic device such as microfluidic device. Gas/liquid separation in an example illustrates that hydrophobic and hydrophilic membranes used together in the end of a channel such as a microchannel achieve gas/liquid separation, but the approach demonstrates incomplete separation when using a hydrophilic membrane in a channel flown with a gas/water mixture. The present subject matter provides an integrated gas separator in a channel such as a microchannel flow circuit. Specific examples provide a hydrophobic membrane integrated into a microfluidic chip and configured to separate gas plugs from a segmented flow. The present subject matter provides example conditions for bubble extraction, and provides four criteria associated with separation of gas from liquid.

Figure 15 illustrates an example assembly of a gas separator. According to various examples, one or more channels 1516 are 500 μπι wide and 500 μπι deep. In various examples, one or more channels 1516 are milled from PMMA 1508 (polymethylmethacrylate) using a mill such as a Minitech CNC milling machine. In various examples, cut portions exhibit less than 500 nm surface roughness. In some examples, one or more channels 1516 are sealed with PMMA 1502, with the 200 μιη thick hydrophobic acrylic copolymer membrane, and 70 μπι thick double-sided tape 1506, as shown in Figure 15. Various examples are sealed with membrane 1504, such as porous hydrophobic membrane.

The three tested porous hydrophobic membranes (e.g., membranes manufactured by PALL CORPORATION) are made of acrylic copolymer and have three respective typical pore sizes, 0.2, 1.2 and 10 μπι (e.g., as illustrated in Figure 15). In some examples, a 500 μπι wide slit is cut through the tape 1506, and aligned on top of the channel 1516 such as a main channel. As such, in some examples, the bubble generation section has four walls made of PMMA while the gas removing section has a channel 1516 made of three PMMA walls and one membrane 1504 wall, not including fasteners such as tape 1506. In various examples, in the bubble generation section, gas plugs are generated at a T-junction, where water is pushed by syringe pumps 1510 (e.g., KDS 210) and the gas pressure is controlled by a pressure controller 1512 (e.g., DRUCK DPI 530, 2 bar gauge, precision ±1% FS). In various examples, generated bubbles are transported to the bubble extraction section, where bubble extraction takes place. A pressure sensor 1514 such as a piezoresistive pressure sensor (e.g., HONEYWELL ASCX15DN, 103.4 kPa differential, repeatability ±0.2% FS) is used to monitor the pressure difference between the atmosphere and the fluid upstream of the hydrophobic membrane, in some examples.

In various examples, to generate gas plugs at a T-junction with different speed, backpressure in the gas and water flow rate are varied. In various examples, bubbles that are smaller than the channel diameter are not extracted. As such, certain examples generate gas plugs that are longer than the channel height, such that they are constrained by a channel such as a microchannel. In various examples, the measured void fraction ranges from 0.25 to 0.78.

According to several examples, the picture sequence in Figure 16 illustrates bubble 1602 dynamics during a extraction process. Figure 16 illustrates a sequence of a bubble extraction process, using a membrane with 1.2 μιη pores. In the examples, bubbles travel at or around a speed of 0.62 m/s and are extracted or completely extracted from the channel through the membrane. Various examples observe that the receding contact angle at the bubble front increases during the vanishing period as the bubble travels through the channel 1604, as shown in frames 0 to 4.4ms Also the vanishing bubble first reduces its length, for example the bubble at 2.8 ms is about half of the original length. Then, after 3.2 ms, the height of the bubble starts to decrease, according to some examples. In certain examples, while the contact area between gas and membrane is also decreasing, the remaining part of the bubble seen from the side assumes a sharp triangular shape, before it fully disappears (see e.g. frames at 0.8 and 1.2ms). In various examples, this curvature change occurs when the Weber number is greater than unity, as shown in Figure 17. In various examples, the shape at large Weber numbers is due to the pressure drop along the bubble length. According to some examples, a reason for this is that competition of inertial forces and surface tension forces over the bubble create a pressure difference across the bubble length large enough to induce a change of curvature.

Several examples record the flow rates and gage pressure used for water to leak through the porous membrane, by flowing pure water in one or more channels, while the gas inlet is closed. In examples including a 0.2 μηι pore size membrane, a syringe pump fails at 46 mL/m and a gage pressure of 81 kPa, and leakage of water through the membrane is found to occur at 40 and 21 mL/m of water flow rate for 1.2 and 10 μιη pore sizes respectively, and the respective gage pressures, measured at the location upstream from the membrane, are 41 and 20 kPa. For experiments described below, the gage pressure is kept lower than these critical pressures to prevent water leakage, in some examples. In examples of complete gas extraction, a maximum extraction rate of about 7.4 μϋβ/ηιιη ² is achieved with a 10 μπι pore-sized membrane of 60 mm ² exposed area. Such extraction rate is four orders of magnitude higher than reported using a PDMS approach. In some examples, this enhancement is due in part to different gas transport mechanisms. In various examples, across PDMS, gas transport is due to solution and diffusion, and the steady-state gas mass flux N (kg/m Is) follows the Equation 16:

N - ^f (16)

h

where h is the membrane thickness, Ap is the pressure difference across the membrane and P is the gas permeability. Nitrogen is used in some examples, and P is 1.34xl0 ^"16 kmol/(Pa s m ² ) for nitrogen. In some examples, gas transport through a porous membrane is caused at least in part by a viscous flow in the parallel pores, and the steady-state gas volume flux q (m ³ /m ² /s) is estimated from Darcy's law according to some approaches:

K Ap

? =— Γ (17) μ h

where μ is the gas viscosity, and Kr is permeability of the membrane, which has been obtained experimentally as follows. In various examples, by varying the gas-flow q through the membrane, the pressure drop across the membrane is recorded and plotted in Figure 18. In various examples, to determine the permeability κ of the membranes, the pressure drop across the membrane is measured and plotted as a function of the volume flux of the gas-flow through the membrane. According to Figure 18, xris calculated to be 7.8xl0 ^"15 , 2.9xl0 ^"13 and 1.3xl0 ^"12 m ² for membranes with 0.2, 1.2 and 10 μιη pores respectively. Calculations in Table 4A-B reveals that, under the same pressure across the membrane, the mass/volume flux in porous membrane is four orders of magnitude higher than in a PDMS membrane with the same thickness.

Table 4A: theoretical mass flow rate across a porous membrane and a PDMS membrane.

Table 4B: theoretical mass flow rate across a porous membrane and a PDMS membrane. According to various examples, two outcomes are unsatisfactory for a gas separation device: membrane leakage and incomplete extraction. During incomplete extraction, the outflow is not pure water but an gas-liquid mixture. During membrane leakage, water and gas go through the membrane. In certain examples, criteria as listed in Table 5 and discussed herein, are satisfied, in some cases simultaneously, to provide gas extraction, such as complete gas extraction, without membrane leakage.

Table 5

As discussed herein with respect to certain examples, the geometry of a bubble trap such as one or more of the bubble traps disclosed herein, uses a bubble diameter larger than the channel height for making degassing possible. In some examples, this is the first criterion for complete gas extraction, criterion 1 in Table 5. In some examples, a second criterion is formulated by considering the time needed to fully extract the gas bubble. According to some examples, the shrinking rate of the bubble dV/dt is substantially equivalent to the gas-flow rate Q through the membrane, which is estimated by Darcy's law (i.e., Equation [16]):

(17)

dt ^~ μ h H where V/H gives the contact area between the bubble and the membrane, and the permeability given in Table 4. Some examples assume that the bubble shrinks by reducing its length keeping its pressure and height constant, and integrate to determine the extraction time τ:

_{T = H ln (18)}

K Ap /, where / ₀ and l _\ are the initial bubble length and final bubble length respectively. According to various examples, this integral does not converge to a finite time, however the analysis corresponds well to most of the extraction process, so that a reasonable estimate of the bubble extraction time is obtained by assuming a small value / _/ of 1% of the channel height. Figure 16 plots an example comparison between experiments and an example, which, in one case, illustrates agreement for a membrane with 0.2 μπι pores. In some examples, to ensure complete extraction, the bubble should moves along the membrane for a time no shorter than τ , which leads to the Equation listed in Table 5 for criterion 2.

In examples in which membranes include 1.2 and 10 μηι pores, the theoretical ris on the order of milliseconds, thus this criterion provides that gas bubbles are extracted from very fast flows, at speed on 10 ⁴ m/s, faster than other examples. In this example the coating liquid films surrounding bubbles travels in channels at non-negligible capillary numbers. In this case, a third criterion is formulated for complete gas separation to account for a liquid film between the wall and the gas plug, which might delay, as seen in Figure 19, or reduce gas extraction. Figure 19 illustrates a comparison between some examples and examples associated with Equation 18 for criteria 2, according to several examples. According to several examples, the x-axis plots the term ln(/( / _/ ) and the y-axis plots the product of the extraction time and the pressure. Some examples show agreement for the membrane with 0.2 μηι pores. In some examples, for membranes with 1.2 and 10 um pores, the extraction time are larger than a determined value, which in some cases is explained by a liquid film formed between the wall and the gas plug, as analyzed in association with Criteria 3. In various examples, a static gas/water interface contacts the wall with a contact angle έ¾ and forms a clear triple line. However, in some cases, an interface moving along the wall exhibits a dynamic contact angle θο, which decreases for increasing bubble velocities. According, in some cases, there is a critical velocity, where the wetting angle approaches zero, and above which a film appears between the plug and the wall because the triple line cannot find a stable position anymore. In some approaches, the critical velocity v _c , is estimated by:

where a = 20 is a dimensionless coefficient that only weakly depends on v. In certain examples, for an gas-water system in respective contact with PMMA and membrane surfaces, v _c is calculated to be 0.38 and 2.3 m/s, respectively, using contact angles measured in the experiments (e.g., 68° for PMMA, 124° for the porous membrane). I various examples, once the film is formed, the thickness e of the film is calculated according to one approach: e = ^Ca ² (20) where D is the channel diameter and Ca is the capillary number. Assuming D as a hydraulic diameter of a channel, Figure 20 (second y-axis) illustrates the theoretical film thickness e as a function of bubble speed v on both PMMA and membrane surfaces. According to several examples, experimental determined or maximum bubble travel distance and theoretical film thickness are functions of bubble travel speed. In some examples, for the bubbles that are slower than Vcjnembrane _> gas is extracted or completely extracted at determined locations in the channel, a situation that is not achieved for bubbles that are faster than

Vc membrane, in some examples. In some examples, a bubble vanishing location distance increases with the bubble travel speed, as illustrated according to some examples with scattered data points. In some examples, scattering of data points is associated with nonuniformity of pore size or nonhomogeneous distribution of pores on a membrane surface, as pictured in Figure 15. According to some examples, bubbles travel along the PMMA wall and then on the membrane so that the corresponding film situations occur as in Table 6:

Table 6

According to certain examples, such as those described in Table 6, if the bubble speed v is greater than v _c _ _mem brane, a stable film between the bubble and the membrane can reduce or prevent gas separation. Conversly, according to the examples, if the bubble speed v is smaller than _{c mem} brane, the film might become unstable on top of the membrane and rupture so that gas is extracted, provided the membrane is long enough. In examples such as those described using the first y-axis in Figure 20, gas plugs slower than v _c _ _mem b _ra ne ^are extracted or completely extracted at certain locations in the channel, a situation that is not achieved for gas plugs that are faster than v _c _ _me mbrane- 1° some examples, the bubble vanishing location generally increases with the bubble velocity, visualized with scattered data points. In some examples this is associated with nonuniformity of the pore sizes and nonhomogeneous distribution of the pores on the membrane surface, as pictured in Figure 15. According to various examples, the third criterion is that the bubble speed v be lower than a critical value, and the corresponding Equation is listed in Table 5 to describe this criterion.

In certain examples, a porous hydrophobic membrane reduces or prevents a water-gas meniscus from passing through the pores because of interfacial tension, a situation analyzed in one approach for a liquid/liquid system. According to that approach, several examples provide a criterion necessary to prevent water from leaking through a porous hydrophobic membrane.

According to several examples, Figure 21 illustrates a bubble 2106 in a channel 2108 including a gas-liquid meniscus 2102 that is held at an entrance of a pore 2104 as the surface tension holds the pressure difference across the meniscus 2102 and discourages or prevents water from leaking through the pore. In several examples, with an increasing pressure difference, the angle between the meniscus and the inner wall of the pores reaches a determined or maximum value of the equilibrium wetting angle Θ. In some cases, a meniscus holds a pressure difference up to a maximum value of,

Ap _LP = -4^ COS c9 / i (21) where yis the surface tension between gas and water, #is the contact angle and d is the pore size, according to one approach. In some cases, as long as the pressure difference Ap across the membrane is smaller than Hp _LP , there is little or no water leaking through the membrane, which provides the third criterion as listed in Table 5. In some cases, a pore size is associated with a membrane, such as by being given by the manufacturer. In some of these cases, the Laplace pressures Ap _LP are calculated as 804, 134 and 16 kPa for 0.2, 1.2 and 10 μιη membrane respectively. In some instances, water begins to leak at > 81 (e.g., where a syringe pump fails), at about 41 and 20 kPa respectively. In some examples, these values are associated with uncertainties on the pore shape and size (see Figure 15) or on the wetting angle, in one approach.

In some examples, a fluidic device such as microfluidic device is manufactured to separate gas from water in a segmentation flow. In some cases, four operating criteria are determined and explained in association with physical examples and achieve a complete separation of the gas from the liquid.

Figure 22 illustrates a method, according to some examples. At 2202, a method for heat exchange between a heat source and a heat sink, includes affixing the heat sink to the heat source, with the heat sink thermally

communicative with the heat source. At 2204, the method includes flowing a liquid through a channel in the heat sink, at a determined flow rate and liquid pressure. At 2206, the method includes flowing a gas into the liquid and forming a plurality of gas bubbles in the liquid, with each of the plurality of gas bubbles monodispersed in the liquid, in the channel, with segments of liquid separating successive gas bubbles of the plurality of gas bubbles. At 2208, the method includes exchanging heat between the heat sink and the heat source.

Various optional methods are contemplated. Some methods include separating the gas from the liquid after exchanging heat between the heat sink and the heat source. Some methods include flowing the gas includes flowing gas separated from the liquid and circulated to a gas pump. Some methods include extracting the gas from the liquid after exchanging heat between the heat sink and the heat source. Some methods include segmenting the bubbles includes controlling the segmenting by adjusting at least one of a gas pressure of the gas, a gas-flow rate of the gas, a wetting angle of the liquid, a liquid flow rate of the liquid and a liquid pressure of the liquid. Some methods include circulating liquid through a circulation loop, and cooling the liquid along a heat emission portion of the circulation loop, wherein exchanging heat between the heat sink and the heat source includes heating the liquid along a heat absorption portion of the circulation loop.

ADDITIONAL NOTES

The above detailed description includes references to the accompanying drawings, which form a part of the detailed description. The drawings show, by way of illustration, specific embodiments in which the invention can be practiced. These embodiments are also referred to herein as "examples." Such examples can include elements in addition to those shown and described.

However, the present inventors also contemplate examples in which only those elements shown and described are provided.

All publications, patents, and patent documents referred to in this document are incorporated by reference herein in their entirety, as though individually incorporated by reference. In the event of inconsistent usages between this document and those documents so incorporated by reference, the usage in the incorporated reference(s) should be considered supplementary to that of this document; for irreconcilable inconsistencies, the usage in this document controls.

In this document, the terms "a" or "an" are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of "at least one" or "one or more." In this document, the term "or" is used to refer to a nonexclusive or, such that "A or B" includes "A but not B," "B but not A," and "A and B," unless otherwise indicated. In the appended claims, the terms "including" and "in which" are used as the plain-English equivalents of the respective terms "comprising" and "wherein." Also, in the following claims, the terms "including" and "comprising" are open-ended, that is, a system, device, article, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. Moreover, in the following claims, the terms "first," "second," and "third," etc. are used merely as labels, and are not intended to impose numerical requirements on their objects.

Method examples described herein can be machine or computer- implemented at least in part. Some examples can include a computer-readable medium or machine-readable medium encoded with instructions operable to configure an electronic device to perform methods as described in the above examples. An implementation of such methods can include code, such as microcode, assembly language code, a higher-level language code, or the like. Such code can include computer readable instructions for performing various methods. The code can form portions of computer program products. Further, the code can be tangibly stored on one or more volatile or non-volatile computer- readable media during execution or at other times. These computer-readable media can include, but are not limited to, hard disks, removable magnetic disks, removable optical disks (e.g., compact disks and digital video disks), magnetic cassettes, memory cards or sticks, random access memories (RAMs), read only memories (ROMs), and the like.

The above description is intended to be illustrative, and not restrictive. For example, the above-described examples (or one or more aspects thereof) can be used in combination with each other. Other embodiments can be used, such as by one of ordinary skill in the art upon reviewing the above description. The Abstract is provided to comply with 37 C.F.R. § 1.72(b), to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. Also, in the above Detailed Description, various features can be grouped together to streamline the disclosure. This should not be interpreted as intending that an unclaimed disclosed feature is essential to any claim. Rather, inventive subject matter can lie in less than all features of a particular disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.