RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application Serial No. 61/085,687, filed August 1, 2008, entitled "Systems and Methods for Bubble and/or Foam Inhibition," by Bick, et al. , incorporated herein by reference.

FIELD OF INVENTION

The present invention generally relates to systems and methods for bubble and/or foam inhibition. BACKGROUND

Foams often result from trapping a large number of gas bubbles within a solid or liquid. Manufacturers rely on a wide range of materials, ranging from pharmaceutical products to building materials, that entrain air or other gases when processed in a liquid state. Biologists examine the great variety of cellular structures that are similar to foam forms, including the cork tree and cancerous bone. Foams play a large role in the daily consumer experience as well in goods as varied as shampoo and soft drinks. While significant research has gone into studying foams, and generating foams under controlled conditions, much is unknown about how a foam fundamentally forms, for example when one pours beer into a stein. SUMMARY OF THE INVENTION

The present invention generally relates to systems and methods for bubble and/or foam inhibition. The subject matter of the present invention involves, in some cases, interrelated products, alternative solutions to a particular problem, and/or a plurality of different uses of one or more systems and/or articles. In one aspect, the invention is a method. In one set of embodiments, the method includes an act of contacting a first fluid with a second fluid, as a series of droplets, at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation under such conditions. In some cases, no more than five bubbles are formed per 100 droplets of first fluid that contact the second fluid.

In another set of embodiments, the method includes acts of contacting a first fluid with a second fluid, as a series of droplets, at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation under such conditions. In some cases, for every 100 droplets of first fluid that contact the second fluid, no more than five pairs of consecutive droplets land within a critical radius of bubble formation in less than the critical time of bubble formation under such conditions.

In one set of embodiments, the method includes an act of contacting a first fluid with a second fluid, as a series of droplets, at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation under such conditions, such that a predetermined number of bubbles is formed per 100 droplets of first fluid that contact the second fluid, where the predetermined number is less than 95.

In another aspect, the invention is generally directed to an apparatus. In one set of embodiments, the apparatus includes a variable nozzle for producing droplets of a first fluid, and a container positioned to receive droplets produced by the nozzle, the container containing a second fluid. In some cases, the variable nozzle is constructed and arranged to direct droplets of the first fluid at the second fluid at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation under such conditions, such that for every 100 droplets of first fluid that contact the second fluid, no more than five pairs of consecutive droplets land within a critical radius of bubble formation in less than the critical time of bubble formation under such conditions.

The apparatus, in another set of embodiments, includes a variable nozzle able to produce droplets of a first fluid, and a container positioned to receive droplets produced by the nozzle. In some cases, the variable nozzle is constructed and arranged to direct droplets at more than one location within the container such that for every 100 droplets of first fluid that contact the second fluid, no more than five pairs of consecutive separate droplets land within a radius of 5 mm in less than 10 ms.

In yet another set of embodiments, the apparatus includes a variable nozzle for producing droplets of a first fluid, and a container positioned to receive droplets produced by the nozzle, the container containing a second fluid. In some cases, the variable nozzle is constructed and arranged to direct droplets of the first fluid at the second fluid at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation under such conditions, such that a predetermined number of bubbles is formed per 100 droplets of first fluid that contact the second fluid, wherein the predetermined number is less than 95. In another aspect, the present invention is directed to a method of making one or more of the embodiments described herein, for example, systems and methods for foam inhibition. In another aspect, the present invention is directed to a method of using one or more of the embodiments described herein, for example, systems and methods for foam inhibition. Other advantages and novel features of the present invention will become apparent from the following detailed description of various non-limiting embodiments of the invention when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and/or inconsistent disclosure, the present specification shall control. If two or more documents incorporated by reference include conflicting and/or inconsistent disclosure with respect to each other, then the document having the later effective date shall control.

BRIEF DESCRIPTION OF THE DRAWINGS Non-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. In the figures:

Fig. 1 shows an annotated phase diagram illustrating regimes where water droplets contacting a fluid can form gas bubbles;

Fig. 2A shows an apparatus for reducing bubble formation, in one embodiment of the invention; Figs. 2B-2E illustrate the formation of a bubble, in accordance with another embodiment of the invention; Figs. 3A-3B illustrate the impact of droplets on a fluid using high speed analysis, in yet another embodiment of the invention;

Figs. 4A-4D are a time sequence of images illustrating multi-drop bubble entrainment, in accordance with one embodiment; Figs. 5A-5D are a time sequence of images illustrating Raleigh instability, in accordance with another embodiment of the invention;

Figs. 6A-6D are a time sequence of images illustrating vortex ring entrainment, in accordance with another embodiment of the invention;

Figs. 7A-7B illustrate crater depths during bubble formation, in accordance with other embodiments of the invention;

Fig. 8 illustrates a plot of crater depth scaled to bubble diameter, in accordance with yet another embodiment of the invention;

Figs. 9A-9F are histograms of various time intervals between droplets, in still other embodiments of the invention; Fig. 10 is a plot of the ratio of droplet areas against the time interval between two droplets, according to another embodiment of the invention;

Figs. 1 IA-I IB are histograms of bubble diameter, in still other embodiments of the invention; and

Figs. 12A-12C illustrate histograms of droplet diameters, in various other embodiments of the invention.

DETAILED DESCRIPTION

The present invention generally relates to systems and methods for bubble and/or foam inhibition. In one aspect, a first fluid can be poured into a second fluid, as a series of droplets, without creating bubbles or foam. For instance, no more than five bubbles may be formed per 100 droplets of first fluid that enter the second fluid. In one set of embodiments, droplets of a first fluid are directed at a second fluid such that the droplets contact the second fluid outside a critical radius of bubble formation and/or outside a critical time of bubble formation. Thus, under such conditions, bubble or foam production may be reduced or even eliminated. In some case, fairly high rates of fluid transfer can be achieved by contacting the droplets of first fluid at the second fluid under such conditions, for instance, by directing multiple droplets of the first fluid at the second fluid at different locations, e.g., outside of the critical radius of bubble formation. For instance, a nozzle able to produce droplets may be rotated such that the droplets contact different locations of a fluid. In some cases, the present invention is also directed to methods of control of bubble formation. For example, by controlling the droplets of first fluid entering the second fluid, a certain number of bubbles may be produced. One aspect of the present invention is generally directed to systems and methods for pouring or otherwise contacting a first fluid with a second fluid, without producing significant amounts of bubbles or foam. Typically, the first and second fluids are each liquids. The first fluid and the second fluid may have the same or different compositions. For instance, one or both of the first fluid and the second fluid may be aqueous, e.g., being substantially miscible in pure water, and/or one or both of the first fluid and the second fluid may be substantially miscible with respect to each other. In some cases, one or both of the first and second fluids may contain a surfactant.

As used herein, the term "fluid" generally refers to a substance that tends to flow and to conform to the outline of its container. Typically, fluids are materials that are unable to withstand a static shear stress, and when a shear stress is applied, the fluid experiences a continuing and permanent distortion. The fluid may have any suitable viscosity that permits at least some flow of the fluid. Non-limiting examples of fluids include liquids and gases.

When a first fluid is poured, typically, the first fluid will break up into a series of discrete droplets under the action of surface tension. Thus, when a first fluid is directed at a second fluid (e.g., poured, sprayed, squirted, atomized, etc.), the first fluid will often contact the second fluid as a series of discrete droplets. It is to be noted that such droplets are not necessarily spherical, but may assume other shapes as well, for example, depending on the external environment. It should also be noted that the droplets need not all be of the same shape or size.

The average diameter of the droplets may be, for example, less than about 10 mm, less than about 5 mm, less than about 3 mm, less than about 2 mm, less than about 1 mm, less than about 750 micrometers, less than about 500 micrometers, less than about 250 micrometers, less than about 100 micrometers, or less than about 50 micrometers in some cases. The actual diameter will depend on factors such as the composition of the first fluid, its density, viscosity, surface tension, etc., the temperature, or the like. The average diameter of a plurality or series of droplets is the arithmetic average of the average diameters of each of the droplets, and the average diameter of a single droplet, for a non-spherical droplet, is the diameter of a perfect sphere having the same volume as the non-spherical droplet. Techniques for determining the average diameter (or other characteristic dimension) of a plurality or series of droplets include, for example, high- speed photography or strobe photography, and techniques such as these and others will be known to those of ordinary skill in the art.

Typically, not all of the droplets of the first fluid will contact the second fluid at the same time. Thus, there may be a series of droplets of the first fluid contacting the second fluid at different times, especially if the first fluid is poured, sprayed, or otherwise is directed at the second fluid at a relatively moderate rate. In one set of embodiments, the first fluid can be thought of a series of consecutive droplets that contact the second fluid, with a certain amount of time between each of the droplets contacting the second fluid (of course, the amount of time between the various droplets does not necessarily have to be constant). This time can also be averaged (arithmetically) to produce an average time between consecutive separate droplets.

Without wishing to be bound by any theory, it is believed that, in some cases, the relationship between two droplets of the first fluid contacting the second fluid may produce bubbles or foam (e.g., as a series of bubbles, often produced in such numbers that the bubbles start to come into contact with each other), and thus, by controlling the amount of time between consecutive separate droplets contacting the second fluid, the amount of bubble production or foaming may be controlled. More specifically, referring now to Fig. 2, droplet 1 and droplet 2 are shown contacting the surface of a fluid 15 in Fig. 2B. The fluids forming droplet 1, droplet 2, and fluid 15 may each be independently substantially the same or different. When droplet 2 contacts the surface of fluid 15, a crater 12 may be formed. (In some cases, there may be a crater present in fluid 15, due to a prior droplet, as is shown in Fig. 2B.) The shape and depth of crater 12 will vary depending on factors such as the size of droplet 2, the speed and angle at which droplet 2 contacts fluid 15, the viscosities of the droplet and the fluid, their surface tensions, their densities, their compositions, or the like. After creation of a crater, droplet 1 contacts fluid 15 (Fig. 2D) and causes the formation of a bubble 20, as is shown in Fig. 2E. Accordingly, by controlling the consecutive droplets that contact the second fluid, the formation of bubbles, such as bubble 20 in Fig. 2E, may be controlled. Thus, according to one set of embodiments, the critical time of bubble formation is the time separating two droplets contacting a fluid, below which time bubble formation may occur. As discussed below, surprisingly, the critical time of bubble formation does not necessarily display a strong dependence on the sizes of the droplets, or on the effect of previous droplets contacting the fluid. In some embodiments, the critical time of bubble formation may be estimated using: where γ (gamma) is the surface tension of the second fluid, p (rho) is the density of the second fluid, and / is the crater depth, which affects the size of the resultant bubble. The crater depth, in some cases, may be taken as 1 mm, roughly corresponding to the formation of bubbles having an average diameter of 1 mm. In other cases, larger or smaller bubbles may be used, for example, by using crater depths of less than about 10 mm, less than about 5 mm, less than about 2 mm, less than about 750 micrometers, less than about 500 micrometers, less than about 250 micrometers, less than about 100 micrometers, or less than about 50 micrometers, etc. For instance, in one set of embodiments, the formation of bubbles above a certain size may be undesired, and that may be used to, in turn, determine the critical time of bubble formation for those bubbles.

Accordingly, in some embodiments, bubble formation can be eliminated, or at least reduced, by ensuring that consecutive droplets of fluid do not contact the surface of a second fluid in less than the critical time of bubble formation, and/or within the critical radius of bubble formation. In some cases, droplets contacting outside of the critical radius of bubble formation (whether within the critical time of bubble formation, or not) are too separated by distance to allow bubble formation to occur as was discussed above with reference to Fig. 2. The critical radius of bubble formation is thus the distance separating the locations of two contacting droplets on a fluid, above which no substantial bubble formation can occur. In some cases, the critical radius of bubble formation may be estimated to be the same order of magnitude as the crater depth, e.g., about 10 mm, about 5 mm, about 2 mm, about 1 mm, about 750 micrometers, about 500 micrometers, about 250 micrometers, about 100 micrometers, or about 50 micrometers in some cases. For example, the critical radius of bubble formation may be 2, 3, or 5 times the crater depth, depending on the particular application.

It should be understood that, in reality, no bubble or foam prevention system will be perfect, and even under conditions such as those described above, some bubbles may still form. Other mechanisms may cause the formation as bubbles, e.g., as discussed in the examples below, and fluid mechanics is not a completely solved art. In addition, there are certain elements of fluid mechanics that are unpredictable or chaotic in nature. However, it is believed that the present invention will reduce the number of bubbles formed. For instance, under certain conditions, no more than ten or five bubbles will be formed per 100 droplets of first fluid that contact the second fluid. It should be understood that this number is a rate of bubble production; in practice, there may be more or fewer numbers of droplets of first fluid that actually contact the second fluid, depending on the particular application. For instance, as one example, there may be only 20 droplets of first fluid that actually contact the second fluid, and no more than 1 bubble is formed.

In another aspect, the invention provides systems and methods of control of bubble formation, e.g., when pouring or otherwise contacting a first fluid with a second fluid. As discussed above, by controlling the amount of time between consecutive separate droplets contacting the second fluid, the amount of bubble production or foaming may be controlled. For instance, by directing droplets of the first fluid at the second fluid such that the time between two consecutive separate droplets is below the critical time of bubble formation, a droplet may be produced; conversely, by directing droplets of the first fluid at the second fluid such that the time between two consecutive separate droplets is greater than the critical time of bubble formation, no droplet may be produced. Accordingly, by controlling the time between droplets, any desired number of bubbles may be produced. As discussed, in one embodiment, a minimal number of bubbles may be desired, e.g., no more than ten or five bubbles will be formed per 100 droplets of first fluid that contact the second fluid. In other embodiments, however, greater numbers of bubbles may be desired, for instance, 15 bubbles, 20 bubbles, 25 bubbles, 30 bubbles, 35 bubbles, 40 bubbles, 45 bubbles, 50 bubbles, 55 bubbles, 60 bubbles, 65 bubbles, 70 bubbles, 75 bubbles, 85 bubbles, 90 bubbles, 95 bubbles, or 100 bubbles may be formed per 100 droplets. In addition, in some cases, greater or less than the numbers of bubbles listed here may also be produced in other embodiments, depending on the particular application. For instance, no more than 15 bubbles, no more than 20 bubbles, no more than 25 bubbles may be produced in some cases.

Certain aspects of the present invention are directed to systems for producing such effects. In one set of embodiments, a variable nozzle is used, where the variable nozzle is constructed and arranged to direct droplets of a first fluid at a second fluid under conditions such as those described above. For instance, the variable nozzle may be constructed and arranged to deliver droplets at a rate such that the average time between consecutive separate droplets of the first fluid contacting the second fluid is less than the critical time of bubble formation, and/or such that no more than five pairs of consecutive droplets land within a critical radius of bubble formation per 100 droplets, per 300 droplets, per 1,000 droplets, per 3,000 droplets, etc. of the first fluid.

In one embodiment, the variable nozzle may include a nozzle for delivery of a fluid, and a mechanism for moving or altering the position and/or angle of the nozzle, such that droplets produced by the nozzle do not all contact the same position. For instance, the mechanism may include a rotational device that rotates the entire nozzle, or only a portion of a nozzle, about a central point or axis. In some cases, the rotational device may be constructed to rotate with a period equal to the critical time, or greater or less than the critical time in some cases. In another embodiment, the mechanism may be constructed to cause the droplets to contact different portions of the second fluid, e.g., such that the droplets do not land within a critical radius of bubble formation. For instance, the mechanism may be a rotational device that rotates the stream of droplets such that the droplets fall in a circular or an elliptical pattern, with the distance between consecutive droplets being greater than the critical radius of bubble formation. In yet another embodiment, however, the position of the nozzle may be fixed, and the production of droplets may be controlled, for example, such that the period at which droplets are produced by the nozzle is greater than the critical time of bubble formation.

The following is incorporated herein by reference in its entirety: U.S. Provisional Patent Application Serial No. 61/085,687, filed August 1, 2008, entitled "Systems and Methods for Bubble and/or Foam Inhibition," by Bick, et al.

The following examples are intended to illustrate certain embodiments of the present invention, but do not exemplify the full scope of the invention. EXAMPLE 1

Observation using high speed photography reveals that pouring a first liquid into another liquid (e.g., pouring a drink into a cup) is not actually a stream of liquid, but rather, the stream of liquid is formed of many of discrete drops, formed from a Plateau- Rayleigh instability. Upon striking the surface of the liquid/air interface, these drops entrain bubbles. Thus, fundamentally, this mechanism is just a matter of entraining air through liquid drops. The impact of liquid droplets is shown in the phase diagram in Figure 1. It was determined in this example that since such conditions were typically below the range of regular entrainment, a single drop mechanism could not explain the observed bubbles. It was further noticed that the frequency was such that the drops interacted with the preceding "crater" formed from a preceding droplet such that multiple drops were involved in entraining a single bubble. Thus, this example illustrates this multi-drop entrainment mechanism qualitatively and quantitatively.

The annotated phase diagram in Fig. 1 summarizes the different regimes where impacting water drops form gas bubbles. The irregular entrainment regime (top right corner) resulted in single drops contacting the surface and unpredictably creating very small gas bubbles. A drop impacted on a quiescent surface within the regular entrainment region (middle shaded area) is highly reproducible and produces a bubble on size order of the impacting drop ever time. A single impacting drop falling in the vortex ring entrainment region (below the regular entrainment region) may result in the formation of many small bubbles (<100 micrometers). There is also a regime where two high-speed impacting drops can form small bubbles. The multi-drop regime may produce bubbles on the size order of the impacting drop and is the subject of this example, and is highlighted in the lower left-hand corner. Multi-drop entrained bubbles were produced using the following apparatus: a syringe pump pushed a jet of Millipore distilled water out of a nozzle of a given diameter (ranging from 0.3 mm to 1.5 mm). The nozzle was mounted vertically 1 cm to 8 cm above a bath of Millipore distilled water. Several different bath sizes were used to ensure the phenomenon was not a result of wall effects. The cross sectional area ranged from 0.5 cm ² to 25 cm ² . Depths between 1 mm and 4 cm were used during experiments. The jet of water broke up into drops (believed to be the result of the Plateau-Rayleigh instability), and thus the drops ranged from 0.25 mm to 3 mm in diameter, depending on factors such as the nozzle diameter size and the Plateau-Rayleigh instability.

Fig. 2A shows a schematic of the setup used in this example. The bubble producing apparatus functioned by created a jetting regime of liquid out of a nozzle (diameter 0.3 m to 1.5 m), located 1 cm to 8 cm above a bath of the same liquid. The jet broke up into drops, which sometimes resulted in bubble formation upon impact. Millipore distilled water was used as the liquid in this example, although other fluids could also be used. By changing the flow rate of the syringe pump, a range of impact velocities from 0.5 m/s to 2 m/s was observed. Using a Photron V9 high speed camera at frame rates of 3000 fjps (frames per second) to 9000 fps, drops could be observed individually contacting the air/water bath interface, as is shown in Figs. 2B-2E. This series of figures shows a schematic of drop impact leading to bubble formation. Initially, the bath surface was disturbed by previously impacting drops. Drop 2 falls onto this disturbed surface creating a crater. Drop 1 then falls into the crater formed by drop 2 at which time the crater became deeper and under certain conditions would create a bubble.

The deflection of the air/water interface (referred to as the crater) was visually discernable in high speed camera images. Formation of bubbles were easily observable within the bath, as the air within each bubble had a different index of refraction than the surrounding water. The resulting objects were identified as bubbles because they were observed to oscillate. This ringing behavior has been previously described in the literature as characteristic of bubble formation. Images of a reference length placed at the same focal position as the water bath were taken before each recording so as to scale the recorded number of pixels with the true length. The apparatus was also used to examine liquids with surfactants present (including Corona Beer and water with 2% wt/wt sodium dodecyl sulfate) and found to similarly entrain bubbles through a multidrop mechanism.

Video image analysis functioned as follows. The first frame of the image sequence was loaded and the user selected which region Matlab (The Math Works, Natick, MA) should monitor for falling drops, for the air/water bath interface and for the resultant bubbles. For each frame in the high speed image sequence recorded by the camera, the grayscale image was converted to black and white based on a certain threshold value (commonly 0.7). Each cluster of pixels greater than a certain minimum size (commonly 25 pixels) was identified. Properties of each object including area, maximum and minimum points and the object boundary were computed and stored for every frame, so that they could be plotted later to verify the accuracy of the image analysis. Fig. 3 A displays a typical frame from this kind of analysis. In this figure, drops 14 were tracked over a region before contact, resulting in data about the drop size and velocity. The crater (lower highlighting) was captured in each frame, with the two circles on the crater portion highlighting the reference point for crater depth observations and the bottom most point in the crater. Bubbles (not shown in Fig. 3A) were also highlighted. All observations were subsequently scaled by camera frame rate and a reference image to convert pixels to millimeters and frames into seconds.

A frame by frame plot of raw data gained from the observations in Fig. 3 A is shown in Fig. 3B. The top pane plots drop area vs. the time of impact with the crater. Drop 14 which is seen in Fig. 3 A as about to impact the surface is labeled. The middle pane plots the crater depth with each unit of time. The bottom pane plots the area of a formed bubble vs. the time of contact. Further processing of these images followed to integrate the information from individual frames into a coherent sequence. The drops were tracked such that any drops that moved less than a certain distance from the drop position in the previous frame were determined to be the same drop. From this sequence of drop data, the trajectory and velocity could be calculated and a predicted impact time with the crater could easily be extrapolated from the last known position. Complications arose when two falling drops coalesced into one drop or one large drop which split into two. These issues were minimized technologically through discarding drops that were not observed to enter or exit the indicated cropped region within a certain distance.

The crater depth was identified by locating searching for the largest object within the cropped region. Identification of it was very straightforward. The minimum y-value point of the crater was observed along with a reference value at the top of the crater which allowed calculations of crater depth. Crater shape was recorded as well.

Bubbles were identified within a region just below that of the minimum value of the crater. When the crater depth was observed to change rapidly (as in Fig. 3B middle trace around 49 ms), the bubble tracking code was triggered to look for the closest circular object to the last known crater minimum location. Any bubble that was found was tracked for 5 frames. Bubble size, shape and position were recorded. The movie was annotated based on the computer analysis for falling bubbles, crater depth and bubble size as depicted in Fig. 3 A. To further ensure the accuracy of the computer analysis and the dataset as a whole, each movie was manually reviewed and each bubble individually confirmed to be an actual bubble and not an artifact. Any bubbles that were not identified by the computer could also be manually selected. The accuracy of the image analysis depended greatly on the quality of the video and the amount of "visual noise" in each frame and ranged from 0-10% false positive identification of bubbles and 0-3% bubbles missed in a given movie.

In short, the video image analysis resulted in the following streams of raw data: drop shape and position in every frame; crater shape and position in every frame; and bubble shape and position in frames which bubbles were created. From the data drop velocity was calculated. Examples of these three data streams are plotted in Fig. 3B. The resulting analysis presented in this example results from a direct extraction or extrapolation from these basic data sources. In observing the formation of several hundred bubbles, three qualitatively different formation events were recognized: a novel-multi drop event, a Plateau-Rayleigh instability event and a vortex ring entrainment event. The novel-multi drop event and Plateau-Rayleigh instability event resulted in bubbles of approximately the same size and may, in fact, result from the same mechanism. The vortex ring entrainment appeared to be different than these two previous kinds of entrainment in that it produced 2-10 drops of size order one tenth to one hundredth the size of the impacting drops. This appeared quite different from the Plateau-Rayleigh and multi drop entrainment processes, each of which produced a single bubble that was approximately of the same size order as the incident drops that created it. The novel multi-drop mechanism was observed in about 97% of the formation and an exhaustive literature search has not found evidence of previous observations of this event in the low speed (<2 m/s), small drop size (<2 mm) regime. The sequence of images immediately preceding bubble entrainment by this mechanism are displayed in Figs. 4A-4D, which shows a time sequence of images illustrating the novel multi-drop bubble entrainment process observed in about 97% of multi-drop bubble formation events. Qualitatively, a crater forms as a result of the first impacting drop. The crater does not have a very high width to height aspect ratio. When the second incident drop hits this crater a bubble appears to be pushed out of it. The resultant bubble then oscillates at around t=0.6 ms. Scale bars are 1 mm.

In 2% of the observations result from what appears to be a qualitatively different drop formation sequence occurs: bubble formation by what may be a Plateau-Rayleigh instability. The two incident drops formed a very high length to width aspect ratio crater which then pinches off in the middle of the crater, resulting in a bubble formation event as shown in Figs. 5A-5D. These are a time sequence of images illustrating the Plateau- Rayleigh instability multi-drop bubble entrainment process observed in about 2% of multi-drop bubble formation events. Qualitatively, an elongated crater appears to form which then pinches off in the middle of the elongated crater resulting in a bubble. Scale bars are 1 mm. Further experimentation appears to suggest that this mechanism is in fact fundamentally the same as the novel multi-drop mechanism that accounted for 97% of the observations.

Finally, 1% of the bubble formation events appear to correspond to the vortex ring entrainment mechanism. When a freely falling oscillating drop hits a water bath, at low velocities the drop creates a vortex ring in the bath. The depth to which the vortex penetrates into the pool appears to be dependent on factors such as the drop shape and minute impurities within the bath surface. When the precisely correct conditions occur, several very small (<100 micrometer diameter) bubbles were entrained, as depicted in Figs. 6A-6D, illustrating a time sequence of images illustrating the vortex ring entrainment process of multi-drop bubble entrainment process observed in about 1% of multi-drop bubble formation events. In this process, an unstable vortex ring forms at the bottom of the crater resulting in 2-10 very small bubbles. Scale bars are 1 mm. The vortex ring bubble entrainment events were highly infrequent and were quite irregular. These very small bubbles may also act as nucleation sites.

The quantitative results presented below were all from 0.22 mm to 1.61 mm diameter drops of distilled water produced by a 0 .6 mm diameter nozzle impacting a 4 cm x 2 cm x 1 cm water bath at 0.6 m/s to 1.5m/s. 120 bubbles produced by a multi-drop mechanism were observed in 10 separate 1 second long trials. Briefly, the results suggest that crater depth and drop time separation are important parameters whereas the relative drop areas (whether a big drop or small drop hits first) does not seem to be as major a factor. Since a bubble can be produced by being detached from a crater, the crater depth was next examined. Charting histograms of all observed crater depths and just those crater depths which resulted in bubble formation, revealed that the craters which immediately preceded bubble formation events were a very distinct subset of the normal crater depth. Fig. 7 A shows a histogram of the observed crater depth (mm) in every frame measured fitted to a normal distribution. Fig. 7B shows a histogram of observed maximal crater depth immediately preceding bubble formation fitted to a normal distribution. It appears that there may be a critical crater depth (1.3 mm) necessary to create a bubble and an optimal crater depth (2.5 mm) for bubble formation. Also, Fig. 7B suggests that the minimum crater depth preceding bubble formation was greater than 1.5 mm. Fig. 7A demonstrated that less than 5% of all observed crater depths met this criteria, with a far smaller percentage meeting the criteria for optimal bubble formation of 2.5 mm.

Plotting the depth of the crater against the size of the bubble that it formed (Fig. 8), several observations can be made. (This figure shows a plot of crater depth scaled to bubble diameter, with the minimum crater depth being plotted.) First, the minimum crater depth can be observed. Second, no bubble diameter was measured at less than 0.2 mm. This is likely not because there were no smaller bubbles, but because 0.2 mm corresponded to a 25px area threshold set in the image analysis software. Any observed objects that were smaller than this threshold were discarded as they were assumed to be either extraneous noise from the video recording or were formed as a result of Vortex ring entrainment, which were excluded from this analysis. Manual confirmation of bubbles ensured that this was a reasonable assumption. Surprisingly, Fig. 8 does not show a direct correlation between crater depth and resulting bubble diameter. The lack of direct correlation between crater depth and bubble diameter suggested that the mechanism behind the entrainment is more complicated than merely having all of the air in the cavity become entrained in a bubble.

Consider a bubble formation event of only two falling drops 1 mm in diameter moving at 1 m/s. If the two drops are separated in time by some very large time scale (say 100 seconds), the first drop will impact, creating a crater but no bubble as it falls below the regular entrainment region for single impacting drops (Fig. 1). As a result, some amount of time (less than 100 seconds) later the air/liquid interface of the bath will approximately return to its unperturbed state. The second drop will fall and but as with the first one, it will form a crater but no drop. Empirically, it was observed that if the time frame is short enough that the drop of one interacts with the crater of the other than a bubble might result. Thus there must be a time scale above which two incident drops behave like a single impacting drop and below which they are capable of a multi-drop bubble formation mechanism.

The critical time can be approximated by determining the amount of time it would take for a crater of depth 1 with surface tension γ (gamma) and density p (rho) to close up. This can be estimated as follows: di

= 3.72 msec

Plotting the time interval between the two drops immediately preceding bubble formation in Figs. 9A-9B, the critical time interval appeared to be less than 5 milliseconds in this particular example, which appeared to be very different than the entire population of observed drop impacts. This critical value is on the same order as the estimate computed above, at least in this example.

Returning to the multi-drop question, the drop that hits immediately prior to bubble formation is called drop 1 , the drop preceding drop 1 is called drop 2, and the time interval between the two drops is called T _2j i. In Figs. 9A-9B, it can be seen that T _2, i was distinct from the population of all incident drops, whereas assuming that drop 50 had no influence on the bubble formation event, it would be expected that T ₄ ^s ₀ would be representative of the population of all drop intervals T _n , _n -i and have no critical value. Figs. 9A-9B are histograms of the time interval (milliseconds) between every two successive drops observed (Fig. 9A) and every two successive drops that immediately preceded bubble formation (Fig. 9B). For the set of experimental conditions observed, there appeared to be a critical time of less 5 miliseconds, such that if two drops fall with a time interval greater than 5, no bubble was produced. With this criteria, any pair of drops m and m-1 preceding the bubble formation that does not distinctly differ from the population of all incident drops did not significantly affect the formation process. Examining histograms of T _5j4 T _4;3 T _3>2 and T^i presented in Figs. 9C-9F (showing histograms of the time interval of drops 1-5 preceding bubble formation), it can be seen that T _2> i exhibited the critical time behavior and overall distribution shape that made it appear different from the overall population of all drop intervals T _niI1-1 that fall. This evidence suggests that only two drops immediately preceding bubble formation have to fall within a critical time frame.

Considering the two drops that result in a bubble formation event, the order in which drops fall was examined to see if that affected the formation of a bubble, and more specifically the bubble size. For example, one might speculate that large drops followed by small drops create larger bubbles or no bubbles at all. Plotting the log of the drop area ratios against the time separation of impact in Fig. 10 suggested that order is not relevant in forming bubbles. This figure shows a plot of the ratio of drop areas against the time interval (milliseconds) between the two drops. The dots are all observations with the circles indicating that a bubble was formed scaled with bubble diameter. The ratio of impacting drop areas is plotted in Logio coordinates so as to center the drops of equal sizes at 1 on the axis. Bubbles were equally likely to form regardless of whether the first drop is bigger or smaller than the second. Also while it appears that the biggest bubbles form when the drops are of approximately the same size, it does not appear that a small drop followed by a large drop or a large drop followed by a small drop necessarily creates a larger or smaller bubble. The critical time threshold for bubble formation can be observed on this plot as well.

Histograms of bubble diameter Fig. 11 further confirmed that there was no significant difference in size of resulting bubbles or number of resulting bubbles when the first drop is larger or smaller than the second drop. Fig. 1 IA shows a histogram of the bubble diameter when the second impacting drop is larger than the first, and Fig. 1 1 B shows a similar histogram when the first impacting drop is larger than the second. It appears that there is no significant difference in bubble production if the first drop is bigger or smaller than the second drop in terms of number (n=51 vs. n=69) or diameter distribution. This observation can be confirmed with the Student T-test which fails to reject that there is any difference between the two sets of observations at the 95% confidence level (p=0.60).

Finally, Figs. 12A-12C illustrates that the drop diameter of both the first drop and second drop were representative of the distribution of all drops that fall, so a particularly big or small drop on an absolute basis was not necessary for this multi-drop bubble formation mechanism to occur; rather it can occur at any drop size within the ranges observed.

In this example, it was reported that multiple drop impacts causing bubble entrainment in a velocity/drop size region where bubble entrainment with single drop impacts does not occur. Three qualitatively different types of entrainment events were observed: novel multi-drop entrainment (about 97%), Plateau-Rayleigh instability entrainment (about 2%), and vortex ring entrainment (about 1%). For a set of experimental conditions, experimental parameters leading to bubble formation were quantified. It was reported that a crater depth of 1.3 mm and a drop time interval of less than 5 ms appeared to be necessary under these conditions for bubble formation through a multi-drop mechanism to occur. These parameters are specific to the experimental conditions, but using the method and apparatus described here could be determined for other conditions. This suggests that the order in which drops fall does not matter, nor is the phenomenon drop size specific. This process does not appear to be critically dependent on more than two drops preceding the bubble formation. One implication of these results is the creation of a mechanical way to eliminate foam, as many manufacturing processes produce foam in the process of combining liquids.

While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the scope of the present invention.

All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms. The indefinite articles "a" and "an," as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean "at least one."

The phrase "and/or," as used herein in the specification and in the claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases.

Multiple elements listed with "and/or" should be construed in the same fashion, i.e., "one or more" of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the "and/or" clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to "A and/or B", when used in conjunction with open-ended language such as "comprising" can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. As used herein in the specification and in the claims, "or" should be understood to have the same meaning as "and/or" as defined above. For example, when separating items in a list, "or" or "and/or" shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as "only one of or "exactly one of," or, when used in the claims, "consisting of," will refer to the inclusion of exactly one element of a number or list of elements. In general, the term "or" as used herein shall only be interpreted as indicating exclusive alternatives (i.e. "one or the other but not both") when preceded by terms of exclusivity, such as "either," "one of," "only one of," or "exactly one of." "Consisting essentially of," when used in the claims, shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase "at least one," in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B," or, equivalently "at least one of A and/or B") can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited.

In the claims, as well as in the specification above, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "composed of," and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases "consisting of and "consisting essentially of shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03. What is claimed is: