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Title:
VACUUM FILTER DEVICE AND METHOD
Document Type and Number:
WIPO Patent Application WO/1996/036428
Kind Code:
A1
Abstract:
A vacuum filter device is disclosed which includes a filter body which is adapted to receive in fluid-tight, sealed relationship a pair of closed containers for solutions to be filtered by means of a membrane filter positioned within the filter body. A vacuum port in the filter body communicates with the downstream side of the membrane and a venting passageway also located in the filter body communicates with the closed sample container to serve as a vent to atmospheric pressure. The venting passageway is made of an air permeable hydrophobic filter or preferably a small enough opening to prevent the sample solutions from leaking out of the device during normal use.

Inventors:
CLARK PHILLIP
FOLEY BRIAN D
PITT ALDO M
Application Number:
PCT/US1996/007316
Publication Date:
November 21, 1996
Filing Date:
May 16, 1996
Export Citation:
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Assignee:
MILLIPORE INVEST HOLDINGS (US)
International Classes:
B01D29/01; B01D29/05; B01D36/00; B01D61/18; B01D61/20; B01D63/08; B01L3/00; B29C65/08; (IPC1-7): B01D63/08; B01D61/18; B01L3/00
Foreign References:
EP0059809A11982-09-15
EP0075405A11983-03-30
US5375477A1994-12-27
US4251366A1981-02-17
US4673501A1987-06-16
US5141639A1992-08-25
US4944876A1990-07-31
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Claims:
CLAIMS
1. A vacuum filter device comprising: a filter body having two junctions disposed from one another, each of said junctions adapted to receive respective closed containers; each of said junctions including sealing means for creating a fluid tight closed system when said containers are coupled to said body, one of said containers for housing a fluid to be filtered and the other of said containers for receiving the filtered fluid; a filter secured within said body; a vacuum port extending through said body and communicating with the downstream side of said filter, said port adapted to be connected to a vacuum source for drawing said fluid from said one container through said filter; and a passageway extending through said body and communicating with the upstream side of said filter.
2. The device of Claim 1 wherein said filter body is of circular crosssection and said passageway extends radially inward from the periphery of said body.
3. The device of Claim 2 wherein said passageway is of circular crosssection and has a diameter of 0.015 inches or less.
4. The device of Claim 2 wherein said passageway is of rectangular cross section and the smallest dimension of said passageway is 0.015 inches or less.
5. The device of Claim 1 wherein said filter is a microporous membrane.
6. The device of Claim 1 wherein said filter is a depth filter.
7. The device of Claim 1 wherein said filter is a combination of a microporous membrane and a depth filter.
8. The device of Claim 1 including a hydrophobic membrane integrally sealing said passageway.
9. The device of Claim 1 including a hydrophobic porous matrix positioned within said passageway.
10. The device of Claim 1 including a hydrophobic tube positioned within said passageway.
11. The device of Claim 1 wherein at least a portion of the surfaces of said passageway are hydrophobic.
12. The device of Claim 1 wherein said filter is a microporous membrane which is segmented into hydrophilic and hydrophobic regions.
13. The device of Claim 12 wherein said hydrophilic region separates said closed containers and said hydrophobic region integrally seals said passageway.
14. The device of Claim 1 wherein said filter body is of circular crosssection, said junctions are threaded holders axially disposed from each other and said containers having mating threads for engaging said recess.
15. The device of Claim 14 wherein said sealing means comprises a raised annular ring adapted to engage said containers to form a compressive fit between said ring and the wall of said holders when said containers are threaded therein.
16. The device of Claim 14 wherein said sealing means comprises an elastomeric gasket positioned within the base of said holders.
17. The device of Claim 1 including a prefilter matrix disposed upstream of said filter.
18. A method of forming a passageway at the interface of two plastic components of a filter device comprising the steps of: inserting a forming tool at the interface between said plastic components prior to integrally joining said components, said tool being of dimensions corresponding to that of said passageway; integrally joining said components together; and removing said forming tool after said components are joined together.
19. The method of Claim 18 wherein said forming tool is tapered at least in the region first inserted into said interface to facilitate removal after said components are joined together.
20. The method of Claim 19 wherein said forming tool is of circular cross section.
21. The method of Claim 20 wherein said passageway has a diameter less than 0015 inches.
22. The method of Claim 19 wherein said forming tool is of rectangular cross section.
23. The method of Claim 22 wherein the smallest dimension of said passageway is less than 0.015 inches.
24. The method of Claim 18 wherein said components are joined by ultrasonic welding.
25. The method of Claim 18 wherein said components are joined by vibration bonding.
26. The method of Claim 18 wherein said components are joined by thermal fusion.
27. The method of Claim 18 wherein said components are joined by solvent bonding.
Description:
VACUUM FILTER DEVICE AND METHOD

BACKGROUND OF THE INVENTION

The present invention generally relates to vacuum filter devices and

particularly to such devices for filtering liquids from one container through a

membrane and depositing the filtrate directly into another container. More

particularly, the invention relates to a liquid-tight filtration system in which

solutions, such as tissue culture media, are vacuum filtered.

Devices for filtering biological solutions generally involve three primary

components, i.e. a membrane filter interposed between two vessels, a feed

container located upstream of the membrane for holding the sample solution to be

filtered and a filtrate container located downstream of the membrane filter for

collecting the filtered sample solution. Often a vacuum is drawn downstream of

the membrane to increase the rate of filtration by creating a pressure differential

across the filter. However, in such cases provisions must be made to maintain the

pressure differential across the membrane and thus assuring that the filtration will

not stop.

The arrangement of components for vacuum filtration can take various

forms; however, especially in laboratory settings, ease of use, reduced storage

requirements and minimal disposable hardware are important concerns as is

avoiding spillage of the biological solution. In certain other applications,

preserving the sterility of the solution being filtered is also important.

An example of a vacuum filter device is described in U.S. Patent No.

4,673,501 wherein an open funnel for receiving a sample of solution to be filtered

is arranged to be sealed to the top of a bottle for collecting filtrate. The base of

the funnel includes a membrane filter positioned such that when the sample to be

filtered is poured into the top of the funnel all of the sample solution is directed to

flow through the membrane filter. A vacuum conduit which is adapted to be

connected to a vacuum source is formed within the base of the funnel and allows a

vacuum to be drawn within the filtrate bottle thereby drawing the sample solution

through the membrane filter. Since the pressure differential across the filter is

constant due to the application of a vacuum on the downstream side of the filter

and atmospheric pressure present on .the liquid surface of the open funnel, rapid

filtration is possible and any reduction in flow rate is due to filter fouling.

Nonetheless, vacuum filter devices of the type described in this patent suffer from

a number of drawbacks which make them inconvenient for laboratory use. First,

these devices require the liquid sample be transferred from its normal laboratory

container to an open funnel. Because of the liquid weight concentrated at the top

of this assembly, they are prone to tipping and hence spilling the biological

solution during pouring of sample or when connecting hoses. Aside from the

inconvenience to the user in handling the fluid to be filtered, there is an enhanced

risk of compromising the sterility of the particular biological solution due to the

open nature of this device. Moreover, the large size of these filter assemblies

results in their taking up limited laboratory storage space. In addition, since the

containers utilized in the filtration process are disposable and intended for one¬

time use, a significant amount of solid waste is generated by these filter

assemblies and the associated pre-and post-filtration containers.

To minimize the amount of solid waste and fluid transfers, U.S. Patent No.

5,141,639 describes a vacuum filter assembly wherein the membrane filter is

disposed in a cover sealable to the filtrate container. The cover is formed with a

feed port in the form of a tubular feed nipple on the upstream side of the

membrane filter. A length of tubing is connected at one end to the feed nipple

and the other end is directly inserted into a sample container housing the solution

to be filtered. The cover also includes a filtrate outlet port and a vacuum port,

both of which fluidically connect with the downstream side of the membrane

filter. When tubing is attached to the vacuum port and a vacuum is drawn the

sample solution to be filtered is caused to flow through the tubing and pass

through the membrane filter to the filtrate container. As is the case with the

aforementioned U. S. Patent No. 4,673,501, the pressure difference in this prior

art assembly remains constant because of the vacuum in the filtrate container and

the atmospheric pressure acting on the liquid surface in the open feed or sample

container. While this device minimizes the amount of solid waste generated

during filtration, it is cumbersome to use as the operator must assemble the tubing

to the cover and hold the cover on the filtrate container until the necessary

vacuum pressure has been achieved in the filtrate container. Additionally, the

feed tubing must be maintained submerged in the sample container to avoid air

being drawn into the sample solution which could disrupt the filtration. In

addition, the sample is housed in an open container; therefore, the risk of

compromising sterility is heightened.

Thus it is apparent that the need still exists for an improved vacuum filter

device that is easy to use, reduces the solid waste generated, minimizes the

number of times the fluid is transferred and reduces the risk of liquid spillage.

SUMMARY OF THE INVENTION

The present invention overcomes the disadvantages and limitations of the

prior art by providing a vacuum filter device for filtering solutions which includes

a filter body having two junctions disposed on opposite sides of a filter. Each

junction is adapted to receive a closed container in a fluid-tight, sealed

relationship. Other aspects of the invention include provisions for foπning a

substantially liquid-tight filtration system and for reducing the risk of

contaminating the sample solution to be filtered. The invention also minimizes the

risk of spillage and contamination of the solution by eliminating fluid transfer

between open containers. The device also includes a vacuum port communicating

with the downstream side of the filter, and hence the filtrate container. When

connected to a vacuum source, the pressure differential will allow a vacuum to

draw the sample solution from the sample container through the filter and into the

filtrate container. To maintain the pressure differential necessary to continue the

flow of sample, a passageway communicates with the upstream side of the

membrane, and hence the sample container, to provide a vent to atmospheric

pressure.

In accordance with a preferred embodiment of the invention, two identical

laboratory containers, for example centrifuge tubes, are screwed onto opposite

sides of a filter body. The filter body has two mating threaded recesses disposed

along the central axis of the body, with each recess having a raised annular ring

for creating a fluid-tight seal with the top of the container when it is screwed into

the body. The portion of the filter body between the two recesses includes a

membrane filter bonded to a suitable support. Two passageways formed in the

filter body communicate fluidically with the opposite sides of the membrane and

ultimately with each of the containers. One of the passageways is a vacuum port

which communicates with the downstream side of the membrane and is adapted to

be connected to a vacuum source for enabling sample to be drawn through the

membrane filter and be collected as filtrate. The other passageway communicates

with the upstream side of the membrane (and the sample container) and serves as

a vent to atmospheric pressure.

When a sample solution is placed in the sample container and both the

sample container and an empty filtrate container are secured to the filter body, a

vacuum is applied to the vacuum port to create a pressure differential between the

two containers. This pressure differential causes sample fluid to pass through the

membrane filter from the sample container to the filtrate container. As the

volume of fluid in the sample container is reduced, air enters through the venting

passageway to maintain the pressure differential across the membrane so that

filtration continues uninterrupted until all the sample is filtered.

In accordance with one aspect of the invention particularly suitable for

applications where leaking of the solution is of concern, the venting passageway is

less than 0.015 inches in its smallest dimension. This passageway is made by

inserting a forming tool between the two halves of the filter body prior to the

integral joining process. Once the two halves have been joined, the foraiing tool

is removed and a passageway between the halves of the body is formed having

dimensions corresponding to that of the forming tool. The creation of such a

small dimension passageway, heretofore unattainable through conventional

molding and assembly techniques, allows it to be used in the filter device of the

present invention as a venting passageway without incorporating any other

structure such as a membrane covering the passageway to prevent solution from

leaking out of the filtration system during normal use. For purposes herein

normal use includes transporting containers witiiin the laboratory and tipping

containers either during use or while being transported.

In certain applications, the liquid-tight feature of the above mentioned small

dimension passageway is enhanced by decreasing the surface energy of the

passageway. This may be achieved by either inserting a hydrophobic liner into

the passageway or applying a hydrophobic surface treatment to all or a portion of

the internal surfaces of the passageway.

These and other aspects and advantages of the invention will become

apparent from the following detailed description taken in conjunction with the

drawings.

DESCRIPTION OF THE DRAWINGS

Fig. 1 is a front elevation view of a preferred embodiment of a vacuum

filter device with laboratory containers coupled thereto in accordance with the

invention;

Fig. 2 is a detailed sectional view of the filter body of the device of Fig. 1 ;

Fig. 3 is an exploded view of the filter body illustrating the assembly of the

membrane filter;

Fig. 4A is an enlarged sectional view of one embodiment of the venting

passageway of the filter body of Fig. 2;

Fig. 4B is an enlarged sectional view of another embodiment of the venting

passageway of the filter body of Fig. 2;

Figs. 5 A, B and C are a series of diagrammatic views illustrating the

process of forming the venting passageway in the device of Fig. 1;

Fig. 6 is a sectional view of an alternate embodiment of a vacuum filter

device in accordance with the invention; and

Fig. 7 is a sectional view of still another alternate embodiment of a vacuum

filter device in accordance with the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Fig. 1 shows a vacuum filter device 10 which includes a filter body

generally indicated by numeral 11 having a pair of axially disposed tubular

holders 12, 13 each having a threaded open end. The holders are bonded back-to-

back (see also Fig. 3) at interface 14 by any suitable welding technique such as

ultrasonic welding to form an integral body. The open end of the holders serve as

a junction to accept a closed sample container 15 for a biological fluid such as

tissue culture media to be filtered and a closed filtrate container 16 for collecting

the filtered sample (filtrate).

The holder 13 includes a face plate 17 with a series of radially extending

ribs 19 molded on the top surface of the plate which act as a support for a porous

membrane 18 which is welded at its periphery to the plate 17 prior to bonding the

two holders together. For applications involving the sterile filtration of tissue

culture media, a particularly suitable microporous membrane is a 0.22 micron

polyethersulfone membrane available from Millipore Corporation under the brand

name Express™. However, depending on the filtration application, the membrane

may be made from any other suitable polymeric materials such as mixed esters of

8

SUBSTITUTE SHEET (RULE 23)

cellulose, cellulose acetate, polycarbonate, polyvinylidene fluoride,

polytetrafluoroethylene, nylon, polypropylene, polyethylene or the like. The use

of inorganic materials is also possible as well as filter structures that are not

microporous (e.g. depth filters). In some applications, a combination of filters

may provide improved performance. For example, for particularly dirty samples

a depth filter in combination with a microporous membrane filter can be used.

Referring also to Fig. 2, the bottom of the holder 12 which abuts the face

plate 17 includes a membrane guard 20 formed as part of the holder. The guard

is wagon-wheeled shaped such that when the two holders 12, 13 are bonded

together sample solution can flow through a series of openings 21 and then be

filtered by the membrane 18. A passageway 30 provides the fluid communication

link between the downstream side of the membrane 18 and the filtrate container

16.

The filter body 11 has respective raised annular rings 22A, 22B which are

molded within each of the holders 12, 13 near to their periphery. A vacuum port

23 in communication with the downstream side of the membrane 18 includes a

filter matrix 24 within the central bore of the port 23. The matrix 24 is used to

prevent the migration of contaminants such as bacteria or oil residues from

entering the filtrate during vacuum operation as well as to protect the vacuum

system from being contaminated by the filtered sample . A tube adapter 26 is

secured to the vacuum port. A venting passageway 25, the details of which are

best shown in Figs. 4 A and 4B, is formed at the interface 14 of the two holders

and is in fluid communication with the upstream side of the membrane and

provides a vent for the sample container 15.

The inclusion of the venting passageway 25 is important to the proper

operation of the vacuum filter device 10 because the sample container 15 is a

closed vessel and the overall filter device is of liquid-tight construction. The

venting passageway allows for mamtøining the necessary pressure differential

across the filter, a feature attributed to the previously described prior art because

of the open nature of their feed containers at a sacrifice of the benefits of the

liquid-tight system of the present embodiment, such as minimizing the risk of

spills and contamination. While a closed sample container would be able to start

the filtration process, it would not provide commercially acceptable performance

over the course of filtration. To explain, the closed sample container starts the

filtration process with an internal starting pressure at atmospheric pressure. As

vacuum is applied to the vacuum port 23, the pressure differential (ΔP) across the

membrane is defined by ΔP = (P sarnp i e - P f ii trate ) where P samp i e is the air pressure in

the sample container and P flltrate is the air pressure in the filtrate container.

Initially, P sample =P filtrate = P atmosPhe.e ; however, as fluid is drawn through the

membrane 18 to the filtrate container 16 the sample volume is being reduced. In

a closed system, this reduction in the amount of sample in the sample container

over time ti to t2 translates to a reduction in pressure, as governed by the

pressure/volume relationship (P sam≠e(tl) V sample(tl) = P^ p ^ t.) V sample(t2) ) where P sample

and V sample relate to the gas within the sample container. As the pressure in the

sample container is reduced, the ΔP is lessened thereby slowing the flow rate. If

allowed to continue P sam pi e w < equal P f ii trate resulting in no flow. To insure the

maximum ΔP and hence the greatest flow rate, the sample container needs to be

maintained as close to P atmos p here as possible. With the present invention, this goal

is achieved by the venting passageway connecting the sample container with the

outside atmospheric pressure.

In accordance with an important aspect of the invention involving

substantially liquid-tight filtration applications, the venting passageway as shown

in Fig. 4A is formed in the filter body in a manner which creates a passageway

whose smallest dimension is 0.015 inches or less. Details of the techniques used

to create this small dimension passageway in the filter body 11 are best discussed

with reference to Figs. 5 A, B and C. As discussed, the filter body is constructed

by ultrasonically welding the two holders 12, 13 at the interface 14. As shown in

Fig. 5 A, a forming tool 50 is placed between the two holders prior to initiating

the weld process. This tool can take a variety of shapes depending on the desired

dimensions of the orifice. In this embodiment a circular wire of diameter 0.015

inches is used, although it will be understood that forms of rectangular cross-

section or even other geometries may be employed. Fig. 5B shows the holders

placed together with the forming tool in position as ultrasonic energy is applied.

After the holders are welded together, the forming tool is removed leaving a

through-hole whose dimensions correspond to that of the tool. To assist in the

removal, the remote end of the forming tool can be slightly tapered such that as

the minimum force required to begin disengaging the forming tool is applied the

remainder of the tool will more readily be removed from the interface 14 between

the two holders.

Injection molding methods generally provide the greatest dimensional

control of shape with plastic parts. To apply conventional molding techniques in

the present instance, it would be desirable to mold a passageway in the wall

section of the filter body 11 remote from the joining surfaces of the two holders

12, 13 in order to eliminate the deformation of the passageway during assembly

thereby retaining the dimensional control. However, conventional molding

processing techniques would not allow a passageway that is molded into the wall

of the holder 12 to be 0.015 inches or less. This is because as the molten plastic

enters the mold cavity the pin used to create the passageway would deflect leading

to fatigue and breakage. Also, for the pin to seal off against the other wall of the

cavity, the sealing end of the pin will be peened over in time leading to flashing.

Flashing is an uncontrollable, undesirable migration of plastic, which in this

example will lead to filling and dimensionally distorting the venting passageway

25.

If, instead of molding a passageway in the wall of the filter body 11 as

discussed above, an attempt were made to mold an interruption or notch on the

joining surrfaces of the holders 12, 13 with dimensions of 0.015 inches or less,

the joining process, whether it be vibrational, thermal or chemical, would distort

or even close the passageway because the two surfaces are joined by softening and

moving the plastic together followed by a stabilization period. The plastic that

moves during joining will be squeezed into available areas, such as the void

created by the molded in interruption. Also the direction of movement of the

plastic during the joining process is not controllable. Thus as the plastic moves

into the interruption it will dimensionally change the shape and possibly close the

interruption altogether.

The use of a forming tool during the joining process provides for a

dimensionally controlled geometry that is independent of the molding process and

controllable with a variety of joining processes in addition to the ultrasonic

welding process of the embodiment described, such as vibration bonding, radiant

heat and other fusion bonding processes as well as solvent bonding.

The ability to form the venting passageway 25 with dimensions of 0.015

inches or less provides significant advantages in that the filtration device maintains

its liquid-tight capabilities without employing an additional membrane covering

the venting passageway to prevent solution from leaking out of the device during

normal use.

In some applications where the solution to be filtered has low surface

tension which allows the solution to readily wet surfaces, such as solutions

containing surfactants, it may be advantageous to impart hydrophobic properties

to all or a portion of the venting passageway 25. One way to maintain the liquid-

tight attributes of the present invention in such applications is to decrease the

surface energy of the passageway. Fig. 4B shows the inclusion of a hydrophobic

liner 44 positioned in the venting passageway 25 which serves as a hydrophobic

porous matrix. Preferred forms of this matrix include porous hollow fiber

membranes, porous polymer rods or micro-bore tubing, all constructed from a

suitable hydrophobic resin. To fabricate the filter body 11 with the liner 44, a

molded slot of predetermined dimension and geometry sufficient to encapsulate

the liner is formed in opposing surfaces 45, 46 of the respective holders 12, 13.

The liner is then crimped in place without collapsing its lumen during the holder

joining process to provide fluid communication between the sample container 15

and the outside atmospheric pressure. Use of a hydrophobic liner allows the

materials of the filter body to be selected based on economics or specific material

properties. As mentioned, the venting passageway need not be completely lined

but only imparted with hydrophobic properties along a portion of the passageway.

Since the liquid-tight characteristic of the present invention is enhanced

when the small dimension venting passage 25 described in accordance with the

embodiment of Fig. 4A is utilized, this attribute may be further enhanced by

applying a hydrophobic treatment to the surfaces of the passageway, preferably in

liquid form during assembly of the Fig. 4A embodiment. A hydrophobic solution

such as polytetrafluoroethylene (PTFE) in suspension may be applied to the

forming tool 50 before the tool is inserted between the holders 12, 13. When the

tool is removed after weld energy is applied, a film of the PTFE remains on the

inner surfaces of the venting passageway. The hydrophobic liquid treatment

decreases the surface energy and prevents leakage of the sample solution during

normal laboratory use.

In operation, a sample solution to be filtered is deposited in the sample

container 15 and is screwed tightly onto the holder 12 with the open end of the

sample container being held upward until the upper lip of the container is

squeezed against the angled surface of the ring 22A. Tightly screwing the

container to the filter body 11 creates a fluid-tight seal. In similar fashion, the

filtrate container 16 is screwed into the holder 13 against the angled surface of the

ring 22B. For sterile filtration of tissue culmre, the filtrate container and the filter

body are pre-sterilized prior to coupling them together.

The device 10 is then flipped over such that the sample container 15 is

oriented upward with respect to the filter body 11 as shown in Fig. 1. A length of

tubing 28 is connected to a vacuum pump (not shown) and a vacuum is applied to

port 23 and the filtrate container is evacuated of air and the pressure therein

correspondingly reduced. The unfiltered sample solution is then passed from the

higher pressure sample container 15 through the membrane guard 20 and the

membrane 18. The filtered solution flows through the opening 30 and collects as

filtrate in the filtrate container 16. To maintain the pressure differential, which

serves as a driving force, air at atmospheric pressure enters through the venting

passageway 25 and replaces the volume of sample solution that passes through the

membrane. The dimensions of the venting passageway discussed with respect to

the embodiment shown in Fig 4A are so small that sample does not leak out from

the sample container 15, thus preserving the liquid-tight nature of the filtration

device.

Fig. 6 shows an alternate embodiment of the device 10 wherein like

numerals refer to the same elements as those shown in Fig. 1. The construction

and operation is similar to the Fig. 1 embodiment except the vent for the sample

container 15 is a passageway 60 whose dimensions are compatible with those

derived from conventional molding techniques (i.e. > 0.015 inches). In this

instance a hydrophobic membrane 62 covers the opening of the passageway 60 to

keep sample solution from spilling out of as well as preventing microbes from

entering the container 15. Thus when used with a sterilizing grade filter such as

the aforementioned Express™ membrane, the filtration system of this embodiment

represents a sterile, closed system which maintains the sterility of the solutions

being processed.

Fig. 7 shows still another embodiment similar to that of the Fig. 6

embodiment except that no vent membrane is used to cover passageway 70.

Instead the membrane 18 includes both a hydrophilic region 71 which separates

the two closed containers 15, 16 and a hydrophobic region 72 which is in direct

fluid communication with the passageway 70. In this instance the membrane is

also sealed to the face plate 17 at bonding point 73 in the vicinity of the interface

between the hydrophilic and hydrophobic regions. To assure that the hydrophobic

region forms an integral seal with the passageway, the membrane seal at point 73

must straddle both the hydrophilic and hydrophobic regions. As vacuum is drawn

through the port 23, the sample solution will flow through the hydrophilic region

of the membrane. At the same time air enters the passageway 70 and ultimately

passes into the sample container 15 through the hydrophobic region of the

membrane. This embodiment thus presents the same attributes of liquid-tight and

sterile sealed filtration as that of the embodiment shown in Fig. 6.