Mark M. Weislogel, Andrew P. Wollman, Ryan M. Jenson, John T. Geile, 

John F. Tucker, Brentley M. Wiles, Andy L. Trattner, and Claire DeVoe

Portland State University, Portland, Oregon

Lauren M. Sharp

Glenn Research Center, Cleveland, Ohio

Peter J. Canfi eld, Joerg Klatte, and Michael E. Dreyer

University of Bremen, Bremen, Germany

Capillary Channel Flow (CCF) EU2–02 on the 

International Space Station (ISS): An Experimental 

Investigation of Passive Bubble Separations in an 

Open Capillary Channel

NASA/TM—2015-218720

June 2015
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated 

to the advancement of aeronautics and space science. 

The NASA Scientifi c and Technical Information (STI) 

Program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI Program provides access 

to the NASA Technical Report Server—Registered 

(NTRS Reg) and NASA Technical Report Server—

Public (NTRS) thus providing one of the largest 

collections of aeronautical and space science STI in 

the world. Results are published in both non-NASA 

channels and by NASA in the NASA STI Report 

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counter-part of peer-reviewed formal 

professional papers, but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or of 

specialized interest, e.g., “quick-release” reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or co-sponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 757-864-6500

• Telephone the NASA STI Information Desk at

 757-864-9658

• Write to:

NASA STI Program

 Mail Stop 148

 NASA Langley Research Center

 Hampton, VA 23681-2199
Mark M. Weislogel, Andrew P. Wollman, Ryan M. Jenson, John T. Geile, 

John F. Tucker, Brentley M. Wiles, Andy L. Trattner, and Claire DeVoe

Portland State University, Portland, Oregon

Lauren M. Sharp

Glenn Research Center, Cleveland, Ohio

Peter J. Canfi eld, Joerg Klatte, and Michael E. Dreyer

University of Bremen, Bremen, Germany

Capillary Channel Flow (CCF) EU2–02 on the 

International Space Station (ISS): An Experimental 

Investigation of Passive Bubble Separations in an 

Open Capillary Channel

NASA/TM—2015-218720

June 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

Level of Review: This material has been technically reviewed by technical management. 

NASA STI Program

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

National Technical Information Service

5285 Port Royal Road

Springfi eld, VA 22161

703-605-6000

This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/

Acknowledgments

Support for this work is shared by the National Aeronautics and Space Administration cooperative agreement NNX09AP66A and 

the German Federal Ministry of Economics and Technology (BMWi) via the German Aerospace Center (DLR) under Grant No. 

50WM1145. Special thanks are due to astronaut Chris Cassidy for installation of CCF–EU2–2 on the ISS. We also wish to thank 

Portland State University personnel W.H. Blackmore, Y. Chen, P.M. Weislogel, and D. Burns, Astrium Engineering, and the NASA 

cadre at Glenn Research Center including R. Green, Johnson Space Center, and especially the MSG crew and cadre at Marshall 

Space Flight Center. A.P. Wollman is supported in part through NASA/Oregon Space Grant Consortium Grant NNX10AK68H, 

C. DeVoe through the NSF REU summer program, and A. Trattner as a summer student from Lincoln High School.

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.
Abstract

It would be signicantly easier to design 
uid systems for spacecraft if the 
uid

phases behaved similarly to those on earth. In this research an open 15:8

 wedgesectioned channel is employed to separate bubbles from a two-phase 
ow in a microgravity environment. The bubbles appear to rise in the channel and coalesce with

the free surface in much the same way as would bubbles in a terrestrial environment, only the combined eects of surface tension, wetting, and conduit geometry

replace the role of buoyancy. The host liquid is drawn along the channel by a pump

and noncondensible gas bubbles are injected into it near the channel vertex at the

channel inlet. Control parameters include bubble volume, bubble frequency, liquid volumetric 
ow rate, and channel length. The asymmetrically conned bubbles

are driven in the cross-
ow direction by capillary forces until they at least become

inscribed within the section or until they come in contact with the free surface,

whereupon they usually coalesce and leave the 
ow. The merging of bubbles enhances, but does not guarantee, the latter. The experiments are performed aboard

the International Space Station as a subset of the Capillary Channel Flow experiments. The 
ight hardware is commanded remotely and continuously from ground

stations during the tests and an extensive array of experiments is conducted identifying numerous bubble 
ow regimes and regime transitions depending on the ratio

and magnitude of the gas and liquid volumetric 
ow rates. The breadth of the publicly available experiments is conveyed herein primarily by narrative and by regime

maps, where transitions are approximated by simple expressions immediately useful

for the purposes of design and deeper analysis.

1 Introduction

Separation of bubbles from a liquid medium is a critical, but non-trivial task aboard

spacecraft due to the absence of a net gravitational force that precludes using buoyancy as a strong separation mechanism. Though any number of methods are pursued

to replace the role of gravity in the multi-phase 
uid systems of spacecraft, the everpresent capillary force which exploits the combination of surface tension, wetting,

and system geometry provides a natural and often passive solution. In Fig. 1 is

sketched an open wedge channel in a zero-gravity environment along which a steady

forced liquid 
ows at 
ow rate Ql. The free surface prole adjusts so that its local capillary pressure balances the convective and viscous pressure losses along the

channel. Bubbles introduced upstream near the channel vertex are asymmetrically

conned by the planar side walls of the wedge and through a combination of mechanisms the bubbles are forced in a cross-stream direction away from the vertex until

they reach approximately inscribed elevations. If the bubbles are large enough, the

channel long enough, and the liquid 
ow rate low enough, there will be ample time

for the bubbles to reach the free surface, coalesce, and leave the 
ow. In doing so,

this simple conduit geometry performs a passive bubble separation operation in an

analogous manner to simple bubble rise in a buoyant open channel 
ow.

When occurring in the nearly weightless environment of an orbiting spacecraft,

NASA/TM—2015-218720 1
R2

x

R1

Rb

x

z

Ql

Ql

Qg

Qg

Free surface

Confined 

bubbles ‘Inscribed’ 

bubbles

Cannula

a

xc

x2

x1

Figure 1. Sketch of an open wedge channel with liquid 
ow Qlleft to right and

with gas 
ow Qg bubbles injected near the vertex at channel inlet. The free surface de
ects inward to resist inertial and viscous pressure losses along the channel.

Capillary pressure gradients drive the bubble away from the vertex toward the free

surface. The bubbles are also convected downstream, eventually reaching an elevation in the channel where they are approximately inscribed. Idealized section views

at the channel entrance and exit are depicted at left and right, respectively.

such processes possess unique characteristics attributable to the large length scale

capillary phenomena possible there: The 
ows are often inertial with highly underdamped low frequency free surfaces, the evidence of buoyancy on unconned bubble

motion is truly negligible, and capillary 
ow rates increase by many orders of magnitude ( 106

-fold), as do various dimensionless groups including the ratio of surface

roughness to characteristic container length ( 103-fold). Regarding research, the

larger length scale systems allow accurate construction of increasingly complex containers and conduits consisting of transparent materials with full optical access. Regarding applications, the demonstration of nearly full scale systems in the relevant

reduced-gravity environment increases technology readiness levels adding condence

to both spacecraft technology developers and adopters. Terrestrial research along

such lines is extensive, but naturally limited to milli-to-microscale systems where

viscous forces play a signicant role|the majority of work focusing on conned bubbles in symmetric geometries such as circular tubes, parallel plates, and rectangular

channels (i.e., [1]). Signicant progress concerning the hydrodynamics of bubbles in

shear 
ows is reported and reviewed by [2]. For a sample of terrestrial micro
uidic

bubble separation and generation methods see [3], [4], [5], [6], [7], and in particular

for the wedge geometry see [8] and [9].

For a quiescent liquid, the fundamental problem of asymmetrically-conned bubble migration in a wedge is addressed in terrestrial experiments by [10] and [11] and

in drop tower experiments by [12]. The passive migration of such bubbles through

a forced convective 
ow is introduced by [8] and [9] with recent experiments also

performed in the microgravity environment reported by [12]. The analytic approach

NASA/TM—2015-218720 2
to the problem often begins from the simplied sketch at left in Fig. 1, where in

the narrow wedge half-angle limit   1 the bubble is approximated as a modulated disc-like body characterized by radii of curvature R1, R2, and Rc (a `squeezed

bubble' according to [10] and an `air puddle' according to [11]). Because R1 < R2,

the capillary under-pressure in the liquid at the narrower end of the bubble is lower

than that of the broader end, and the resulting pressure gradient drives the liquid

upward displacing the bubble downward.

Employing a genetic algorithm to a force balance on such a bubble, [10] consider

the impact of liquid viscosity, partial wetting and contact line pinning, dynamic

contact angle, and the presence of thin lms on the inertia of the `bubble' (via the

liquid). For their laminar 
ows, Metz et al. nd that viscous resistance dominates

the 
ow near the vertex when the bubble is more or less a modulated disc and

velocities are high. Dynamic contact line aects arising from local viscous normal

stresses play a more important role as velocities decrease and the bubble eventually

achieves a more spherical shape.

Using an energy balance, [11] employs the same narrow wedge limit   1 with

2xc=(x2  x1)  1 to nd the transient bubble center migration position xc in two

distinct viscous regimes: a near-vertex regime where

xc 



3

t (1)

and a contact line dissipation regime far from the vertex

xc 

 

13

8  2

1=23=2







Vb

23=4

t

!4=13

; (2)

where , , Vb, and t are the liquid surface tension, liquid dynamic viscosity, bubble

volume, and time, and  = 1:1 is a viscous resistance coecient. The investigations

of both Metz et al. and Reyssat do well to predict accompanying data.

As systems increase in size, inertial forces dominate viscous resistance and the

simplied schematic of Fig. 1 gives way to more complex behavior. Fig. 2 provides

images of a sealed wedge vessel that is mounted to an experiment rig which is

placed inside a drag shield and dropped 21.6 m in a drop tower providing a lowgravity test duration of 2.1 s, [13]. Here, a wedge conduit of acute included angle

2 = 15:5



is shown oriented vertex upward though tilted with respect to g at angle

0  
  90 with a bubble of known volume centered and balanced. The tilt angle


 allows further control of the initial condition. Release of the experiment into free

fall reduces the body force by a factor of  105 and the asymmetrically conned

bubble is driven downward by capillary forces.

In Fig. 3 are presented ve such passive capillarity-driven bubble migration

experiments performed in a drop tower. The bubble volume and 
uid types are

listed for each example shown. Relevant nominal thermophysical properties for 10

cs polydimethylsiloxane (PDMS) are density  = 953 kg/m3, dynamic viscosity

 = 0:00935 kg/ms, surface tension  = 0:0201 N/m, contact angle  = 0, and

index of refraction Nd = 1:399. Such properties for Novec HFE-7500 are  = 1614

kg/m3,  = 0:00125 kg/ms,  = 0:0162 N/m,  = 0, and ND = 1:29. Fig. 3a

NASA/TM—2015-218720 3
c. 

b. 

a. 

60 fps 

HD video

c. 

b. 

g

2a

Battery

Bubble

Backlight

13 cm

Figure 2. Drop tower test equipment: a. free-falling drag shield that houses b. the

experiment rig that supports c. the sealed inverted wedge test channel of acute

vertex half-angle  = 7:75 at tilt angle 
.

0.000

0.167

0.250

0.333

0.417

0.583

0.750

0.917

1.750

0.000

0.050

0.100

0.150

0.250

0.333

0.500

1.667

1.750

0.000

0.050

0.083

0.117

0.200

0.250

0.417

0.000

0.083

0.167

0.333

0.500

0.833

1.833

0.000

0.050

0.083

0.167

0.333

0.583

0.667

0.500

0.267

1.833

a. b. c.

d. 

e.

2 cm

xbci

Figure 3. Downward capillary bubble migration in drop tower tests depicted in

Fig. 2: a. bubble volume Vb = 0:093 ml, 
uid 10 cs PDMS (drop test number 2313),

b. 0.029 ml, 
uid HFE-7500 (3168), c. 0.041, HFE-7500 (2326), d. 0.099, HFE-7500

(2317), and e. 0.495, HFE-7500 (3180). All images are shown to the scale shown

in e. and for times listed next to each projected prole. All tests are performed for


 = 0except e. where 
 = 82. Projected bubble center ideal inscribed locations

xbci are identied using dashed lines.

NASA/TM—2015-218720 4
t = 0 s

0.4

0.8

1.2

1.6

2.0

xbci

Vertex

a. b.

Figure 4. Depictions of wake vortices for small-to-intermediate inertial capillary

bubble migrations: a. Drop tower test of Vb = 0:495 ml HFE-7500 
uid with Ql = 0

ml/s and 
 = 82 with 
ow pattern identied from particle seeding. The bubble is

still moving at t = 2 s. b. Conceptual superposition of eld in a. and non-zero base


ow with intermediate Ql. The inscribed bubble center elevation xbci is sketched as

a dashed line.

provides a viscous example more in line with the experiments performed by [10].

The more inertial 
ow in Fig. 3b reveals early stage opposing corner 
ows that

create a small geyser distorting the bubble enroute to its spherical conguration.

The initially larger, longer bubble of Fig. 3c distorts signicantly to the point of

break-up. In this example, the ssioned bubbles re-merge migrating further away

from the vertex toward the new inscribed elevation. However, re-mergers do not

always occur as shown in Fig. 3d. Tilting the test cell, as noted by 
 in Fig. 2c,

allows much larger single bubbles to be studied without break-up. Such a test is

shown in Fig. 3e, where 
 = 82. Following a step reduction in gravity, the interior

corner 
ows are again observed to wick across the vertex where they collide forming

a geyser. The distorted bubble avoids the breakup observed in 3c, but the highly

inertial capillary 
ow displaces the oscillating non-circular projection of the bubble

well away from the vertex. A sequence of overlayed images from a similar drop

tower experiment employing a particle seeded liquid is shown in Fig. 4a where wake

vortices are obvious as also observed by [10]. Inertia in the recirculating 
uid is

sucient to carry the bubble past the ideal inscribed elevation xbci beyond which

capillary forces no longer provide a motive force. For the end state images shown

for each test in Fig. 3, in 3a the over-damped bubble is creeping toward its ideal

spherical inscribed elevation xbci. In 3b the bubble is slowly circulating clockwise

in the left eddy (ref. Fig. 4). In 3c and 3e all bubbles are still moving past their

ideal inscribed elevations, but in 3d the bubbles appear to be caught in their own

wake vortices which act to reverse their motion back in the direction of the vertex

and the inscribed location xbci.

Considering only tests with appreciable inertia, Fig. 5a provides projected bubble

centroid histories for the drop tower tests of Figs. 3b and e with select data from [10]

NASA/TM—2015-218720 5
and a selection of CCF EU2 experiments performed on ISS, the latter with convective


ow rate set to the minimum value of 0.5 ml/s, as will be described shortly. The

relevant properties and dimensions of the tests in Fig. 5 are listed in Table 1. The

time coordinate of Fig. 5a is scaled by (=)

1=2

in 5b which achieves a useful linear

collapse and not as observed by [12]

xc  0:335 

2

V 1=3

b 2=3

!1=2

t; (3)

with  the density dierence across the interface{approximately equal to the liquid

density. But the linear region of the Fig. 5b curves appear independent of bubble

volume Vb and wedge half-angle  as expressed in eq. 3.

Much is yet to be learned. For example, inertial bubble migration is further

complicated when an inertial convective liquid base state is present as investigated

herein. Coupling the capillary bubble migration 
ow eld with the base 
ow eld

produces a variety of outcomes that are not adequately understood. Low volume

bubbles achieve essentially low inscribed elevations in regions within the base 
ow

boundary layer where path lines are over-damped. Larger inertial bubbles are driven

beyond their inscribed elevations where free stream-like developing base 
ow velocities displace them downstream in such a manner that they are entrained in their own

recirculating wakes and driven back toward the vertex and their inscribed elevations.

This general behavior is depicted in Figs. 1 and 4b for a base 
ow. Fig. 1 adds the

presence of a free surface. We note that such bubble motion reversals are also readily observed in quiescent host liquids due to slight 
ow geometry asymmetries; i.e.,

Fig. 3d. As will be seen, and as identied by [12], the overshoot phenomena is less

pronounced as the liquid 
ow rate is increased. But questions remain concerning

bubble elevations in such developing shear 
ows. For example, do the bubbles drift

away from inscribed elevations? Are they forced into slightly conned elevations?

Or both ( [2])?

The details of such phenomena are important to the design of large length scale

bubble separation processes and capillary 
uidic devices aboard spacecraft. They

are also ideally studied aboard spacecraft. Related microgravity experiments have

been performed aboard the International Space Station (ISS), but have focused on

imbibing bubbly capillary 
ows with 
ow velocities that are intrinsically tied to irregular and often tapering polygonal conduit geometry (i.e., [14], [15], and [16]). As

the large bubbles are displaced across the containers due to corner wicking 
ows,

smaller bubbles convect into narrow bubble bypass regions where they are in turn

conned and coalesce with the free surfaces of the larger bubbles. In this way such

constructs serve the function of passive phase separation. But in such experiments,

both liquid and gas 
ows are coupled and capillarity-driven. In reference to the


ow geometry of Fig. 1, the ability to drive the liquid 
ow independently of the

gas 
ow enables a wide range of test conditions. Employing a pump and an open

wedge channel of variable length, the Capillary Channel Flow experiments (CCF)

are conducted aboard the International Space Station (ISS) to collect a large unearthly data set to inspire advanced capillary 
uidics design as well as guide further

fundamental and applied research. The implications to terrestrial applications and

NASA/TM—2015-218720 6
0

5

10

15

20

25

30

35

40

0.0 0.5 1.0 1.5 2.0

xc (mm)

t (s)

DT 3168; 29

DT 3180; 495

ISS; 22

ISS; 190

Metz 1; 0.53

Metz 2; 0.86

Metz 8; 1.28

Metz 11; 3.09

a.

0

5

10

15

20

25

30

35

40

0.000 0.001 0.002 0.003 0.004 0.005 0.006

xc (mm)

b. t

Figure 5. a. Projected bubble center location xbc for a variety of predominately

inertial bubble migration tests for bubble volumes listed in l: drop tower (DT),

ISS, and selected tests from [10]. For the drop tower tests refer to Fig. 3b and e,

respectively. The data of a. is re-plotted with   t(=)

1=2

. The apparent linear

region of the collapse suggests bubble volume-independent behavior. Refer to Table

1 for specic properties and test conditions.

NASA/TM—2015-218720 7
Table 1. Fluid properties and test cell dimensions for test data in Fig. 5. Metz

et al. [10] employ a 120 g/l concentration of aqueous isopropyl alcohol. Su+ 

(V 1=3

b

=2) tan8=3  is viewed as a measure of inertia in an otherwise visco-capillary


ow [12].

Source Fluid Test Vb      Su+

# (l) (N/m) (kg/m3) (kg/ms) (deg.) (deg.)

DT HFE-7500 3168 29 0.0162 1614 0.00124 0 7.75 268

DT HFE-7500 2326 41 0.0162 1614 0.00124 0 7.75 301

DT HFE-7500 2317 99 0.0162 1614 0.00124 0 7.75 404

DT HFE-7500 3180 495 0.0162 1614 0.00124 0 7.75 691

ISS HFE-7500 - 22 0.0162 1614 0.00124 0 7.9 264

ISS HFE-7500 - 190 0.0162 1614 0.00124 0 7.9 536

Metz Isopropyl 1 0.53 0.035 967 0.0017 9 2.75 2.9

Metz Isopropyl 2 0.863 0.035 967 0.0017 9 2.75 3.4

Metz Isopropyl 8 1.28 0.035 967 0.0017 9 2.0 1.7

Metz water 11 3.09 0.072 1000 0.001 9 2.75 32.2

the overlap with terrestrial research are also important aspects of the work.

2 Regime Map Denitions, and Nomenclature

As a means of introducing most of the denitions and nomenclature for this work,

in Fig. 6 we provide a sketch of a generic xed bubble frequency 
ow regime map for

a narrow open wedge channel similar to that sketched in Fig. 1. For xed channel

geometry, injected bubble frequency f, and 
uid properties including a perfectly

wetting liquid, each map will be presented in terms of the gas Qg and liquid Ql

volumetric 
ow rates. The gas 
ow rate is controlled by varying the bubble volume

Vb such that Qg = fVb. As in related investigations (see [17] and many references

contained therein), the magnitude and ratio of Qg and Ql determines the particular

regime. Flow conditions outside of these regimes are unsustainable in terms of timeaveraged steady liquid 
ow. At least 6 regimes and 3 regime boundaries are identied

in Fig. 6. Each is named from the perspective of such channels serving as low-gravity

passive bubble phase separation devices. A selection of representative images for

each regime and regime boundary described is provided in Fig. 7. Corresponding

denitions and descriptions are provided as follows:

1. 0% Singles: All single bubbles with 0% separation. In other words, the relatively small bubbles do not reach the free surface. We call this the 0%

separation condition where all bubbles convect through the exit of the open

wedge channel.

2. Partial Singles: All single bubbles with partial separation. For the xed length

channel, and for a variety of reasons, at least one of at least ten of these

relatively intermediate-sized bubbles reach the free surface, coalesce, and leave

the 
ow. Only a portion of the bubbles convect through the channel exit.

NASA/TM—2015-218720 8
Qg

Ql

a

b

g

f

e d

c

i

h

Qling

Qgmin

Figure 6. Sketch of a generic xed-bubble frequency regime map in an open wedge

channel: a. 0% separated single bubbles, b. partial singles, c. 100% singles, d. 0%

mergers, e. partial mergers, f. 100% mergers. The single phase ingestion limit Qling

(choking) is identied by the dashed horizontal line g. The map is bounded above

by a region of bubble enhanced free surface stability h. and free surface bubble

coalescence enhanced ingestion i. (Refer to text for denitions and to Fig. 7 for

images of the various regimes.)

NASA/TM—2015-218720 9
a.

g. h. i.

d. e. f.

b. c.

Bubble injection/cannula

Free surface

Channel vertex

Ql

Qg

Gas ingestion No ingestion

100% Separation

Gas ingestion

Figure 7. Characteristic images corresponding to the generic xed-bubble frequency

regime map in an open wedge channel from Fig. 6: a. 0% singles, b. partial singles,

c. 100% singles, d. 0% mergers, e. partial mergers, f. 100% mergers, g. gas

phase ingestion, h. bubble enhanced stability, and i. free surface bubble coalescence

enhanced ingestion. Refer also to Fig. 1 for the approximate orientation on the

conduit.

NASA/TM—2015-218720 10
3. 100% Singles: All single bubbles with 100% separation. 100% of these relatively large single bubbles reach the free surface, coalesce, and leave the 
ow.

No bubbles pass through the channel outlet.

4. 0% Mergers: At least one of at least ten bubbles merge with each other with 0%

separation. The single bubbles may merge, and merged bubbles may merge,

and so on, but the merged bubbles are still not large enough to reach the free

surface for the xed length channel. This is a 0% separation state since all

single and merged bubbles convect through the channel exit.

5. Partial Mergers: At least a portion of the bubbles merge with partial separation. Single-, double-, triple-, and so on, mergers produce a variety of bubble

volumes, a portion of which are large enough to reach the free surface, coalesce, and leave the 
ow. Only a portion of the single as well as merged

bubbles convect through the channel exit. Here, `mergers' denes bubble to

bubble coalescence events, while `coalescence' denes bubble to free surface

coalescence events.

6. 100% Mergers: A 100% separation state where at least some bubbles are

observed to merge. Merger rates generally decrease with increasing Qg. No

bubbles pass through the channel outlet.

7. Single Phase Ingestion Limit: Without any bubbles injected, for xed channel

dimensions, Qlis limited by the stability of the free surface and values of

Ql > Qling lead to collapse of the free surface near the channel exit and

periodic ingestion of ambient gas bubbles into the liquid 
ow loop (choking).

8. Bubble Enhanced Stability: 0% single bubbles enhance the stability of the free

surface and allow Ql to achieve values above the ingestion limit Qling.

9. Coalescence Enhanced Ingestion: The advent of bubbles leaving the free surface results in an abrupt drop in the maximum value of Ql possible for the


ow. Partial single- and increasingly merged-bubbles, towards 100% separation at intermediate to high gas 
ow rates, continue to reduce the liquid depth

and thus ingestion limit Qling.

The eect of wetting conditions on the regime maps is expected to be signicant,

[18]. We expect mergers to dominate behavior in interesting ways as Ql ! 0.

A brief narrative of the space experiment, components, procedures, and calibration is provided before introducing the experimentally determined regime maps.

Following some discussion, simple heuristic arguments are used for eective prediction of the regime boundaries.

3 CCF Story

The Capillary Channel Flow experiment (CCF) hardware was launched to the International Space Station (ISS) aboard the Space Shuttle Discovery (STS-131) on April

5th, 2010. For all subsequent operations, the equipment is installed by an astronaut

NASA/TM—2015-218720 11
into the Microgravity Science Glovebox (MSG) facility of the Destiny Module of the

ISS, [19]. Once installed, the MSG is sealed, the equipment is powered, and the experiment is commanded remotely and continuously from ground stations primarily

at ZARM-Bremen and PSU-Portland, but also from Astrium-Friedrichshafen and

NASA-MSFC as needed. The hardware includes three open test channel geometries: parallel plate, rectangular groove, and wedge channels. Beginning December

27, 2010, CCF was rst operated 24 hours per day for 80 continuous days with the

parallel plate and rectangular channels. The primary objective of these tests was

to determine the critical liquid 
ow rates of such channels that mark the collapse

of the free surface and the initiation of bubble ingestion|a condition often called

choking by [20], and herein referred to as the ingestion limit Qling (refer to Fig. 7g).

A description of these experiments, including a more thorough review of the experiment equipment and function, is provided in [21]. Future CCF ISS experiments

with parallel plate and rectangular groove channels are scheduled.

The rst operation of the wedge test channel experiments began on September

13, 2011 and continued for 33 24-hour days. The results of these initial tests are

reported in part in [12]. These tests also identied the ingestion limits for this geometry, but included exploratory tests on bubble and bubbly 
ows in the wedge

channel where the upstream gas 
ow boundary condition was that of a constant

volume reservoir. In this series of tests, short bursts of bubbles were studied such

that the upstream gas pressure did not decrease signicantly during the injection,

enabling the assumption of an essentially constant pressure gas reservoir condition.

This approach was eective in dening a limited variety of 
ow regimes as a function

of gas 
ow rate, liquid 
ow rate, and bubble frequency, but not always the bubble

volume, [12]. Conditions demarking the 100% passive bubble separation conditions

were also identied. Much was learned during the rst round of wedge channel tests

not the least being the breadth of capabilities of the experiment hardware despite

the numerable challenges presented when seeking to precisely control multi-phase

systems in a reduced-gravity environment, [22]. For example, the CCF 
ight hardware incorporates a minimum of four, what might be called, passive phase separation

devices in addition to the primary wedge test channel which was designed to study

passive phase separation! Thus, there were many opportunities to destabilize the

system, invert the 
uid phases, and/or otherwise leak or spill away the liquid contents of the triply-contained system. Most fortunately, complete recovery following

all purposeful or inadvertent destabilizations was possible through nearly continuous

commanding of the experiment from the ground and sending over 200,000 commands

to ISS for CCF at average rates exceeding one per minute with peaks of over ve

commands per minute.

A second operation of the wedge test channel experiments continued for 40 24-

hour days beginning June 17, 2013. The ingestion limit investigations continued

during these operations, but extensive bubble phase separation tests using new

xed bubble volume conditions were conducted. It is these specic tests that are

the subject of this paper. The xed bubble volume approach combined with ampleresolution real-time video downlink from the ISS provided a wealth of data that are

highly complimentary to the previous `constant upstream pressure' tests of [12]. A

brief review of the CCF hardware is followed by system calibration data used to

NASA/TM—2015-218720 12
`parachute' into the desired experimental conditions and determine the uncertainty

limits of the measurements. Over 5,000 data points were collected for a variety

of conditions and these are presented here primarily in the form of regime maps.

The many regime transitions are discussed in light of simple idealized models that

describe much of the complex behaviours observed. Further insights are learned

from subsets of the data that quantify velocity elds, bubble coalescence lengths,

bubble merger transients, and more. The paper is concluded with a description of

the continued directions of the work highlighting the immediate application of the

results towards passive phase separations in low-gravity environments, as well as in

micro
uidics systems on earth. The unique, approximately 1TB dataset and video

log including image rectication algorithms, recommended instructions for use, etc.

is made publicly available following a request for access at http://psi.nasa.gov.

4 CCF Flow Loop Overview

A highly simplied schematic of only the pertinent components of the CCF 
ow loop

is presented in Fig. 8. Referring to the gure, a self-priming external Micropump

GB-P25 gear pump (a) is employed, which at low 
ow rates, pumps liquids and

gases equivalently. Vane structures in the Phase Separation Chamber (b) reroute

the HFE-7500 liquid around the coalesced Nitrogen gas bubbles and a screen serves

as a bubble trap. Thus, only liquid passes through the Phase Separation Chamber

(b) and into the Flow Preparation Chamber (c) where a converging duct delivers a

highly laminar, though developing, 
ow to the Test Channel (d).

The pressure of the system is set by a 60 mm diameter meniscus in what is referred to as the Compensation Tube (e) connected to the Flow Preparation Chamber

(c) upstream of the Test Unit (f). The transparent Compensation Tube (e) is open

to the ambient gas environment of the Test Channel (d). The quartz Test Channel is a 15:8

 open wedge 48 mm in length and 30 mm in height. A sliding lid

allows variation of the free surface length 0:1  L  48 mm within the eld of

view. The channel is backlit by a diused incandescent source and the two Hitachi

HV-C20 Series 640 px by 480 px color CCD camera elds of view are identied by

the red dashed domains in Fig. 8. Bubbles are injected  2 mm upstream of the

Test Channel inlet from a 223 mm long, 0.8 mm OD, 0.6 mm ID cannula (g) with

centerline 3.6 mm from the channel vertex. The gas 
ow is driven by a gas plunger

(h) delivering 0:0273  Qg  273 ml/s, which is regulated using a high speed Festo

MHE2-MS1H-3/2O-M7-K solenoid valve (i) capable of a wide range of frequencies

0:01  f  10 Hz and duty cycles 0:001  d  10 s. Further geometric details

of the 
ow path are conveyed in the half-section solid model of Fig. 9, including a

more faithful depiction of the cannula conguration. The entrance region leading

to the test channel is an elliptic contraction from the Flow Preparation Chamber.

The exit contraction begins 19.5 mm downstream of the test section and consists of

a rather abrupt transition to a 10.7 mm ID tube that is centered with respect to

the Test Channel height at 15 mm.

During the tests, bubbles coalescing with and leaving through the free surface, at

times, eject droplets that 
oat or 
y within the Test Unit until colliding, sometimes

NASA/TM—2015-218720 13
a.

e.

h.

o.

c. b.

k.

d.

j.

liquid

gas

l.

m.

i.

f.

g.

n.

p.

RCT

Figure 8. Schematic of primary plumbing elements for the CCF open wedge channel

experiment (CCF EU2). The two camera elds of view are identied by the red

dashed domains. As mentioned in order of the text the key items are a. the gear

pump, b. Phase Separation Chamber, c. Flow Preparation Chamber, d. transparent

Test Channel, e. transparent Compensation Tube, f. transparent Test Unit, g.

notional cannula (ref. 9), h. N2 gas reservoir and plunger, i. bubble valve (solenoid),

j. liquid recovery port valve, and k. slider. Control valves l., m., and n., and HFE7500 liquid reservoir and plunger o. are used to position the 
uid phases, and p. is

the 
ow meter.

NASA/TM—2015-218720 14
Elliptic

Nozzle

Exit Contraction

Glass

Test Channel

Cannula

Slider

To Pump

Flow 

Preparation 

Chamber

Free Surface

Entrance

Duct

30

5

24 62.5

48

19.5

z

30

9.5

Figure 9. Half-section solid model of 
ow geometry into, through, and out of the

Test Channel with critical entrance 
ow lengths noted (cf. Fig. 8). The viewable

region of the Test Channel is outlined in black: 48 mm long, 30 mm high, and of

half angle  = 7:9



. Notional velocity elds are sketched in white.

rebounding, and ultimately adhering to the Test Unit interior walls. Such `splashing' in addition to ingestions and other interface destabilizations lead to capillary

connections outside the Test Channel that leak liquid away by capillarity. These

splash and leak rates were measured and found negligible compared to the pump


ow rates Qpump for the tests conducted. However, over time these liquid losses

accumulate large amounts of liquid in the Test Unit. Fortunately, this liquid could

be recovered by either drawing the liquid through a Liquid Recovery Port (j), or

by closing the slider (k) and running the pump at a high 
ow rate such that an

under-pressure in the Test Channel returned the liquid by suction via an unbroken

capillary connection past the slider surfaces and to the liquid throughout the Test

Unit. These liquid recovery methods would almost certainly not have worked if the

liquid was not perfectly wetting. Other valves (l)(m)(n) are employed along with a

liquid reservoir and plunger (o) to re-position the 
uid phases between tests.

A custom Electrical Ground Support Equipment (EGSE) interface is tailored

for telemetry with NASA's Telescience Resource Kit (TReK). Exactly 494 discrete

states are monitored at 1 Hz, 82 of which are directly manipulable by the experiment

operator team. Only 36 of the states are critical to this report and include system

temperatures, pressures, valve states, 
ow rates, 
uid levels, etc. Key control parameters include pump 
ow rate Qpump, gas plunger volume displacement rate V_

1

(ml/s), plunger volume V1 (ml), slider position L (mm), bubble valve frequency f

(Hz), and bubble valve duty cycle d (s). During each test, data is collected manually from the EGSE display and entered into spreadsheets, generating control curves

NASA/TM—2015-218720 15
and guiding the data collection process and strategy. During the 640 hours required

of these tests, 5,315 data points were collected requiring hundreds of thousands of

keystroke entries. Accompanying the data are individual GMT time-stamped video

recordings linked to the precise conditions of each test.

Both data and video logs are made publicly available at http://psi.nasa.gov.

Suggestions concerning the structure and use of the archive are presented in part

in Appendix A. Upon completion of the experiment operations, the telemetry logs

are extracted from the TReK databases to correct typographical, transcription, and

omissions errors that occurred during the manual collection of data. The majority of

the data collected is presented here in the form of regime maps for either xed bubble

frequency or xed bubble volume conditions. These approaches are all enabled by

the ability to deliver known bubble volumes at desired frequencies, as conrmed by

in-
ight calibrations to ensure this capability.

5 Calibration Experiments

5.1 Cannula P and Bubble Volume Vb

To quickly establish injected bubbles of known volume in a closed loop system, a

quasi-steady pressure dierence across the Bubble Valve and cannula P  P1 P2

needed to be rapidly achieved using a priori target values for gas 
ow rate Qg 

fVb  V_

1(1 + P=P2), where f and Vb are the bubble frequency and volume, the

quantity V_

1 is the gas plunger displacement rate in ml/s, and P1 and P2 in mBar are

the eective upstream and downstream pressures across the cannula. Referring to

Fig. 8, P1 is measured in the gas line just downstream of the gas reservoir h and P2

is measured in the Flow Preparation Chamber c just upstream of the test channel.

A zeroth order approach assumes a steady process where the gas within the cannula

is compressible, viscous, and fully-developed such that

P 

8lc

A2

c

V_

1(1 + P=P2)

f d

 12:47V_

1(1 + P=P2)

f d ; (4)

where lc = 223 mm is the cannula length, Ac = 0:283 mm2is the cannula cross

sectional area, and  = 18  106 kg/ms is the dynamic viscosity of the N2 gas at

29:4  0:6

C, which are substituted and evaluated in the right hand form of eq. 4.

The experimental data serves the double purpose of system calibration and a best

t using eq. 4 yields

P

1 + P=P2

 16:62

V_

1

f d; (5)

where the coecient 16.62 (mBar s/ml) accounts for additional viscous resistance

in the Bubble Valve and other gas supply plumbing (compare with the theoretical

coecient 12.47 in eq. 4). Eq. 5 is presented in Fig. 10a against experimental

measurements. For the range of parameters tested (0:04  f  8 Hz, 0:0035  d  5

s, 0:0273  V_

1  1:1466 ml/s, and 1093  P2  1190 mBar where P2  1128:813:3

mBar), average uncertainties for the prediction of P are less than 10% and

usually less than 5% in the primary test range of 20  P=(1 + P=P2)  30

NASA/TM—2015-218720 16
1

10

100

1 10 100

DP/(1+DP/P2

)pred (mbar)

DP/(1+DP/P2)meas (mbar)

0.0273 ml

0.0409

0.0546

0.0955

0.1365

0.1991

 eq. (5.2)

a.

0.01

0.1

0.01 0.1

Vbpred (ml)

Vbmeas (ml)

1.0 ml/s

2.0

3.0

4.0

eq. (5.3)

b.

Figure 10. Predicted vs. measured results for a. P as a function of bubble volume

Vb (ml) and b. injected bubble volume Vb as a function of liquid 
ow rate Ql (ml/s).

The shaded region in a. identies conditions for the wide majority of the tests

conducted and the 7% uncertainty is identied in b.

mBar, where typically 20  P  30 mBar with standard deviations of prediction

uncertainties 1:3 mBar. Thus, on average P1  1129 + 25  1154 mBar.

With knowledge of P, bubble volumes may then be estimated using

Vb 

V_

1

f



1 +

P

P2



; (6)

and for experimental values 0:004  Vb  2:14 ml, values for 0:027  Qg  1:179

ml/s are achieved for the tests conducted. Bubble volume measurements are nonlinearly dependent on the image resolution of bubble diameter measurements, the

latter of which are at worst 4% for the smallest bubbles and at best 1:5% for the

largest bubbles. Thus, the uncertainty for the smallest bubble volume is less than

12% while that for the largest bubble bubble is less than 5%. Uncertainty of

bubble volume determines the uncertainty of the gas 
ow rate, and indirectly, the

liquid 
ow rate in situations where gas bubbles leave the Test Channel exit as will

be discussed. The results of calibration experiments comparing measured spherical

bubble volumes to predictions using eq. 6 are shown in Fig. 10b. A t coecient

in eq. 6 is once again expected to correct for un-modelled eects such as added

resistances in the bubble valve, but we nd here that none is needed for bubble

volume predictions within typically 7%, as identied in Fig. 10b. Thus, measured

Qg uncertainties are on average <  7%. Eqs. 5 and 6 are used to predict the test

conditions required to construct the regime maps that will be presented shortly; the

latter which employ the subsequently measured conditions.

For a higher order accounting of the transients and compressibility in the gas

delivery system, the compressible viscous 
ow model applied to Fig. 11 is used to

NASA/TM—2015-218720 17
derive the governing dimensionless nonlinear transient rst order ODE for pressures

P



1 = P1=P1i and P



2 = P2=P1i

, where

(1  t)

dP

1

dt

+ P

2

1



1  

2

(1  t)

2



 P



1

(  2(
 + ) (1  t)) = (
 + )

2

;

(7)

subject to P



1

(0) = 1, and

P



2 = 
 +   P

1

(1  t): (8)

P



2

(0) = P2i=P1i  
 is the initial pressure ratio,  = V1i=V2 is the initial gas volume

ratio, and  = 2V_

1=cP 1i

is the dimensionless upstream plunger volume displacement

rate, where V1(0)  V1iis the initial known gas plunger volume, V_

1 is the steady

gas plunger rate (this time in m3/s), and c = A2

c=(1:25)8lc is a cannula viscous

resistance parameter in m4s/kg, where the correction coecient 1.25 accounts for

bubble valve and line losses. This model extends that employed by [12] for a constant

V1 gas delivery approach which is recovered from eq. 8 when  = 0 (V_

1 = 0). Here,

the dimensionless time employed is t

 = cP1it=2V1i

, where t  V1i=V_

1 is time in

seconds (ref. to Fig. 11 for notation). With knowledge of P



1

and P



2

from eqs. 7

and 8, the dimensional quasi-steady gas 
ow rate may be determined using

Qg = cP1i

 

P

2

1  P

2

2

2P



2

!

: (9)

For the wide majority of the experimental conditions 109  V1i  247 ml and V2 

110876 ml; V2 is essentially equal to the sum of the average gas volumes in the Test

Unit (716  VgT U  816 ml), the Phase Separation Chamber (115  VgP SC  239

ml), and the Compensation Tube (124  VgCT  206 ml). Thus, in general,  < 0:2,

  1, and 
  0:987. In the vicinity of this parameter space, eqs. 7-9 are solved

and presented in Fig. 12 for  = 0, 0.003, 0.031, and 0.05. Trends of both initially

decreasing or increasing P1 are observed, and though constant pressures are never

achieved, these experiments seek states where P



1  P



2

approaches a steady value,

producing a nearly steady non-zero value for Qg. Such is only possible for  > 0.

This capability is the signicant dierence between the current experiments and

those of [12] where  = 0 and experiments were performed over short durations for

t

  1 in hopes of limited decreases in Qg=cP 1i during each test.

With further regard for the present  > 0 approach, locally steady 
ow rates

are observed as t ! 1. Taking t = 1, eqs. 7 and 8 reduce to

P



1 =



2

+ (
 + )

 

1 +



2

4(
 + )

2

!1=2

; (10)

and

P



2 = 
 + ; (11)

respectively. Eq. 9 becomes

Qg =

cP 1i

2

0

@

 

1 +



2

4(
 + )

2

!1=2

+



2(
 + )

1

A ; (12)

NASA/TM—2015-218720 18
Bubble valve

P2, V2 P1

, V1

lc

Cannula

V1

.

Ac

Figure 11. Simplied closed loop model of fully-developed isothermal ideal gas 
ow

through a narrow cannula. The 
ow is driven by the upstream gas plunger.

which for 

2=4(
 + )  1 yields

Qg 

cP 1i

2



1 +



2(
 + )



: (13)

Re-dimensionalizing the terms in eq. 13 noting that at zeroth order c  Qg=P and

Qg  V_

1, eq. 13 reduces to

Qg  fVb  V_

1



1 +

P

P2i



; (14)

which recovers the form of eq. 6 used to predict the test conditions and establish the

control curves for the majority of the data collection operations, P=P2i providing

a small correction to the expected O(1) balance Qg  fVb  V_

1 (refer to Fig. 10).

5.2 Liquid Flow Rate Ql

The schematic of Fig. 13 provides a further simplied view of the 
ow loop. During

each run, the system contained within the dashed boundary in the gure is slightly

pressurized as gas is injected into it. As shown in x5.1, this pressurization is limited

by the ratio of the mass of gas injected during each test to the initial mass of gas

in the large volume system V2. In agreement with the foregoing analysis for the

volume of gas downstream of the cannula V2, considering the worst case of a 2.8%

compression and average compressions of < 0:10:04% for all tests conducted, the

gas phase within this dashed region may be eectively considered incompressible

during each individual test. Following from this assumption, a volumetric 
ow rate

balance may be applied to the Test Channel, where at steady state Qin = Qout.

The controlled volumetric 
ow rates are the gas injection rate Qg  Qgin = fVb

and the pump 
ow rate Qpump. Referring to Fig. 7, by counting single and/or

merged bubbles, review of the video data readily yields values for the rate of gas

leaving the Test Channel through the free surface Qgsout and through the channel

exit Qgout. When bubbles are injected into the 
ow, the pressure increases in the

primary circulation loop sketched in Fig. 13 and a portion of liquid leaving the

Phase Separation Chamber is diverted to the slightly lower but constant pressure

Compensation Tube. This rate is denoted by QlCT . At steady state the Phase

Separation Chamber collects all gas entering it but passes only liquid, Qlpump. Thus,

NASA/TM—2015-218720 19
0.000

0.005

0.010

0.015

0.020

0.025

0.0 1.0 2.0 3.0 4.0

Qg

/cP1i

t*

β = 0.050

0.031

0.003 0.0

0.98

0.99

1.00

1.01

1.02

1.03

0.0 1.0 2.0 3.0 4.0

P1

, P2

t*

β = 0.05

0.031

0.003

0.0

β = 0.05

0.031

0.003

0.0

a.

b.

DP

DP

DP

Figure 12. Numerical solution to eqs. 7{9 for a. P



1

, P



2

, and b. Qg=cP 1i:  = 0:2,


 = 0:987, and  = 0, 0.003, 0.031, and 0.05. Qg is approximately constant as

t ! 1.

NASA/TM—2015-218720 20
Phase

Separation

Chamber

Pump

Qlout

to Compensation

Tube

Ql ≡ Qlin

Qg ≡ Qgin, P2

Qgsout Qlleak

Qlsout

Qlpump

QlCT

Qgout

Qpump

Qlout

Qgout

Qpump

Cannula

Qg1, P1

Figure 13. Simplied schematic of gas and liquid volumetric 
ows. Gas and liquid


ow into the channel (Qgin, Qlin). Gas leaves the channel through the free surface

and/or channel exit (Qgsout, Qgout). Liquid leaves the channel by splashing and

leaking at the free surface as well as by convecting through the channel exit (Qlsout,

Qlleak, Qlout). The pump pumps both gas and liquid equivalently. The Phase

Separation Chamber traps gas and passes liquid. A portion of the liquid 
ow is

diverted to the Compensation Tube (QlCT ). Neglecting Qlsout and Qlleak, one nds

that Qgout = QlCT and Qlin = Qpump  Qgout.

NASA/TM—2015-218720 21
noting that Qpump = Qlout + Qgout  Qlpump, and that Ql  Qlin = Qlpump  QlCT ,

balancing the volumetric 
ow rates into the channel with those leaving yields

Qgin + Qpump  QlCT = Qgout + Qlout + Qgsout + Qlsout + Qlleak; (15)

where Qlsout represents liquid leaving the channel through the free surface via droplet

ejections (splash) during coalescence with the free surface, and Qlleak is the everpresent and aforementioned capillary liquid leak rate from the channel. Specic tests

conducted to determine the latter reveal that including a worst case 1:12 probability

of droplet ejection during bubble-free surface coalescence, a worst case 1.5 mm

diameter droplet, and a worst case frequency of 2 hz, Qlsout < 0:0038 ml/s, which is

1% of the lowest 
ow rate of 0.38 ml/s employed in the experiments. By measuring

the long duration decrease of the liquid level in the Compensation Tube, in the

absence of bubbles with a fully open slider L = 48 mm, the liquid leak rate could be

correlated with Qpump to nd Qlleak  0:00990:0024Qpump (ml/s). This linearized

relationship suggests that Qlleak = 0 when Qpump  4:08 ml/s, suggesting further

that the channel is continuously leaking for all tests, albeit at varying rates, since

Qpump < 4:08 ml/s for the wide majority of tests conducted. This correlation

also implies that for values of Qpump > 4:08 ml/s the leak rate takes negative values

implying suction of liquid from outside the Test Channel back into loop, as described

earlier as a method employed to recover leaked liquid to the 
ow loop. For the range

of 
ow rates 0:38  Ql  3:0 ml/s it is found that 0:009  Qlleak  0:003 ml/s

which connes the leak rate between 0.1% and 1.8% of Qlfor all tests conducted.

Thus, by neglecting Qlsout and Qlleak and by applying Qpump = Qlout + Qgout and

Qgsout = Qgin  Qgout, eq. 15 reduces to

QlCT  Qgsout: (16)

It is then found that

Ql  Qlin  Qpump  Qgout; (17)

which is used to determine the liquid 
ow rates into the test channel since both

quantities on the right hand side are readily measured. For the majority of tests

performed at or above the 100% separation condition Qgout = 0 and the liquid in
ow

rate is equal to the pump 
ow rate, Ql = Qpump. The quantitative results of [12]

were largely restricted to this 100% separation condition.

The pump 
ow rate Qpump is calibrated in-
ight using the 
ow meter accurate

to 0:1 ml/s to nd the liquid 
ow rate Ql = 0:987Qpump  0:11 ml/s . Thus, Ql

uncertainties are expected to be as high as 25% for the lowest 
ow rates of 0.38

ml/s, but <  4% for 
ow rates at and above 3 ml/s. As a result, the lowest

accuracy 
ow rate measurements arise for low Ql and the highest values of Qg

where the single or merged bubbles do not leave through coalescence with the free

surface (0% separation states). But uncertainties in Qg contribute little under these

restrictive conditions and Ql uncertainties are expected to peak at 21% at the

lowest Ql, while average uncertainties in Ql are calculated to be 7%. Recall that

Qg average uncertainties are also coincidentally 7%, with worst cases of 12%

for the lowest gas 
ow rates and less than 5% for the highest. Thus, the 
ow

rate measurement accuracy increases with increasing 
ow rate and 7% serves as a

nominal estimate for the majority of data presented herein.

NASA/TM—2015-218720 22
5.3 Image Processing

All images are rectied during image analysis to correct for slight camera rotation

and skew lingering from the manual alignment of the optic elements by the astronaut

during set-up. The rectication algorithm and instructions for use are included with

the data archive at http://psi.nasa.gov. Absolute accuracy is better than 0.5 mm

with approximately 0.112 mm/px resolution.

5.4 Data Reduction: Bubble Velocity Prole

Full CFD computations of developing forced single phase liquid 
ow through the

wedge channel are conducted by [23], but computations accounting for the presence

of highly deformable inertial bubbles are incomplete. Particularly for larger bubbles,

the liquid 
ow eld is highly perturbed often by their inertial capillary cross 
ow

trajectories. Specic calibration tests are presented here to determine the velocity

eld using the bubbles themselves; in eect determining the `bubble velocity prole'

of the wedge 
ow geometry without resolving smaller scale structures such as wakes,

eddies, waves, and disturbances to boundary layers, though all of these are observed.

In general, the various video events are further digitized to determine statistical

transient free surface proles and bubble cross sections, volumes, positions, and

velocities. Sample video frames at 3 Hz of single bubble trajectories are overlayed

in Fig. 14 for 10 bubbles of increasing volume at xed 
ow rate Ql = 1:86 ml/s and

fully open slider, L = 48 mm. The frames are selected that assure the alignment

shown at right in the gure where the wedge section is sketched to scale identifying

the degree to which the bubbles are or are not inscribed within the channel. These


ows are labeled as 0% singles and from eq. 17, Ql  Qpump  fVb. As identied in

Fig. 14, the positions of the bubbles are readily tracked by digitizing the locations of

their rightmost edge xb, which closely approximates both the projected area centroid

and the halfway point between minimum and maximum x-coordinate elevations of

the bubble surface xbc. This is because the bubbles move downstream along nearly

inscribed paths and are thus nearly spherical. For example, the leading edge bubble

position data for the tests of Fig. 14 are presented in Fig. 15 with bubble volumes

noted. Comparing xb elevations at z = 35 mm with ideally inscribed elevations

listed reveals that for these data the bubbles take inscribed or higher elevations.

For the case of Fig. 15, the blue data suggest viscous (over-damped) boundary

layer behaviour for small bubbles near the wedge vertex (Vb

< 0:049 ml) and the red

data inertial (under-damped) free stream-like behaviour nearer to the free surface

as bubbles increase in size (Vb > 0:072 ml). Values in yellow 0:049 < Vb

< 0:072 ml

appear to be transitional, breaking the otherwise monotonic relationship between

increasing bubble elevation xb with bubble volume Vb.

As computed by [23], the velocity eld experiences an abrupt change at z = 0

at the free surface where the no slip condition is replaced by the zero shear stress

condition. With knowledge of this fact, fully-developed 
ow entrance lengths Le are

estimated assuming only free surface (F S) or only fully enclosed conduits (EC) to

nd

LeF S 

Ql



and LeEC 

Ql

(1 + )

2

: (18)

NASA/TM—2015-218720 23
48

30

z

x

2a

35

(xb,zb)

Figure 14. Image overlays of single bubbles tracked at 3 Hz intervals for bubble

volumes identied in Fig. 15 for Ql = 1:86 ml/s and L = 48 mm. At right is drawn

the  = 7:9

 wedge section to aid in visualizing the degree to which the bubbles

inscribe at the z = 35 mm location. xb identies the rightmost edge of the bubbles

tracked for elevation comparisons.

Referring to Fig. 9 the channel length from the inlet nozzle to the viewable channel

exit is 30 + 24 + 9:5 + 48 = 63:5 + 48 = 111:5 mm. From eq. 18, for the conditions of

the present experiments, a fully developed base 
ow is expected only for Ql

< 0:612

ml/s for a free surface and Ql

< 0:793 ml/s for a fully enclosed channel (slider

closed), respectively. Details for these forms are provided in Appendix C. The

respective z-dependent fully-developed x-elevations for the two conditions in eq. 18

are approximated by

xeF S 

 

zchH2

Ql

!1=2

and xeEC  (1 + )

 

zchH2

Ql

!1=2

; (19)

where zch  z + 63:5 mm. The boundary layer elevation xeF S is plotted against z

in Fig. 15 establishing the approximate location of the developing boundary layer.

The ideal bubble center inscribed elevations xbci with expected measurement

uncertainties are shown at right in Fig. 15a. Though fully developed conditions are

never achieved, discrepancies at z = 35 mm are blamed on the inertial capillary

overshoot described in connection with Fig. 4 and the unique conditions where

bubbles appear to interact with the edge of the boundary layer. The transitional

bubble volumes 0:049 < Vb

< 0:072 appear most impacted, occupying elevations far

higher than xbci. Ten bubbles are used to determine the 10-point moving average

ts shown in Fig. 15a. The repeatability of such data is high. For example, and

for clarity, 10 sequential bubble paths for four bubble volumes Vb = 0:018, 0.043,

0.056, and 0.138 ml are shown in Fig. 15b. Even the transitional bubbles Vb = 0:056

ml take highly repeatable paths, but a bimodal behavior is observed in the case of

Vb = 0:043 ml where 8 of 10 paths overlap while 2 of 10 diverge in the direction of

NASA/TM—2015-218720 24
10

15

20

25

5 10 15 20 25 30 35

xb

zb

10

15

20

25

5 10 15 20 25 30 35

x

z

a.

b.

0.138

0.043

0.018

0.056

xb

zb

xb

0.098 0.138

0.043

0.037

0.049

eq. 5.16

0.018

0.018

0.072

0.056

0.115

0.081

eq. 5.16

0.043

0.037

0.049

0.056

0.072

0.081

0.098

0.115

0.018

0.138

0.138

0.056

0.043

0.043

Figure 15. a. 10-point average bubble leading edge paths xb(t) for specied bubble

volumes in ml with Ql = 1:86 ml/s, L = 48 mm. Ideal inscribed bubble center

elevations xbci with uncertainties are shown at right. b. Bubble path data from a.

of 10 consecutive bubbles for specied bubble volumes in ml. 2 of the 10 paths for

Vb = 0:043 ml scatter. xeF S(zeF S) from eq. 19 is shown as solid line. Representative

bubble diameters are sketched in b. for Vb = 0:018, 0.056, and 0.138 ml.

NASA/TM—2015-218720 25
the boundary layer. Comparing Fig. 15b with the corresponding paths in Fig. 15a

associates the degree of repeatability with the smoothness of the 10-point moving

average ts shown in Fig. 15a.

Average z-coordinate bubble velocities hwbi at the channel location z = 35 mm

are presented in Fig. 16 using square symbols again for Ql = 1:86 ml/s and L = 48

mm. The `bubble velocity prole' is predominately linear within the boundary layer,

but clearly loses this character beyond it as identied empirically by the dashed line

and by eq. 19 identied by large + symbols and tted with a smooth line, which

suggest that the end of the linear behaviour is near the edge of the boundary layer.

Idealized spherical bubbles are drawn at the terminus of the linear domains. The

linear portions collapse such that hwbi=Ql / 1:205  0:067 mm/ml (not shown).

The general trends of Fig. 15 arise despite the presence of the free surface and

Figs. 17 and 18 repeat the results of Figs. 14 and 15, but for Ql = 2:85 ml/s with the

slider closed, L = 0 mm. At higher Ql, xb is often closer to xbci accept for Vb = 0:162

ml which yield conned bubbles at z = 35 mm. Average bubble velocities for these

conditions as well as other conditions for dierent slider locations are overlaid on

Fig. 16 for further comparisons.

5.5 Discussion

From Figs. 15 and 18, in the boundary layer region of the 
ow a slight drift away

from the vertex is observed to which local hydrodynamics may contribute such as

Saman lift, but such weakly non-parallel trajectories are observed from numerical

simulations of the 
ow that show similar magnitude behavior due to local accelerations caused by the increasingly occluding free surface de
ection and channel

exit contraction eects, [23]. As suggested in Fig. 9, the exit contraction eventually drives all bubbles toward the exit tube elevation. An example full 3-D CFD

simulation of the single phase liquid 
ow eld provides a more quantitative picture

in Fig. 19 (see [23] for further details). Thus, one might expect that nearer to the

channel exit, small bubbles will be weakly driven away from the vertex and away

from inscribed elevations, while large bubbles will be driven toward the channel

vertex and toward or even past their fully inscribed elevations. Without further

insights from theoretical and numeric analysis it is dicult to assess the magnitude

of such eects though they are clearly less apparent with increasing Ql as might be

expected.

The simple 
ow visualization from drop tower tests shown in Fig. 4, and reported

also by [12], reveal that for a quiescent liquid the inertial capillary bubble migration

produces wake vortices that persist in carrying the bubble signicantly past their

inscribed elevations. When a base state liquid 
ow is present the liquid velocity pro-

le convects the bubble downstream and increasingly away from these trailing wake

vortices. As depicted in Fig. 4b, we currently conjecture that it is the recirculation

of these vortices that results in the oscillatory nature of the intermediate-to-large

bubbles at intermediate liquid 
ow rates. Such eects are less noticeable as Ql

increases (e.g., compare Fig. 15 with 18). It is also noted that at high bubble frequencies, subsequent bubble injections perturb previous bubble trajectories leading

to further complexities of the 
ow.

NASA/TM—2015-218720 26
8

10

12

14

16

18

20

22

24

26

28

0 5 10 15 20 25 30 35 40

xb at z = 35 mm (mm)

Bubble Velocity (mm/sec)

< 0.020 mL

0.02 -0.029

0.03 - 0.039

0.04 - 0.049

0.05 - 0.059

0.06 - 0.069

0.07 - 0.079

0.08 - 0.089

0.09 - 0.099

0.10 - 0.119

0.12 - 0.139

> 0.139

0.88o 1.86c

3.84c

2.85c

1.37o 1.86o

eq. 5.16

(mm/s)

Figure 16. z-component bubble velocity hwbi = fcn(xb; Vb) at z = 35 mm. Flow

rates and slider positions are identied for each data set where squares are for open

slider conditions (L = 48 mm; i.e., Q = 1:37o implies Ql = 1:37 ml/s, slider open)

and circles are for closed slider conditions (L = 0 mm; i.e., Q = 2:85c implies

Ql = 2:85 ml/s, slider closed). Eq. 19 values are denoted by + symbols and t with

a smooth line as noted.

NASA/TM—2015-218720 27
2a

35 48

30

z

x

(xb,zb)

Figure 17. Image overlays of single bubbles tracked at 3 Hz intervals for bubble

volumes identied in Fig. 18 for Ql = 2:85 ml/s, L = 0 mm{no free surface. At

right is drawn the wedge section to aid in visualizing the degree to which the bubbles

inscribe at the z = 35 mm location.

5.6 Minimum Bubble Volume, Vbmin

From Figs. 14 and 17 it is clear that the elevation where the bubbles rst become

inscribed is central to the bubble behavior. For a fully developed parallel 
ow,

whether or not the bubbles remain at inscribed elevations is dependent on the sign

of the lift force in the asymmetric shearing 
ow. Both the direction and magnitude

of these forces are yet to be learned. In fact, for our developing 
ow, according

to [2] these forces may both change dramatically across the boundary layer. We

do observe that for a 
ow rate of 2.85ml/s and closed slider the smaller bubbles in

Fig. 18 take essentially parallel paths at essentially inscribed elevations. This might

suggest a negative lift force if any. But we also observe in Fig. 15 for a 
ow rate

of 1.86 ml/s and an open slider with a 48 mm long free surface that such bubbles

migrate slightly away from the vertex { the smaller bubbles migrating away from

inscribed elevations and the larger bubbles away from slightly conned elevations.

This observation might suggest a potential combination of positive lift and capillary

forces. However, we also acknowledge that the combined eects of the developing


ow, free surface de
ections, and the exit contraction contribute to non-parallel

convective components, the degree of which is presently uncertain. Guidance from

further theoretical and full CFD analyses is expected to clarify these issues.

With conrmation that the bubbles generally follow their inscribed trajectories,

Fig. 20 provides a sketch of the wedge channel cross-section, liquid free surface,

and minimum static inscribed spherical bubble volume that is tangent to the free

surface. Values for key geometric quantities for these models are listed in Table

2. Though several model free surface congurations might be considered based

NASA/TM—2015-218720 28
10

15

20

25

5 10 15 20 25 30 35

x

z

10

15

20

25

5 10 15 20 25 30 35

x

z

a.

b.

0.125

0.037

0.015

xb

zb

0.106

0.162

0.037

0.031

0.049

0.015

0.015

0.072

0.056

0.125

0.081

eq. 5.16

0.049

0.037

0.056

0.072

0.081

0.106

0.125

0.015

0.162

0.125

0.056

0.037

0.056

xb

0.031

eq. 5.16

Figure 18. a. 10-point average bubble leading edge paths xb(t) for specied bubble

volumes in ml with Ql = 2:85 ml/s, L = 0 mm. Ideal inscribed bubble center

elevations xbci with uncertainties are shown at right. b. Bubble path data from a.

of 10 consecutive bubbles for specied bubble volumes in ml. Most bubbles establish

approximate inscribed elevations by z = 35 mm, with bubbles such a Vb = 0:162

ml clearly in conned elevations. xeF S(zeF S) from eq. 19 is shown as solid line.

Representative bubble diameters are sketched in b.

NASA/TM—2015-218720 29
0 0.25 0.5 0.75 10 cm/s

a.

b.

Free Surface

Free Surface

Vertex

x

z

Exit

Contraction

Figure 19. CFD velocity eld predictions for a representative channel with representative xed free surface proles along center-plane with a. slight and b. signicant

free surface de
ection to clarify the impact of free surface curvature and channel

exit contraction on the non-parallel nature of the developing 
ow. The free surface

is modelled as a rigid, zero shear stress surface where an elevated (normally super

critical) 
ow rate of Ql = 5 ml/s is achieved to amplify gradients. Note that the

CCF exit port is centered at x = 15 mm and not shifted toward the vertex as

computed here.

NASA/TM—2015-218720 30
RCT

a. b. c. d.

RFS

HFS

a

xb

H

qFS

Rb

y

x

Figure 20. Models of minimum bubble volume Vbmin based on selection of tangential

positions with the free surface: a. Arbitrary pinned free surface condition, b. no


ow RCT radius of curvature condition, c. 
at interface, and d. tangent free surface.

The 
at surface model c. is selected as an easy guide for regime map predictions.

Convex free surface models might also be considered. (Note that for a tangent

bubble and free surface HF S = xbt.)

Table 2. Vbmin for the various models of Fig. 20:  = 7:9



, l = 0, H = 30 mm,

RCT = 30 mm. (Angles are expressed in radians unless otherwise specied.

Quantity a. Arbitrary RF S b. RF S = RCT c. RF S = 1 d. F S = 0

F S cos1(H tan =RF S)   74:1

 =2   0

HF S (mm) RF S(cos F S  sin )= sin  29.72 30.00 26.37

Rb (mm) HF S sin =(1 + sin ) 3.59 3.62 3.28

Vbmin (ml) 4R3

b

=3 0.194 0.200 0.135

on arbitrary free surface curvature as in Fig. 20a, a 
at surface approximation of

Fig. 20c is simple, yields Vbmin  0:20 ml for the CCF experiments, and is essentially

equivalent to the case of the Compensation Tube curvature in Fig. 20b, which more

or less matches the Test Channel inlet pressure with radius of curvature RCT = 30

mm. The minimum bubble volume that can reach the free surface with hopes of

contacting, coalescing, and leaving the channel is selected to be Vbmin  0:20 ml.

Obviously, and as reported by others, the value for Vbmin is foundational to the

bubble separating characteristics of the wedge channel geometry.

6 Regime Maps

A wide variety of tests are conducted varying Qpump (Ql), f and Vb (Qg), and slider

length L. The majority of the results presented here are for xed f and L, or for

xed Vb and L.

NASA/TM—2015-218720 31
6.1 Fixed Bubble Frequency (L = 48 mm)

In Fig. 21 is presented the lowest complete bubble frequency regime map for f = 0:2

Hz (L = 48 mm). The data is also presented with expanded time coordinate in the

inset. The symbols identify the various regimes using the denitions of x2 and are

employed uniformly in all maps to follow. Figs. 22-27 present maps for f = 0:5,

0.75, 1, 1.25, 1.5, and 2 Hz using the same coordinate scale for ease of comparison.

Approximate regime boundaries are sketched by eye on each map. The maps are

combined in Fig. 28 with data and regime map boundaries provided in 28a and with

regime boundaries and shaded regimes provided in 28b. Inspection of such maps

elucidates several immediate conclusions. Other insights are drawn from inspection

of the video data for each test condition. The observations listed here culminate in

the generic map of Fig. 6 and correspond to the various xed frequency regimes and

regime boundaries associated with that gure in x2:

1. Low gas 
ow rates imply small gas bubbles that are too sparse to merge at

elevated liquid 
ow rates Ql. Single bubble volumes less than Vbmin = 0:20 ml

cannot reach the free surface, coalesce, and separate.

2. Single bubbles with volumes slightly less or slightly greater than Vbmin = 0:20

ml on occasion reach the free surface, coalesce, and leave the 
ow. Qgmin =

fVbmin is identied in all maps where applicable. Bubble separations are

enhanced due to the capillary overshoot depicted by the bubble position data

exemplied in Figs. 4, 15, 18, and the inset of Fig. 21. A leftward hook in the

vertical boundary between partial and 100% singles is observed near Qling due

to increased free surface curvature. The severity of the `hook' in these maps

is muted compared to that of the dierent test conditions of [12].

3. Provided the channel is of sucient length, single bubbles with Vb > Vbmin

(Qg > Qgmin) eventually reach the free surface, coalesce, and leave the 
ow.

4. At low Qg small bubbles inscribe closer to the wedge vertex, well-within the

boundary layer where the liquid 
ows are slower and mergers are enhanced.

Merged bubble volumes Vb < Vbmin cannot reach the free surface, coalesce,

and separate.

5. Somewhat erratic mergers and multi-mergers lead to a distribution of bubble

volumes, some of which exceed Vbmin, reach the free surface, coalesce, and

leave the 
ow.

6. If Vb > Vbmin=2, mergers create bubbles of volume larger than Vbmin, and all

such bubbles eventually reach the free surface, coalescence, and leave the 
ow.

Thus, if Qlis low enough the condition Qg = Qgmin=2 = fVbmin=2 serves

as a delimiter for 100% separating double-mergers. Mergers are enhanced for

increasing frequency f, increasing bubble volume Vb, and decreasing liquid


ow rate Ql as easily observed in Fig. 28b.

7. The single phase liquid ingestion 
ow rate Qling approximately intersects the

backwards-extrapolated terminus of the bubble coalescence enhanced ingestion

boundary at Qg  0.

NASA/TM—2015-218720 32
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.02 0.04 0.06 0.08 0.1 0.12 0.14

Ql

Qg

Singles, 100%

Singles, partial

Singles, 0% Mergers, 100% Mergers, partial Mergers, 0%

Ingestion (singles)

Ingestion (mergers)

Ql

Qg

Qling

Qgmin

Ql

Qg

Qling

Qgmin

Figure 21. Regime map for bubble frequency f = 0:2 Hz with expanded scale inset.

8. At high Ql, single bubbles of volume Vb < Vbmin and frequency f > fing

stabilize the free surface and permit liquid 
ow rates slightly higher than

the ingestion limit Qling. The stabilization is enhanced for increasing bubble

frequency as observed Fig. 28b. To be reported separately, it is found that

for channel lengths L > 10 mm, bubbles injected into the 
ow at frequencies

higher than the gas ingestion frequency fing stave o the ingestion limit to 
ow

rates as much as 2.2-fold the single phase 
ow ingestion limit, [24]. The source

of this stabilization is still somewhat in question, but is likely attributable to

the altered time-averaged boundary condition at the inlet which increases the

system pressure, decreasing the free surface curvature, and increasing the 
ow

cross section in the test channel allowing for higher 
ow rates with reduced

viscous resistance. Note that fing is the frequency of gas bubble ingestion into

the liquid stream at the channel exit at Qling.

9. At high Ql, for Vb > Vbmin, single bubbles coalesce with the free surface

reducing the local depth of the liquid and enhancing ingestion of ambient gas

through the free surface at the channel exit. The slope of the bubble enhanced

ingestion boundary is common to all xed frequency maps.

6.2 Fixed Bubble Volume (L = 48 mm)

Each of the regime maps of Figs. 21-28 hold bubble frequency f constant and vary

Vb and Ql. In Figs. 29 and 30 two maps are presented where Vb is xed and f

NASA/TM—2015-218720 33
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 22. Regime map for bubble frequency f = 0:5 Hz. (Refer to Fig. 21 for

symbols.) The small black open circles are taken from [12] as the 100% separation

limit for the `xed volume' upstream condition of those experiments.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 23. Regime map for bubble frequency f = 0:75 Hz.

NASA/TM—2015-218720 34
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 24. Regime map for bubble frequency f = 1:0 Hz.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 25. Regime map for bubble frequency f = 1:25 Hz.

NASA/TM—2015-218720 35
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 26. Regime map for bubble frequency f = 1:5 Hz.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Ql

Qg

Qling

Qgmin

Figure 27. Regime map for bubble frequency f = 2:0 Hz.

NASA/TM—2015-218720 36
Qg

Ql

Ql

f

Qg

a.

b.

Figure 28. 3-D representation of regimes maps of Figs. 21-27, for f = 0:2, 0.5,

0.75, 1.0, 1.25, 1.5, and 2.0 Hz: a. data with regime boundary sketch, b. regime

boundaries and shaded regimes. In b., for high Qg, the 100% single bubble regime

is extrapolated for f = 0:2 Hz and interpolated for f = 0:75 Hz.

NASA/TM—2015-218720 37
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Qling

Figure 29. Regime map for xed bubble volume Vb = 0:15 ml.

and Ql are varied. Values for Vb of 0.15 and 0.25 ml are selected that are 0:05

ml o the minimum separation bubble volume of Vbmin = 0:20 ml. These maps

are signicantly dierent in character from the xed frequency maps. For these

tests low Qg values imply low f. In Fig. 29 at low Qg, single bubble separations are

observed despite Vb < Vbmin due to the capillary overshoot mechanism. Interestingly,

these rarely complete separations do not appear to impact the ingestion limit, which

steadily increases with increasing Qg at a common slope provided Vb

< Vbmin. The

overshoot-coalescence phenomena ends with increases in Ql and Qg.

In Fig. 30, since Vb > Vbmin, the 100% separation condition for singles and

mergers is the norm, though an island of mixed partial separation behaviour is

evident. Though Figs. 29 and 30 represent the only true xed bubble volume maps

completed, binning bubble volume data within 0:0125 ml of select values, the

regime map transitions can be observed from Fig. 31a for the data and regime

map boundaries and from Fig. 31b for the regime boundaries and shaded regimes.

Inspection of Fig. 31 identies how various regimes grow and decay with Vb.

6.3 Fixed Bubble Frequency, Variable Channel Length (L = 15; 25; 48

mm)

The length of the channel plays a critical role in the ability of such conduits to

separate bubbles. Shorter channels allow less time for bubbles Vb > Vbmin to reach

the free surface. They also support signicantly higher base 
ow ingestion limits

Qling further reducing the time available for cross 
ow bubble migration, free surface

NASA/TM—2015-218720 38
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Qling

Figure 30. Regime maps for xed bubble volume Vb = 0:25 ml.

coalescence, and separation. For a xed frequency of f = 1:25 Hz, Figs. 32 and 33

present maps for free surface lengths L = 15 and 25 mm, respectively. The case

of f = 1:25 Hz with L = 48 mm was presented in Fig. 25. The liquid 
ow rate

at ingestion Qling varies with L and empirically determined values are identied

in the gures along with Qgmin (cf. Fig. 37). The 100% separation condition is

achieved only in the case of mergers at low Qlfor the conditions established in these

tests. Signicantly higher Qg values would be required for 100% for single bubbles

to coalesce and exit. Particularly in Fig. 32, the shorter channel does not permit

sucient time for coalescence to occur. The shorter stier free surface also promotes

the bouncing of larger bubbles, preventing coalescence within the free surface length

L.

7 Examples of Data Reduction Directions

Various aspects of the general phenomena may be studied in greater depth using

the video archive. Though eorts are continuing, we brie
y address a few such

topics here: merger transients and limits, bubble exit locations, and free surface

wave dynamics.

7.1 Merge Transients and Approximate Limit Analysis

The large dataset is replete with bubble merger events of which only a subset will

be touched on here. For example, a selection of 0% separation mergers are shown

NASA/TM—2015-218720 39
Qg

Ql

Ql

Vb

Qg

a.

b.

Figure 31. 3-D representation of regimes maps for constant bubble volume including

data of Figs. 29 and 30: a. data with regime boundary sketch, b. shaded regimes.

Values of Vb are provided 0:0125 ml for Vb = 0:050, 0.075, 0.10, 0.125, 0.15, 0.175,

0.20, 0.225, 0.25, 0.275, 0.30, 0.325, and 0.35 ml.

NASA/TM—2015-218720 40
0.0

1.0

2.0

3.0

4.0

5.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Qling

Qgmin

Figure 32. Regime map for xed bubble frequency f = 1:25 Hz for free surface/slider

length L = 15 mm with Qling = 3:4 ml/s. Compare also to Fig. 25 where f = 1:25

Hz and L = 48 mm.

in Fig. 34 with specic conditions listed. These are cases of pure channel exit

mergers 34a, alternating bubble mergers 34b, pure channel entrance mergers 34c,

and mixed mid-channel intermediate bubble volume mergers 34d. Other merger

patterns are observed that could be dened to further subdivide the merger regime

domains. For example, with generally increasing Qg and Ql we observe multimergers, several entrance merger types, pure mergers, harmonic mergers, sparse

hydrodynamic mergers, and 100% singles with occasional mergers due to rebounds

o the free surface. We restrict our attention here only to mergers resulting from

over-packing bubble trains as typied in Fig. 34.

Merge dynamics are readily measured by digitizing the elevation of the top of

the merged bubble xbt(t) for any merge event. This is accomplished in Fig. 35 for

various 0% mergers varying Vb holding Ql xed, and holding Vb xed while varying

Ql. A cursory inspection of the gure reveals that for this selection of conditions

the migration velocity is nearly independent of Vb and Ql, and that the initially

slightly conned single bubbles are capable of only slightly overshooting their ideal

merged bubble inscribed elevations xbti, as was also demonstrated in the drop tower

experiments in Fig. 3c-d. Note in this gure that for spherical bubbles xbt = xb+Rb,

or xbt = Rb(1+sin )= sin . From Fig. 35 the common migration rate of the merged

bubbles is  6:4  0:4 mm/s, which is signicantly less than the common single

bubble migration rate of  37:5  1:5 mm/s from Fig. 5.

We note that for ideally inscribed single and merged bubbles, the merged bubNASA/TM—2015-218720 41
0.0

1.0

2.0

3.0

4.0

5.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Qling

Qgmin

Figure 33. Regime map for xed bubble frequency f = 1:25 Hz for free surface/slider

length L = 25 mm with Qling = 3:0 ml/s. Compare also to Fig. 25 where f = 1:25

Hz and L = 48 mm.

ble occupies an elevation that should not interfere with other single bubbles if the

distance between bubble surfaces satises

rm =



3Vb

2

1=3

 

1  sin   2

1=3

(1 + sin )

sin 

!

> 0; (20)

where rm is identied in Fig. 34b and d. The condition rm = 0 occurs when  =

6:6



(0.115 radians) and is independent of Vb. For wedge sections where  < 6:6



,

the merged bubbles may be expected to re-merge with other single bubbles at least

once, whereas if  > 6:6



, the merged bubble will move to an elevation that will

not permit further interaction with other un-merged single bubbles. This conclusion

emerges from the present study where  = 7:9



, as observed in Fig. 34a and d, where

the inertial capillary overshoot also works in favor of no re-merges. (The pure merger

case of Fig. 34c has no chance to re-merge since all single bubbles merge.) However,

re-mergers do occur as shown in Fig. 34b, suggesting that local hydrodynamics often

trumps the simple inscribed bubble packing arguments presented here. Further

details of re-mergers must be reported on a separate occasion.

Mergers are obviously increasingly likely with increasing bubble density. As the

distance between bubbles decreases, any number of second order mechanisms can

trigger the merge phenomena. A partial list of observed mechanisms includes: (1)

variations in bubble volume and/or elevation, (2) pulsatile disturbances to the 
ow

and free surface induced by subsequent bubble injections, (3) forward stagnation

NASA/TM—2015-218720 42
a.

c. d.

b.

Bubble injection/cannula

Free surface

Channel vertex

Ql

Qg

db

z

x

parabolic

linear

plug

drm

drm

(xbt,zbt)

(xbt,zbt)

Figure 34. Examples of 0% separation bubble merger dynamics: a. 6 Hz images of

mid-channel merger without re-merger for f = 0:4 Hz, Vb = 0:007 ml, Ql = 3:84

ml/s, Qg = 0:0028 ml/s, L = 0 mm; b. 3 Hz images of alternate bubble mergers

where re-mergers do occur for f = 3 Hz, Vb = 0:009 ml, Ql = 2:61 ml/s, Qg = 0:028

ml/s, L = 48 mm; c. 3 Hz images of pure channel entrance mergers for f = 3 Hz,

Vb = 0:009 ml, Ql = 2:36 ml/s , Qg = 0:028 ml/s, L = 48 mm; d. 3 Hz images

of intermediate mid-channel mergers without re-mergers f = 2 Hz, Vd = 0:055 ml,

Ql = 1:36 ml/s, Qg = 0:111 ml/s, and L = 48 mm. Approximate horizontal bubble

separation b, vertical re-merge bubble separation rm, bubble top location xbt, and

3-region velocity prole are identied as sketched.

NASA/TM—2015-218720 43
15

20

25

0.0 0.5 1.0 1.5 2.0

xb (mm)

t (s)

 0.877, 0.055

 1.074, 0.055

 1.272, 0.055

 1.469, 0.055

 1.074, 0.037

 1.074, 0.041

 1.074, 0.055

Q Ql, Vb l (ml/s), Vb(ml)

0.11

0.041

0.037

0.055

0.082

0.074

Figure 35. Bubble top surface elevation xbt(t) (ref. Fig. 34c-d) for mergers as functions of xed Vb varying Ql and xed Ql varying Vb. For these tests the single bubbles are slightly conned while the merged bubbles migrate slightly beyond their

ideal inscribed elevations shown with approximate measurement uncertainties. The

common slope is approximate by 6:4  0:4 mm/s.

NASA/TM—2015-218720 44
point 
ows generated by the capillary migration forcing previously injected bubbles

ahead to merge with their predecessors, (4) entrainment of bubbles in adjacent

bubble wakes, (5) unique 
ow harmonics, and (6) a channel exit contraction eect

that can trip the merge phenomena from its densest bubble train condition, setting

o a sequence of mergers that propagate upstream to the channel entrance where the

bubble train is then gradually reestablished and the process repeated. Concerning

variations in bubble volume, assuming that the bubbles take inscribed elevations,

one might argue that any variation in Vb will ultimately lead to mergers, since larger

bubbles move along slightly higher elevations where the base 
ow is faster enabling

them to catch up and merge with any slightly smaller bubbles. Long channel lengths

are likely to reveal additional details and an increased variety of merger phenomena.

But the length of open capillary channels is limited by Qling. Such studies might

best be conducted using closed channels as demonstrated in Fig. 34a.

Simple merge limit predictions are possible with knowledge of the critical bubble

spacing b and the base 
ow velocity prole wb(xb), both of which are sketched in

Fig. 34a for a train of bubbles with conditions specied. At steady state, the time

period between bubble injections (1=f) must equal the time required for a bubble

to convect one bubble diameter plus the distance between bubbles b, or

1

f

=

2Rb + b

wb

: (21)

As suggested by bubble velocity plots such as Fig. 16 and from previous observations

by [12], the developing velocity prole sketched in Fig. 34a consists of a parabolic

boundary layer region near the vertex, a lengthy intermediate linear region potentially also in the boundary layer, and a plug 
ow-like free stream region near the

free surface. The extent of each region depends primarily on the value of Ql, the

z-location, and free surface length L.

Assuming a vertex region parabolic prole of the form

wb 

4mQl

H2

x

2

b

H2

; (22)

substituting into eq. 21 and solving for Ql yields the low Qg merge limit

Qlm1 

H4f

4mx2

b

(2Rb + b): (23)

The ideal merge limit achieves b = 0 with t coecient m. Applying the geometric

relationships xb  Rb= with Rb = (3Qg=4f)

1=3

, eq. 23 becomes

Qlm1 



3H4f

2m

 

4f

3Qg

!1=3

: (24)

A value m  0:60  O(1) will be shown to estimate the division between single and

merged bubble regimes within the boundary layer in the near-vertex region of the


ow.

NASA/TM—2015-218720 45
Assuming an intermediate boundary layer region linear prole

wb 

nQl

H2

xb

H

 wbo; (25)

where wbo is a velocity oset, substitution into eq. 21 and solving for Ql yields a

high Qg merge limit

Qlm2 



2H3f

nxb

(f(2Rb + b)  wbo): (26)

Again, the ideal merge limit achieves b = 0 with t coecient n. Neglecting wbo

and applying xb  Rb= with Rb = (3Qg=4f)

1=3

, eq. 26 reduces to the bubble

volume-independent relationship

Qlm2 

2fH3

2

n

: (27)

As will be shown, adequate estimates of the merger limit away from the vertex

is achieved for n = 3=2  O(1). Theoretical and numerical hydrodynamic merge

models are being considered, but the facility of the simple eqs. 24 and 27 will be

demonstrated shortly in x8.

7.2 Bubble Exit length

Knowledge of the distance the bubble travels down the channel before coalescing

with the free surface z = lH is an important metric for such 
ows since it permits one

to determine the desired channel length to achieve a desired result. Data is recorded

for the average value of lHmeas for 10 bubbles for 100% separation conditions. Only

a single example is provided in Fig. 36 for xed frequency f = 0:75 Hz and for the

variety of bubble volumes specied. For inertial-capillary bubble migration (Su+

b 

V 1=3

b 

8=3=2  O(100)) and inertial base liquid 
ows (Re  Ql=H  O(100)),

the form suggested by [12]

lH = Cf

Ql

H

 

V 1=3

b

24=3

!1=2

(28)

is found to approximate the linear trends observed, where the t coecient for

f = 0:75 Hz is 3:66  0:32. [12] found Cf  10:5 for f = 0:2 Hz. The strong

dependence of Cf on f is indicative of the sensitivity of coalescence to the various

oscillations of the system. A wide variety of outcomes due to bubble frequency

eects, harmonics, bouncing, bimodal behaviour (where two lH values arise for one

test condition), and other free surface interactions are readily observed in the data

archive but will not be discussed further herein. For Ql

< 0:7Qling, the value of lH

from eq. 28 serves as a reasonable prediction of the minimum channel length required

to separate bubbles > Vbmin. At higher values of Ql eq. 28 becomes increasingly

conservative as the free surface is de
ected increasing inward enhancing bubble

coalescence. We also observe that for short channels, when the 1-D free surface

NASA/TM—2015-218720 46
0

5

10

15

20

25

30

0 5 10 15 20 25 30

lHmeas (mm)

lHcalc (mm)

f = 0.75 Hz

 0.257

 0.264

 0.272

 0.333

 0.395

 0.471

 0.740

average

lH = 3.656*(Ql/H)(rVb

1/3/2sa4/3)1/2

eq. 7.9

Figure 36. Measured bubble exit location lHmeas against calculated exit location

lHcalc from eq. 28 with Cf = 3:66. For these tests bubble frequency is xed at

f = 0:75 Hz for the bubble volumes listed in ml.

curvature condition (H=L)

2  1 is not satised, the increased `stiness' of the free

surface leads to signicant rebounds that deny single bubbles a second opportunity

to coalesce with the free surface before being swept through the channel exit. In

such cases eq. 28 is inadequate.

7.3 Free Surface Wave Dynamics

Bubbles that coalesce at the free surface generate capillary waves with wavelength

and speed tied to the bubble diameter and liquid 
ow rate Ql. As expected, the

smaller the bubble the faster the wave according to the well-known capillary wave

dispersion relation !

2 = k3=, with wave angular frequency !, wave number k =

2=, and wavelength . Choosing  = 4Rb, where Rb is the bubble radius, and

dening capillary wave speed wcwave  !,

wcwave 





2Rb

1=2

: (29)

For Vbmin = 0:2, Rbmin = 3:6 mm and for our tests we estimate wcwavemin = 66

mm/s. Under-estimated as the average liquid velocity hwi, the free surface velocity

is

wF S  hwi  Ql

H2 tan 

; (30)

NASA/TM—2015-218720 47
and for Ql = 1:86 ml/s, wF S  15 mm/s is predicted. For comparisons, experiments

for Ql = 1:86 ml/s in Fig. 16 with an open slider show elevated velocities indicative

of wF S in the range of 20 mm/s.

The capillary waves propagate downstream at speeds equal to the capillary wave

speed plus the free surface velocity|highs of 80 mm/s are observed for Ql = 1:86

ml/s. Re
ected waves return at speeds equal to the same capillary wave speed

minus the free surface velocity|
ows of 40 mm/s are observed from the data for

Ql = 1:86 ml/s. This general behaviour is estimated from the above approximations

where wwave  wcwavemin  wF S = 66  15 mm/s which compares well to terse

observations of the data where 60  20 mm/s. This approximate approach may be

extended quickly to predict the time required for the wave produced by a bubble-free

surface coalescence at z = lH to travel downstream a distance L  lH, re
ect, and

return to location z = lH (ref. eq. 28). The time for this process is given by

tr =

L  lH

wcwave + wF S

+

L  lH

wcwave  wF S

=

2L(1  lH=L)

wcwave(1  
2)

; (31)

where 
  wF S=wcwave. For the values of these experiments 
 = 0:227, and for

Ql = 1:86 ml/s, from eqs. 29-31, tr  1:07 s. This `re
ection time' corresponds to a

frequency fr = t

1

r  0:93 Hz. This frequency for this 
ow rate is surprisingly close

to the conditions identied by [12] (Fig. 15c in that article), where coalescence with

the free surface could not be achieved at f = 1 Hz and Ql = 1:91 ml/s. The present

arguments support the claim that the natural frequency of the re
ected waves match

the bubble injection frequency f, providing a timely bounce to the free surface that

prevents coalescence.

By such mechanisms the free surface waves can have local impact on coalescence

and can set up harmonics within the system that retard or enhance bubble mergers

and/or bubble coalescence. In general, however, the free surface waves serve as

perturbations to the bubble paths and not as a primary mover, as can be gleaned

from Figs. 15, 16, and 18, where bubble paths appear similar whether a free surface

is present or not. Room is not aorded here to elaborate on such waves but their

presence and impact is noted and may be pursued more quantitatively from the

video archive.

8 Heuristic Regime Map

As guided by observations of the regime maps, simple heuristic models may be

applied to predict the various regime boundaries observed and, as an example,

we demonstrate approximate map construction for the xed frequency case; i.e.,

Figs. 21-28. For our example, we will `re-construct' the f = 1:25 Hz map of Fig. 24

piecemeal by introducing each regime limit mechanism. Comparisons are then made

to all experimental maps. We view this as a preliminary eort with anticipated improvements and generalizations following further analysis of the data and of subsequent third party theoretical and numerical work. In the meantime such capabilities

are immediately of value for design.

NASA/TM—2015-218720 48
8.1 Single Phase Liquid Ingestion Limit, Qling

The primary objective of the CCF experiments on ISS was to determine the single

phase liquid ingestion limit Qling as a function of channel length L for three open

channel geometries: parallel plate, rectangular groove, and wedge. These results are

reported in detail elsewhere by [21] and [25]. The ingestion limit experimental data

for the wedge channel is reproduced in Fig. 37. An image of the phenomena was

presented in Fig. 7g. In general, Qling is computed by solving an approximate 1-D

nonlinear ODE subject to CFD computed inlet boundary conditions. These results

are included in Fig. 37. Additionally, to speed the assessment of designs and to

rapidly compute this regime boundary for known channel length L, a closed form

expression for this limit may be approximated by

Qling 

L

22

0

@

 

1 +

4

3



2

H3

5

L2

!1=2

 1

1

A 

L

22

 

1 +

4

3

Su+

1=2

 1

!

; (32)

where Su+  (H=2)(H2=L)

2  Su(H2=L)2

is a geometrically modied

channel 
ow Suratman number Su that measures inertia in a visco-capillary 
ow.

Su is essentially a Reynolds number based on the capillary velocity scale =. For

the present tests, 0:015  L  0:048 m and 100  Su+  10. Eq. 32 may be

inverted to predict critical channel length Ling given liquid 
ow rate Ql to nd

Ling 

H3

3

3Ql

 

1 

3Q2

l

H3

!

: (33)

Eqs. 32 and 33 are determined via scaling arguments that assume a narrow wedge

  1, dominant cross-channel curvature (H=L)

2  1, and an inertial-capillary


ow that ingests once the contact line de-pins from the channel edge at the channel

exit. Further details of the scaling arguments are provided in Appendix B. Eq. 32

along with a representation of its uncertainty  Qling  (1  (H=L)

2

) is presented

in Fig. 37. The error is < 5% for L  15 mm. The observed agreement of the

experiments with the upper uncertainty curve for the scale prediction is fortuitous.

For the present study Qling for L = 48 mm is computed from eq. 32 and plotted on

Fig. 38.

8.2 Minimum Gas Flow Rate For Separation, Qgmin = fVbmin

It has already been observed from the xed frequency maps of Figs. 21-30 that single

bubbles of radii larger than the maximum inscribed circle of the wedge section can

be expected to reach the free surface, coalesce, and leave the 
ow. For the tangent

bubble-free surface model shown in Fig. 20c we nd

Qgmin = fVbmin  f

4

3



H sin 

1 + sin 

3

: (34)

A vertical line is drawn on Fig. 38 at this location and values of Qg larger than this

amount are expected to be increasing favorable to separation. It is also clear that

single bubbles of volume Vbmin=2 that merge will then possess the minimum bubble

NASA/TM—2015-218720 49
2

3

4

5

6

0 10 20 30 40 50

Qling (ml/s)

L (mm)

experiments

eq. 8.1

eq. 8.1 uncertainty

CCFlow w/ BI-CFD BCs

Figure 37. Single phase liquid 
ow limit above which the gas phase is ingested at

the channel exit; i.e., the ingestion limit Qling. Experimentally determined values

from [21] (symbols sized proportional to uncertainty) are provided with numerical

predictions of [25] (dot-dash lines) and closed form scale predictions of eq. 32 (solid

line) and expected uncertainty (dotted lined).

NASA/TM—2015-218720 50
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

Ql

Qg

Qlbes eq. 8.7

Ql0pm

eq. 8.8

Qlm1

eq. 7.5

Qlp100m

eq. 8.9

Ql0spm

eq. 8.10

Qlm2 eq. 7.8

Qling eq. 8.1

Qlcei eq. 8.6

Qgmin/2 

eq. 8.4

Qgmin eq. 8.3

Q+

gico eq. 8.5

Qgico

eq. 8.5

Hook 8.6

Figure 38. Example re-constructed xed-frequency regime map. Each regime

boundary lists the corresponding equation number. This map is constructed for

the worst case condition of f = 1:25 Hz where discrepancies for Qlbes, Qlcei, and

Qlm2 are most apparent. Improved predictions are demonstrated in Fig. 39. The

red dashed oval identies the region of sparse hydrodynamic mergers not captured

by the simple packing density approach of Qlm1 and Qlm2.

NASA/TM—2015-218720 51
volume required to reach the free surface. Thus, a dashed vertical line is drawn on

the Fig. 38 at

Qg = Qgmin=2  fVbmin=2: (35)

8.3 Inertial Capillary Overshoot Limit, Q



gico

From observations of Figs 4, 14, and 15, due to the inertial-capillary bubble migration, bubbles can at times be propelled approximately 25% further than their ideal

inscribed elevations. As a consequence, occasional partial single bubble separations

are possible both below and above Qgmin. The transition from 0% to 100% single

bubble separations is therefore blurred and a region

Qg = Q



gico  Qgmin(1  1=8) (36)

does well to bracket the majority of outcomes, where the subscript ico refers to

`inertial-capillary overshoot.' Two vertical lines identify Q



gico in Fig. 38.

8.4 Merge Limits

As brie
y summarized in x7.1, small single bubbles within the boundary layer vertex

region of the 
ow begin to merge below the liquid 
ow rate Qlm1 predicted by eq. 24

with m = 0:60. If the single bubble volume Vb

< Vbmin=2, the merged bubble volume

will remain below Vbmin and be unable to reach the free surface. However, if the

single bubble volume Vb  Vbmin=2, the merged bubble volume will be  Vbmin and

such bubbles are capable of coalescing with the free surface. Thus, eq. 24 is plotted

in Fig. 38 only up to the point it intersects with the vertical boundary associated

with Qgmin=2. This segment of eq. 24 is a vertex region merge limit where small

single bubble mergers produce 0% separating mergers.

For larger bubbles that inscribe further away from the vertex, it was shown in

Fig. 16 that the forced `bubble velocity prole' is eectively linear. As developed

in x7.1 for this situation, inscribed bubbles begin to merge for liquid 
ow rates

below Qlm2 from eq. 27 with n = 3=2. Partial separations of single and merged

bubbles within the Q



gico band are expected with 100% merger separations expected

for Qg

> Q

+

gico. Thus, eq. 27 is plotted in Fig. 38 beginning from the point it

intersects with the leftmost vertical boundary associated with Q



gico. This segment

of eq. 27 represents a linear boundary layer 
ow region merge limit below which

intermediate-to-large single bubble mergers are observed along with single bubble

separations yielding what we dene as partial and 100% separating mergers. As Qg

increases the percent of merging bubbles that coalesce with the free surface decreases

compared to that of single bubbles that coalesce.

8.5 Bubble and Free Surface Coalescence Enhanced Ingestion Limit,

Qlcei

The common, apparently linear, bubble coalescence enhanced ingestion boundary

(ref. line i., Fig. 6) begins for Qg > Q

gico and is found from the empirical maps to

obey

Qlcei  Qling  0:81Qg: (37)

NASA/TM—2015-218720 52
Subscript cei denotes `coalescence enhanced ingestion,' where bubbles coalescing

with the free surface lower the ingestion (choking) limit of the liquid base 
ow at

the channel exit. The case of f = 1:25 Hz yields an interesting outlier slope in eq. 37

of 1:02. A slope of  1 suggests that Ql + Qg = Qling for Qg

> Q



gico and that the

channel can never transport more combined volumetric 
ow rate than its maximum

single liquid phase 
ow rate Qling when Qg

> Q



gico. But the f = 1:25 Hz case is an

outlier, which if included in the average would yield a slope of 0:850:1. Ignoring it

establishes 0:81  0:07, which is presented in eq. 37. With knowledge of Qling from

eq. 32, Qlcei is computed from eq. 37 and plotted on Fig. 38 for Qg > Q

gico.

8.6 The `Hook' and the Bubble Enhanced Stability Regime

As described in x6, the Q

+

gico vertical boundary possesses a leftward hook as it

nears the Qling limit. This hook approximately intersects with Qling and Q



gico,

where it apparently triggers the end of the bubble enhanced stability regime (bes).

Interestingly, within this regime the maximum value for Ql  Qlbes > Qling is

correlated by

Qlbes = Qling + 0:81Qg; (38)

with an uncertainty in the slope of less than 2%. This value agrees with that of

Qlcei in eq. 37, but with opposite sign. Therefore the collapse of the bubble enhanced

stability region decreases the liquid 
ow rate by Ql  20:81Q



lico. Eq. 38 is plotted

and the hook is sketched in Fig. 38.

8.7 Analytical Map Comparisons and the Partial Merger Island

The merger regimes are complicated for Ql values below the testable limits of the

CCF hardware. The boundaries between 0% and partial mergers and partial and

100% mergers might be expected to emanate from the origin, the former intersecting

with the terminus of the vertex region merge limit Qlm1 and the latter intersecting

with Q

+

gico and free stream merge limit Qlm2. Connecting the terminus of Qlm1

and the intersection of Q



gico with Qlm2 closes o the partial merger regime completing the map for practical purposes. The relationships for these boundaries are

represented here by the following:

0% mergers to partial mergers (0pm)

Ql0pm 

Qlm1(Qgmin=2)

Qgmin=2

 Qg =



3H4

0:60 

8

3V

4

bmin !1=3

 Qg; (39)

Partial mergers to 100% mergers (p100m)

Qlp100m 

Qlm2

Q

+

lico

 Qg =

2

5

3

3

H3

2

Vbmin

 Qg; (40)

0% singles to partial mergers (0spm)

Ql0spm  Qlm2 +

Qlm2  Qlm1(Qgmin=2)

Q



gico  Qgmin=2





Qg  Q



gico

NASA/TM—2015-218720 53
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2

a. b. 

c. d. 

Ql 

Ql 

Qg Qg

Figure 39. Fixed-frequency regime maps with calculated boundaries drawn: a.

f = 0:5, b. 1.0, c, 1.5, and d. 2.0 Hz bubbles.

= Qlm2 +

8

2H3

3Vbmin

0

@

4

3





0:60 

H3

3Vbmin !1=3

1

A



Qg  Q



gico

; (41)

where Qlm2 and Q



gico are given by eqs. 27 and 36, respectively. Eqs. 39{41 are also

plotted on Fig. 38 approximately enclosing the partial merger regime.

9 Discussion

All of the heuristic regime limits discussed in x8 and culminating in Fig. 38 are

computed and plotted for comparisons to four of the xed frequency regime maps in

Fig. 39. The agreement is encouraging if not adequate. The best results are observed

for Qling, Qlbes, and Qlcei, but taken together they allow one to quickly estimate

expected performance for expected values of Qg and Ql. The worst result is the lack

of prediction of the partial merges observed clustered near the bottom of the Q



gico

regime as identied by the red dashed oval in Fig. 38 and data of Fig. 39. After

a closer look, these mergers occur for sparse bubbles where b

> 2Rb, well below

the packing limits of x7.1 and are enabled by strong hydrodynamic interactions

between bubble pairs. This additional class of sparse hydrodynamic mergers is

NASA/TM—2015-218720 54
clearly identied by the fact that they do not conform to simple packing arguments.

Observations point to bubble wake vertex interaction and entrainment complicated

by a growing base 
ow boundary layer. Further investigation of such mechanisms

is postponed for the time being.

From the x8 arguments, for similar systems ( Su+) one is able to establish

specic geometric dimensions, gas and liquid 
ow rates, and even margins of safety

to prevent or ensure passive bubble separation in the open wedge conduit. For

processes such as boiling, one must establish means to assess Vb distributions. But

even a light inspection of the present results will greatly speed such eorts. These

results compliment, but also signicantly extend, the quantitative results of [12].

10 Conclusions

These CCF space experiments aboard the ISS employ an unusually large buoyancyfree 2-phase 
ow of bubbles driven along an open wedge channel. The experimental

apparatus is congured to study the passive phase separating characteristics of the

geometry providing a large database for further fundamental and applied investigations of the inertial capillary phenomena. The problem is of particular relevance to


uids management aboard spacecraft, but is also relevant for fast 
ows of low viscosity liquids in terrestrial applications. The space experiments conducted record

thousands of events during 40 days of continuous commanding from ground stations and the  O(1TB) video archive is made publicly available on the internet for

broader dissemination.

Enough important characteristics of the 
ow are gathered from inspection of the

data combined with heuristic scaling arguments to provide a fair reconstruction of

the 
ow regimes arising in such systems. Based on the importance of the inscribed

bubble elevation, these include a priori design guides predicting minimum bubble

volumes required to separate, or merge and separate, within the length of channel

specied. The regime map is bounded above by a gas ingestion limit in a bubble

enhanced stability region at low gas 
ow rate and a bubble-free surface coalescence

enhanced ingestion region at moderate to high gas 
ow rates. Theoretical and

numerical analyses can draw from the data set to investigate a variety of interesting

aspects of the 
ow; such as the further division of the merger regimes (multi-mergers,

entrance mergers, harmonics, etc.), merger hydrodynamics, the often retarding or

enhancing eect of free surface waves on coalescence, the coupled hydrodynamics of

the inertial cross-
ow capillary migration with the inertial developing base 
ow, and

the changes in bubble behaviour above and below the growing boundary layer within

the 
ow|in particular, the long-time elevation of bubbles driven below or beyond

their inscribed elevations due to the developing shear 
ow in the asymmetric channel.

Such behaviours within fully-developed 
ows would be a practical rst step. Further

data reduction eorts are ongoing that include signicant drop tower experimental

results and numerical analysis. The CCF experiment hardware resides on the ISS

and experiments are resumed in August 2014 and will be reported separately.

NASA/TM—2015-218720 55

Appendix A

CCF EU2-02 Video Archive

The video archive for the 2nd (02) run of the Capillary Channel Flow (CCF)

wedge Experiment Unit (EU2) is publicly available at http://psi.nasa.gov requiring

only a request for access. It is referred to as CCF-EU2-02. The approximately 880

GB database contains the video results of over 5000 set points varying Vb, f, Ql,

and L. The les may be downloaded on a case by case basis or in total. The data is

largely provided and referenced from a single Microsoft Excel spreadsheet with all

critical experiment conditions listed and with each associated video hyper-linked.

Fig. A40 provides an image of the spreadsheet that conveys the general format. The

Excel le employs a variety of macros to sort the data and the most populated maps

of Figs. 21-27 (xed f), Figs. 29 and 30 (xed Vb), and Figs. 32 and 33 (xed L) are

provided where one may select any data point in the plots to pull up the associated

video. This `hyper-linking' considerably facilitates the understanding of the general

regime behaviour and is an enjoyable way to peruse the data.

For subsequent quantitative data reduction via image analysis, each video le

must be rectied to correct for camera skew. Instruction and batch les are available

in the archive to perform this operation. For indices of refraction NDquartz = 1:458

for the test channel and NDHF E = 1:29 for the test liquid, for the wedge of  = 7:9



one determines that refraction eects are < 0:3% and may eectively be ignored if

desired. Further instructions regarding the CCF-EU2-02 database are provided at

http://psi.nasa.gov.

Appendix B

Qling Scale Analysis

A scale form for the z-component zero-gravity steady momentum equation is

wwz  Pz; w; (B42)

where w is the imposed z-component of velocity, Pz is the free surface capillary

under-pressure gradient along the channel, and  is the 2-D Laplacian operator in

the x-y-plane. Subscript notation is employed for partial dierentiation. Following

the line of scaling arguments for corner 
ows taken by [26], [27], [23], and [12], in

the narrow wedge limit   1 with  = 0, and with negligible streamwise curvature

(H=L)

2  1, choosing scales w  hwi  Ql=h2, P  =h, and   1=h2Fi2

,

eq. B42 is re-written as



2CdQ2

l

h

52

hz  



h

2

hz; 

Ql

h

4Fi3

; (B43)

where Cd is an O(1) unknown inertial drag coecient and Fiis an unknown O(1)

inverse viscous resistance coecient|the larger Fi the lower the viscous resistance.

NASA/TM—2015-218720 57
Figure A40. Sample screen shot from the CCF-EU02 data/video archive. Listed

along with all of the most relevant test conditions is the video name identied by

the large red dashed oval. Clicking the small red dashed oval brings up the video

for the event. The most complete maps of Figs. 21{27 (xed f), Figs. 29{30 (xed

Vb), and Figs. 32{33 (xed L) are accessible from the tabs at the bottom of the le.

For example, the black dashed oval identies the location of the f = 0:75 Hz map,

Fig. 23. Each data point of the maps is hyper-linked to the video record which is

accessed by simply clicking the data point in question.

NASA/TM—2015-218720 58
The negative sign on the viscous dissipation term is informed by the elliptic nature

of the developing velocity eld. By scaling quantities h  H and hz  H=L,

eq. B43 is converted to an algebraic expression

2Cd

H4L

Q

2

l +



H4Fi3

Ql 



HL

= 0; (B44)

which when Cd = 3=2 and Fi = 1=3 is solved for Ql or L presented in eqs. 32 and 33,

respectively. For the fully developed vertex region of the 
ow Fi = 1=6 is expected,

but this region contributes little to the overall 
ow rate and away from the vertex

the wedge geometry may be modelled by nearly parallel walls where Fi  1=3 is a

better choice. The value Cd = 3=2 then brings about the agreement observed in

Fig. 37.

Appendix C

Entrance Length Issues

A scale for the entrance length of the acute wedge duct may be estimated by

balancing streamwise convection with cross 
ow viscous resistance such that



2

@w2

@z  w; (C45)

where  is the Laplacian operator. Substituting scales z  ze, w  Ql=H2tan ,

and the Laplacian scale for the free surface case   s = 1=x2

e

sin2  ( [27]) one

obtains

Ql

2zeH2 tan 





x

2

e

sin2 

; (C46)

from which eq. 19 is found taking   1. Subscript e denotes and entrance length

quantity. Eq. 18 is found by setting xe = H and taking   1. The enclosed

conduit values are found by employing the hydraulic radius approach to estimate

s = (1 + )

2=x2

e

sin2 . As a check on this approach note that for a circular

cylindrical tube of radius R = D=2, s = 2=R2 and from eq. C45 one nds Le 

DReD=16. Despite the qualitative nature of such scaling arguments the coecient

1/16 is quite close to the accepted typical value of 0.06, [28].

NASA/TM—2015-218720 59

References

1. V. Ajaev and G. Homsy, \Modeling shapes and dynamics of conned bubbles,"

Annu. Rev. Fluid. Mech., vol. 38, pp. 277{307, 2006.

2. D. Legendre and J. Magnaudet, \The lift force on a spherical bubble in a viscous

linear shear 
ow," J. Fluid Mech., vol. 368, pp. 81{126, 1998.

3. B. Zhao, J. Moore, and D. Beebe, \Surface-directed liquid 
ow inside microchannels," Science, vol. 291, p. 1023, 2001.

4. J. Melin, W. van der Wijngaart, and G. Stemme, \Behaviour and design considerations for continuous 
ow closed-open-closed liquid microchannels," Lab on

a Chip, 2005.

5. A. Skelleya and J. Voldmana, \An active bubble trap and debubbler for micro
uidic systems," Lab on a Chip, August 2008.

6. J. Xu, R. Vaillant, and D. Attinger, \Use of a porous membrane for gas bubble

removal in micro
uidic channels: physical mechanisms and design criteria,"

Micro
uid Nano
uid, March 2010.

7. T. John, Investigation of microbubble/droplet formation in cross-
ow and co-


ow micro devices. PhD thesis, Louisiana Tech University, 2011.

8. C. Litterst, S. Eccarius, C. Hebling, R. Zengerle, and P. Koltay, \Increasing

ldmfc eciency by passive co2 bubble removal and discontinuous operation," J.

Micromech Microeng, vol. 16, pp. 248{253, 2006.

9. R. Dangla, S. Kayi, and C. Baroud, \Droplet micro
uidics driven by gradients

of connement," PNAS, vol. 110, pp. 853{858, January 2013.

10. T. Metz, N. Paust, R. Zengerle, and P. Koltay, \Capillary driven movement

of gas bubbles in tapered structures," Micro
uidics and Nano
uidics, vol. 9,

pp. 341{355, April 2012.

11. E. Reyssat, \Drops and bubbles in wedges," J. Fluid Mechanics, 2014. (accepted

for publication).

12. R. Jenson, A. Wollman, M. Weislogel, L. Sharp, R. Green, P. Caneld, J. Klatte,

and M. Dreyer, \Passive phase separation of microgravity bubbly 
ows using

conduit geometry," Int. J. Multiphase Flow, 2014. (submitted).

13. D. Wollman, \Capillarity-driven droplet ejection," Master's thesis, Portland

State University, June 2012.

14. M. Weislogel, Y. Chen, S. Collicott, C. Bunnell, R. Green, and D. Bohman,

\More handheld 
uid interface experiments for the International Space Station

(CFE-2)," No. AIAA-2009-0615 in 47th AIAA Aerospace Sciences Meeting, (Orlando), pp. 1{10, 2009.

NASA/TM—2015-218720 61
15. W. Blackmore, M. Weislogel, Y. Chen, C. Bunnell, L. Kiewidt, and J. Klatte,

\The Capillary Flow Experiments (CFE-2) aboard the ISS: Status," No. AIAA2011-1196, (Orlando), pp. 1{10, 49th AIAA Aerospace Sciences Meeting, Jan.

2011.

16. M. Weislogel, J. Baker, and R. Jenson, \Quasi-steady capillarity driven 
ow,"

J. Fluid Mechanics, vol. 685, pp. 271{305, 2011.

17. L. Cheng, G. Ribatski, and J. Thome, \Two-phase 
ow patterns and 
owpattern maps: Fundamentals and applications," Appl. Mech. Rev., vol. 61, p. 28

pages, July 2008.

18. A. Barajas and R. Panton, \The eects of contact angle on two-phase 
ow in

capillary tubes," Int. J. of Multiphase Flow, vol. 19, no. 2, pp. 337{346, 1993.

19. R. Spivey, W. Sheredy, and G. Flores, \An overview of the Microgravity Science Glovebox (MSG) facility, and the gravity-dependent phenomena research

performed in the MSG on the International Space Station (ISS)," No. AIAA2008-0812., 46th AIAA Aerospace Sciences Meeting, 2008.

20. U. Rosendahl, A. Ohlho, and M. Dreyer, \Choked 
ows in open capillary channels: theory, experiment and computations," J. Fluid Mech., vol. 518, pp. 187{

214, 2004.

21. P. Caneld, P. Bronowicki, Y. Chen, L. Kiewidt, A. Grah, J. Klatte, R. Jenson,

W. Blackmore, M. Weislogel, and M. Dreyer, \The capillary channel 
ow experiments on the international space station: Experiment setup and rst results,"

Experiments in Fluids, vol. 54, pp. 1519{1532, 2013.

22. M. Weislogel, \Survey of present and future challenges in low-g 
uids transport

processes," NASA Contract Report C-74461-N, 2001.

23. J. Klatte, Capillary 
ow and collapse in wedge-shaped channels. PhD thesis,

Universitaet Bremen, 2011.

24. P. Caneld, \Stabilization of free surface 
ow due to bubbly 
ows," 2014. in

preparation.

25. M. Conrath, P. Caneld, P. Bronowicki, M. Dreyer, M. Weislogel, and A. Grah,

\Capillary channel 
ow experiments aboard the international space station,"

Physical Review E, vol. 88, no. 063009, p. 8 pages, 2013. Rapid Communication.

26. M. Weislogel and S. Lichter, \Capillary 
ow in an interior corner," J. Fluid

Mech., vol. 373, pp. 349 { 378, 1998.

27. M. Weislogel, Y. Chen, and D. Bolledulla, \A better nondimensionalization

scheme for slender laminar 
ows: The laplacian operator scaling method," Phys.

Fluids, vol. 20, no. 2, pp. 163 { 170, 2008.

28. B. R. Munson, D. F. Young, and T. H. Okiishi, Fundamentals of Fluid Mechanics. New York: Wiley, fourth ed., 2002.

NASA/TM—2015-218720 62