Mapping Bubble Formation and Coalescence in a Tubular Cross-Flow Membrane Foaming System

membranes

Article
Mapping Bubble Formation and Coalescence in a Tubular
Cross-Flow Membrane Foaming System
Boxin Deng , Tessa Neef, Karin Schroën and Jolet de Ruiter *

 Food Process Engineering Group, Department of Agrotechnology & Food Science, Wageningen University,
 Bornse Weilanden 9, 6708 WG Wageningen, The Netherlands; boxin.deng@wur.nl (B.D.); tessa.neef@wur.nl (T.N.);
 karin.schroen@wur.nl (K.S.)
 * Correspondence: jolet.deruiter@wur.nl

 Abstract: Membrane foaming is a promising alternative to conventional foaming methods to produce
 uniform bubbles. In this study, we provide a fundamental study of a cross-flow membrane foaming
 (CFMF) system to understand and control bubble formation for various process conditions and fluid
 properties. Observations with high spatial and temporal resolution allowed us to study bubble
 formation and bubble coalescence processes simultaneously. Bubble formation time and the snap-off
 bubble size (D0 ) were primarily controlled by the continuous phase flow rate (Qc ); they decreased
 as Qc increased, from 1.64 to 0.13 ms and from 125 to 49 µm. Coalescence resulted in an increase
 in bubble size (Dcoal > D0 ), which can be strongly reduced by increasing either continuous phase
 viscosity or protein concentration—factors that only slightly influence D0 . Particularly, in a 2.5 wt %
 whey protein system, coalescence could be suppressed with a coefficient of variation below 20%. The
 stabilizing effect is ascribed to the convective transport of proteins and the intersection of timescales
 



 
 (i.e., µs to ms) of bubble formation and protein adsorption. Our study provides insights into the
Citation: Deng, B.; Neef, T.; Schroën, membrane foaming process at relevant (micro-) length and time scales and paves the way for its
K.; de Ruiter, J. Mapping Bubble further development and application.
Formation and Coalescence in a
Tubular Cross-Flow Membrane Keywords: cross-flow membrane foaming (CFMF); whey protein; (sub)millisecond; bubble forma-
Foaming System. Membranes 2021, 11, tion; bubble coalescence; convective transport
710. https://doi.org/10.3390/
membranes11090710

Academic Editors: George Chen, 1. Introduction
Filicia Wicaksana and Zhenzhou Zhu
 Foams are widely used in our daily life such as in pharmaceuticals, cosmetics and
 foods. Each application has specific demands for stability and functionality of the foams,
Received: 3 August 2021
Accepted: 12 September 2021
 and thus targets different bubble properties (i.e., bubble size and bubble size distribution),
Published: 15 September 2021
 which are strongly influenced by the foaming techniques. Foams are conventionally
 produced and studied in high speed stirrer/mixer [1] and rotor-stator systems [2] that
Publisher’s Note: MDPI stays neutral
 operate based on continuous fragmentation of larger bubbles into small bubbles. These
with regard to jurisdictional claims in
 traditional techniques are relatively easy to scale-up, but are also associated with limitations,
published maps and institutional affil- including high energy input and limited control over the bubble properties. High shear and
iations. high surfactant concentration are needed to obtain a foam with relatively monodisperse
 and small bubbles. Alternatively, other methods like packed-bed system [3], microfluidic
 devices [4], and membrane systems [5–8] can directly generate individual bubbles with
 desired size and improved monodispersity. The packed bed and membrane systems are
Copyright: © 2021 by the authors.
 capable of achieving high throughput, while that is not the case yet for microfluidic devices
Licensee MDPI, Basel, Switzerland.
 that are still in need of up-scaling.
This article is an open access article
 In a cross-flow membrane foaming (CFMF) system, the dispersed phase is injected
distributed under the terms and into the continuous phase passing through a porous membrane matrix, and bubbles are
conditions of the Creative Commons detached at the membrane surface by the cross-flowing continuous phase. Compared
Attribution (CC BY) license (https:// to membrane emulsification, which has been substantially studied and reviewed [9–13],
creativecommons.org/licenses/by/ only few studies were conducted on membrane foaming and in most of these cases a
4.0/). high surfactant concentration (e.g., 10 wt % whey protein) was used and any short-term

Membranes 2021, 11, 710. https://doi.org/10.3390/membranes11090710 https://www.mdpi.com/journal/membranes

few studies were conducted on membrane foaming and in most of these cases a high sur-
 factant concentration (e.g., 10 wt % whey protein) was used and any short-term destabili-
Membranes 2021, 11, 710 zation process (in particular, coalescence) was thus not taken into account. The 2 of bubble
 12
 properties and resulting foam stability were evaluated at the outlet of the foaming systems
 and were then explained in terms of the applied process parameters and/or the membrane
 destabilization process (in particular, coalescence) was thus not taken into account. The
 properties such as pore size [5,8]. However, these final bubble properties are an equilib-
 bubble properties and resulting foam stability were evaluated at the outlet of the foaming
 rium state following the formation and re-coalescence of bubbles flowing in the continu-
 systems and were then explained in terms of the applied process parameters and/or
 ousmembrane
 the phase, with the latter
 properties process
 such as porecausing an increased
 size [5,8]. bubble
 However, these sizebubble
 final and higher polydis-
 properties
 persity [14]. To make a monodisperse foam, choosing a membrane
 are an equilibrium state following the formation and re-coalescence of bubbles flowing with uniform pores is
 notthe
 in sufficient,
 continuousas wasphase, foundwithwith
 the alatter
 micro-engineered
 process causingmembrane
 an increasedfor emulsification
 bubble size and [15]. It
 is thuspolydispersity
 higher crucial to first[14]. understand
 To makethe bubble production
 a monodisperse foam, process
 choosingwithin very short
 a membrane withtime-
 scales, and
 uniform thereafter
 pores manipulate
 is not sufficient, as other factorswith
 was found accordingly, such as themembrane
 a micro-engineered surfactant concen-
 for
 tration to stabilize
 emulsification [15]. It theis freshly-generated
 thus crucial to firstbubbles.
 understandTo the
 the best
 bubbleof production
 our knowledge,
 process such a
 within very short
 fundamental studytimescales,
 of bubble andformation
 thereafterin manipulate other factors
 a cross-flowing membraneaccordingly,
 foamingsuch as
 system is
 the
 stillsurfactant
 missing. concentration to stabilize the freshly-generated bubbles. To the best of our
 knowledge, such
 The goal of athis
 fundamental
 study is tostudy of bubble
 investigate theformation
 cross-flow inmembrane
 a cross-flowing membrane
 foaming process by
 foaming system is still missing.
 in-line high-speed visualization of bubble formation and mapping of potential bubble co-
 The goal
 alescence. Wheyof this studyisolate,
 protein is to investigate the cross-flow
 which is often membranefood
 used in commercial foaming process
 foams, is used as
 by in-line high-speed visualization of bubble formation and mapping of potential bubble
 the surfactant, and we study the bubble properties such as bubble size (distribution) and
 coalescence. Whey protein isolate, which is often used in commercial food foams, is used
 formation frequency under the effects of transmembrane pressure, continuous phase flow
 as the surfactant, and we study the bubble properties such as bubble size (distribution)
 rate and viscosity, as well as protein concentration. To indicate the occurrence of coales-
 and formation frequency under the effects of transmembrane pressure, continuous phase
 cencerate
 flow (if and
 any),viscosity,
 we observe theas
 as well bubbles
 proteinatconcentration.
 two distinct positions
 To indicateinthe theoccurrence
 foaming system:
 of
 first, bubbles that are initially formed at the membrane surface,
 coalescence (if any), we observe the bubbles at two distinct positions in the foaming and second, bubbles
 system:flow-
 ing through
 first, an observation
 bubbles that chamber
 are initially formed at amembrane
 at the short distance downstream
 surface, and second,from theflowing
 bubbles membrane.
 through an observation chamber at a short distance downstream from the membrane.
 2. Materials and Methods
 2. Materials and Methods
 2.1. Materials
 2.1. Materials
 In a cross-flow membrane foaming (CFMF) system, air bubble formation was studied
 In a cross-flow membrane foaming (CFMF) system, air bubble formation was studied
 in aqueous (Milli-Q, Merck Millipore) solutions of whey protein isolate (BiPro, 97.5% pu-
 in aqueous (Milli-Q, Merck Millipore) solutions of whey protein isolate (BiPro, 97.5% purity,
 rity, Agropur, Granby, Canada) at various concentrations and viscosities. Viscosity was
 Agropur, Granby, Canada) at various concentrations and viscosities. Viscosity was adapted
 adapted
 using using(99.5%
 glycerol glycerol (99.5%
 purity, VMRpurity, VMR International,
 International, Leuven, Belgium).
 Leuven, Belgium). The viscosity
 The viscosity was
 was measured at
 ◦ 20 °C in triplicate using an Anton Paar Rheometer
 measured at 20 C in triplicate using an Anton Paar Rheometer (MCR301, Anton (MCR301, Anton
 Paar Paar
 GmbH,Graz,
 GmbH, Graz,Austria)
 Austria)which
 which is is equipped
 equipped with
 with a Couette
 a Couette cell cell (C-DG26).
 (C-DG26).
 AAtubular-type
 tubular-typepolypropylene
 polypropylene membrane
 membrane withwith a macroscopic
 a macroscopic water
 water contact
 contact angleangle
 of of
 120◦ °was
 120 wasused
 used ininthethe CFMF
 CFMF system.
 system. The
 The membrane
 membrane hashas
 outerouter diameter
 diameter ofmm
 of 2.7 2.7 and
 mm and
 lengthof
 length ofapproximately
 approximately2020mm. mm.The The outer
 outer surface
 surface of the
 of the membrane
 membrane shows shows a partially-
 a partially-
 interconnected pore network, with pore sizes ranging from a few to
 interconnected pore network, with pore sizes ranging from a few to tens of micrometerstens of microme-
 ters (Figure
 (Figure 1). 1).

 Figure1.1.SEM
 Figure SEMphotograph
 photograph ofof
 thethe outer
 outer membrane
 membrane surface.
 surface. A snapshot
 A snapshot formacroscopic
 for the the macroscopic contact
 contact
 angle measurement is shown on top of the SEM image. The measurement is performed on
 angle measurement is shown on top of the SEM image. The measurement is performed on a piece of a piece
 of unused membrane and the measured contact angle is about ◦ 120 °.
 unused membrane and the measured contact angle is about 120 .

the set-up is the membrane module (that holds a membrane) where foaming takes place.
 The membrane module has two inlets for the air and continuous phase, a tubular chamber
 of 3.8 mm inner diameter in which foaming takes place, and one joint outlet. The mem-
 brane was inserted in the middle of the module, and a pressure controller fed air and
Membranes 2021, 11, 710 continuous phase (via a feed tank) to the module. Between the inner wall of the module 3 of 12
 and the outer surface of the membrane, there is a gap of 0.55 mm. Bubble formation takes
 place by the action of the cross-flowing continuous phase that shears off the bubbles from
 2.2.
 the Set-up
 membrane surface, and next transports them towards the exit.
 The set-up
 Bubble for the can
 formation CFMF be experiment
 observed along is schematically
 the membrane shown in Figure
 (see Figure 2). 2.
 WeThe corea
 chose
 of the set-up is the membrane module (that holds a membrane) where
 position near the continuous phase inlet albeit on the opposite side, marked by a rectanglefoaming takes
 place. The 2.
 in Figure membrane module
 Additionally, has two
 a quartz inlets
 flow cellfor the air
 (Type 55, and continuous
 Fireflysci, phase,
 Ottawa, a tubular
 Canada) was
 chamber
 connected ofto
 3.8observe
 mm inner diameter
 bubbles at 10 in
 or which
 100 cmfoaming takes of
 downstream place, and one joint
 the membrane outlet.while
 module, The
 membrane
 keeping the was inserted
 total tubinginlength
 the middle
 (andofthetheflow
 module, and a pressure
 resistance) constant.controller
 The flowfed airhas
 cell anda
 continuous phase
 height of about 0.4(via
 mm,a which
 feed tank)
 allowsto the module.
 us to observeBetween
 undeformedthe inner wall
 bubbles inof the module
 a more-or-less
 and theflow
 single outerplane.
 surfaceToofinvestigate
 the membrane, there isproperties
 the bubble a gap of 0.55
 overmm. Bubble
 time, formation
 we analyzed takes
 bubbles
 place
 formed upstream across from the continuous phase inlet and compared them withfrom
 by the action of the cross-flowing continuous phase that shears off the bubbles bub-
 the
 blesmembrane surface, andthrough
 flowing downstream next transports
 the flowthem towards
 cell (see insetsthe exit. 2).
 of Figure

 Figure2.
 Figure 2. Schematic
 Schematic overview
 overview of
 of the
 the experimental
 experimentalset-up.
 set-up.The
 Theimages
 imagesshow
 showbubble
 bubbleformation
 formationat
 atthe
 the
 membrane surface across from the continuous phase inlet and bubbles in the flow cell. The sche-
 membrane surface across from the continuous phase inlet and bubbles in the flow cell. The schematic
 matic is not drawn to scale.
 is not drawn to scale.

 2.3. Membrane Foaming can be observed along the membrane (see Figure 2). We chose a
 Bubble formation
 positionThenear
 flows theofcontinuous
 the air andphasecontinuous phases
 inlet albeit were
 on the both driven
 opposite by pressure
 side, marked and con-
 by a rectangle
 trolled
 in Figure with
 2. the digital pressure
 Additionally, a quartzcontroller
 flow cell that is operated
 (Type with Smart
 55, Fireflysci, Ottawa,Interface
 Canada)Software
 was
 (Elveflow®to
 connected , Paris,
 observe France).
 bubbles First,
 at 10theor (dispersed)
 100 cm downstream air phaseofwas the injected
 membrane intomodule,
 the systemwhileat
 pressurethe
 keeping total
 . Thetubing
 pressure drop
 length over
 (and thethe air resistance)
 flow phase occurs mainlyThe
 constant. across
 flowthe relatively
 cell nar-
 has a height
 row
 of pores
 about 0.4of mm,thewhich
 membrane,allowssuch
 us tothat the air
 observe pressure inside
 undeformed bubbles theinmembrane
 a more-or-less is also .
 single
 flow plane. To investigate
 The continuous phase wasthe bubble
 then fed from properties
 the feed over
 tanktime, we analyzed
 at pressure , which
 bubbles formed
 drops more
 upstream
 graduallyacross
 over the fromfullthe continuous
 flow path, from at
 phase inlet
 the and
 flowcompared
 controllerthemto zerowith bubblespressure)
 (absolute flowing
 downstream
 at the outlet. through the flow
 We estimated thecell
 flow (see insets of of
 resistance Figure
 each 2).
 system component and found that
 at the continuous phase inlet of the membrane module, the pressure has dropped by
 2.3. Membrane Foaming
 approximately 55%; and the effective continuous phase pressure is thus defined as ,
 that The flows
 equals = air
 , of the × (1
 and− continuous
 0.55). Fromphases this, the were both driven by
 transmembrane pressure
 pressure andiscon-
 cal-
 trolled
 culatedwithby the digital
 = −pressure
 , . The controller
 pressure that is operated with Smart
 is the effective Interface
 pressure dropSoftware
 over the
 (Elveflow ® , Paris, France). First, the (dispersed) air phase was injected into the system
 pores and drives the bubble formation.
 at pressure Pd . The
 The bubble pressurewas
 formation drop over the airunder
 investigated phasethe occurs mainly
 effects acrossconditions
 of process the relatively
 and
 narrow
 fluid properties. Firstly, the bubble formation was studied as a function of is also
 pores of the membrane, such that the air pressure inside the membrane Pd .
 in the
 The continuous phase was then fed from the feed
 range of 100–400 mbar. The corresponding air flow rate ( ) was estimatedtank at pressure Pc , which drops more
 from the vol-
 gradually over the full
 umetric production flow
 rate of foam from Pc atatthe
 path, collected theflow controller
 outlet, with the to liquid
 zero (absolute
 entrapped pressure)
 within
 at the outlet. We estimated the flow resistance of each system
 the foam being subtracted. A constant continuous phase flow rate ( ) was applied to component and found
 that at the continuous phase inlet of the membrane module, the pressure Pc has dropped
 by approximately 55%; and the effective continuous phase pressure is thus defined as
 Pc,e f f that equals Pc,e f f = Pc × (1 − 0.55). From this, the transmembrane pressure Ptrm is
 calculated by Ptrm = Pd − Pc,e f f . The pressure Ptrm is the effective pressure drop over the
 pores and drives the bubble formation.
 The bubble formation was investigated under the effects of process conditions and
 fluid properties. Firstly, the bubble formation was studied as a function of Ptrm in the
 range of 100–400 mbar. The corresponding air flow rate ( Qd ) was estimated from the
 volumetric production rate of foam collected at the outlet, with the liquid entrapped within

Membranes 2021, 11, 710 4 of 12

 the foam being subtracted. A constant continuous phase flow rate (Qc ) was applied to
 eliminate potential differences in convective transport of proteins towards the air/water
 interface. Secondly, for a given Ptrm , the bubble formation was evaluated under the effect
 of Qc —the volumetric flow rate measured by weighing the outflow of the system. It varies
 between 6.4 × 10−6 m3 /s and 2.1 × 10−5 m3 /s, which corresponds to a cross-flow velocity
 of 1.6–5.4 m/s in the membrane module. Our window of operation is determined by pore
 activation and possibility of visualization. Operation at low Ptrm or high Qc is limited by
 low activation of the pores. Operation at high Ptrm or low Qc is in principle possible and
 leads to high bubble productivity, but the bubble fraction is then too high for visualization.
 Lastly, to study the effect of continuous phase viscosity (η) and protein concentration (c),
 process conditions were fixed to Ptrm = 200 mbar and Qc = 1.5 × 10−5 m3 /s, using either
 constant c = 1 wt % with η varying as 1.3, 1.5 and 2 mPa·s, or constant η = 1.3 mPa·s with
 c varying as 0.5, 1.0 and 2.5 wt %.
 For practical reasons, protein solutions were re-used (for up to 10 times) during
 the experiments. Since the reduction of protein concentration over time was under 20%
 (Figure S1), this effect was ignored. The module and tubing were cleaned with MilliQ-
 water between different experimental conditions, and the membrane was replaced once
 the pressure applied on the air phase was switched off and on again (every day). All the
 experiments were performed at ambient temperature.

 2.4. Image Analysis
 A high-speed camera (FASTCAM SA-Z, Photron Limited, Tokyo, Japan) is attached
 to the inverted microscope (Axiovert 200 MAT, Carl Zeiss B.V., Breda, The Netherlands)
 and used to observe and visualize bubbles in the CFMF system. Videos were recorded at
 20,000 frames per second and with a resolution of 0.314 pixel/µm. For each experimental
 condition, two videos were recorded at two distinct positions in the CFMF system: captur-
 ing either bubble formation at the membrane surface across from the continuous phase
 inlet (Figure 2); or bubbles flowing through the flow cell during their transport to the outlet.
 A custom-written code in MATLAB R2018b was used to calculate the diameters of
 bubbles that are directly formed at the pore openings (D0 , averaged for up to 100 bubbles)
 and that are the result of coalescence (Dcoal , averaged for up to 100 bubbles), respectively.
 Histogram plots of the bubble diameters were made to visualize the number-averaged
 bubble size distribution. Moreover, the bubble size distribution was also characterized by
 the coefficient of variation (CV), defined as CV = δ/D × 100% (in which, δ the standard
 deviation and D the number-averaged bubble diameter). Average bubble formation fre-
 quencies were estimated by f 0 = Qd /V0 and f coal = Qd /Vcoal , where V0 and Vcoal are the
 volumes corresponding to D0 and Dcoal , respectively. Furthermore, two timescales were
 estimated during a bubble formation cycle using the videos. The interval time is the lag
 time between two bubble growing processes at the same pore opening, and the bubble
 growing time is the time of actual bubble growth at a pore opening. These were measured
 for each experimental condition, and the values were averaged for up to 30 bubbles.

 3. Results and Discussions
 3.1. General Bubble Behavior in CFMF
 We study bubble formation as function of the transmembrane pressure (Ptrm ). Bub-
 ble formation only occurs if the transmembrane pressure exceeds the activation pressure.
 This activation pressure equals the capillary pressure of the meniscus in the narrow pore,
 4γ cos(θ )
 which is defined as Pcap = dp , where γ is the surface tension between the air and
 the continuous phase, d p is the diameter of the pore (opening), and θ is the contact angle
 between the continuous phase and the membrane surface [12]. At Ptrm as low as 50 mbar, a
 few pores form bubbles at an extremely low formation frequency (too low for quantitative
 analysis of D0 and corresponding f 0 ). The activation pressure for bubble formation is thus
 assumed to be approximately 50 mbar. For contact angles >90◦ , the air phase would flow
 out of the pores automatically, and the growing bubble would possibly spread out at the

Membranes 2021, 11, x FOR PEER REVIEW 5 of 12

Membranes 2021, 11, 710 5 of 12
 flow out of the pores automatically, and the growing bubble would possibly spread out
 at the (hydrophobic) membrane surface, which would lead to extensive coalescence at the
 membrane surface
 (hydrophobic) [11,16],surface,
 membrane which which
 is not observed
 would lead in to
 theextensive
 present coalescence
 study. Thus,atthe themacro-
 mem-
 scopic contact angle (120 ° as measured for an unused membrane)
 brane surface [11,16], which is not observed in the present study. Thus, the macroscopic is not the actual contact
 angle in
 contact the (120
 angle ◦ as measured
 system. Possible explanations
 for an unusedare differences
 membrane) between
 is not micro-
 the actual andangle
 contact macro-in
 scopic contact angle, which is known to occur on porous surfaces
 the system. Possible explanations are differences between micro- and macroscopic contact such as membranes, but
 more probably
 angle, proteintoadsorption
 which is known renders
 occur on porous the membrane
 surfaces surface more
 such as membranes, hydrophilic
 but more probably(< 90
 °).
 protein adsorption renders the membrane surface more hydrophilic (

Membranes 2021, 11, 710 6 of 12

 increased to up to 300 mbar, showing a similar trend as that was reported in [8]; and it
 increases relatively more at Ptrm = 400 mbar. In contrast to the overall slight variation in
 D0 , the coalesced bubble diameter Dcoal significantly increases with Ptrm . The difference
 indicates the co-existence of bubble formation and bubble coalescence in the 1 wt % whey
 protein system. Dcoal increases much more strongly than the rather constant D0 for increas-
 ing Ptrm (Figure 3B), which is indicative of an increasing extent of bubble coalescence. Last
 but not least, with increasing Ptrm the frequency of coalesced bubbles was increasingly
 lower than the corresponding f 0 (Figure 3C). For a given continuous phase flow rate,
 bubble formation frequency is determined by both the Ptrm and the bubble size, which
 have opposite effects [17]. As shown in Figure 3C, f 0 first increases and then decreases
 with increasing Ptrm . The decrease may be explained by the increased size of the bubbles,
 possibly in combination with more extensive coalescence (at high Ptrm ), and this may lead
 to the much lower overall f coal .
 To confirm whether coalescence mainly occurs in the membrane module or continues
 downstream, we measured Dcoal at two distinct positions along the flow path, namely at a
 distance of 10 cm and further of 100 cm downstream the membrane module (Figure S2).
 The obtained Dcoal values are similar, which proves that bubbles coalesce mostly in the
 membrane module during or shortly after their formation, reaching a stable situation
 within a short term. This also allows us to limit ourselves to a flow cell position of 10 cm
 downstream for all the remaining experiments.

 3.2. Bubble Formation at the Membrane Surface
 We first introduce the forces which dictate bubble formation. As was reported for
 cross-flow membrane emulsification systems, the bubble is subjected to four forces while
 growing at the membrane surface, which are the shear force imposed by the continuous
 phase flow rate and viscosity, the buoyancy force, the inertia force and the interfacial
 tension force [10,17]. For bubble formation in the present system, the interfacial tension
 γR2
 force is the holding force, and scales as either R0p or γR p , depending on the applicability of
 a force or torque balance (R p is the radius of the pore and R0 is the in-line radius of bubble
 which grows towards D0 ) [18]. The shear force, which scales as vc ηR0 , is considered to be
 the only driving force among the rest of the forces since the other two forces are at least
 two orders of magnitude smaller. The bubble stays attached to the pore opening and snaps
 off when, for a certain bubble size, the shear force exceeds the surface tension force [19,20].
 The force or torque balance leads to D0 ∼ Ca−n , with Ca = γ c the capillary number of
 ηv

 the flow and power-law exponent n whose value is between 0.5 and 1.
 In our experiments, the continuous phase flow rate (Qc ), protein concentration (c) and
 continuous phase viscosity (η) are varied, and bubble formation at the membrane surface
 is studied. In accordance with the definition of forces, our experimental parameters can
 influence this force or torque balance: by increasing either the flow rate or the viscosity of
 the continuous phase, the shear force increases; by increasing the protein concentration,
 faster protein adsorption can lower the (dynamic) surface tension faster and thus rapidly
 reduce the holding force (that is if protein adsorption can appreciably take place within the
 very short timescales for bubble formation). In both cases, bubbles can be detached earlier
 from the pore openings [21,22].
 The bubble size is firstly investigated as function of continuous phase flow rate. Please
 note that bubbles growing at the membrane surface tend to be deformed by the flow of
 the continuous phase, particularly when a high continuous phase flow rate (Qc ) is applied.
 D0 significantly decreases as Qc increases (see Figure 4A), which is in line with what was
 reported for other membrane foaming systems [8,19] or membrane emulsification [23,24].
 At lower Qc , the bubble stays attached to the pore for a longer time, thus obtaining a
 larger size, while at higher Qc , D0 reduces to about 50 µm for the highest Qc ’s measured.
 The results agree with the proposed scaling with Ca with a fitted power-law exponent
 n = 0.8 ± 0.1.

Membranes 2021, 11, 710 7 of 12

 Figure 4. Properties of bubbles (with D0 ) formed at the membrane surface. (A) Shear effect investi-
 gated for Ptrm equal to 100 (O), 200 (O) and 300 (O) mbar. Results at Ptrm = 400 mbar are not included,
 because bubbles that are initially formed at the pores cannot be measured due to bubble crowdedness.
 (B) Protein concentration effect. (C) Continuous phase viscosity effect. Corresponding D0 values
 of figures (A–C) shown as size distribution obtained at Ptrm = 200 mbar are given in (D–F). Darker
 colors indicate the increase in the evaluated parameter.

 D0 almost shows no dependency on transmembrane pressure for Ptrm = 100–300 mbar
 for any given Qc (Figure 4A). At Ptrm = 400 mbar, the small increase in D0 represents the
 volume of air added during the final detachment process of the bubble due to a higher
 air flow rate [24]. The strong dependency of D0 on Qc indicates that the high shear flow
 dominates overall behavior; the effects of transmembrane pressure and fluid properties on
 bubble formation at the membrane surface can be neglected.
 Additionally, only a minor decrease can be observed in D0 as function of protein
 concentration and continuous phase viscosity (see Figure 4B,C), which are both evaluated
 at Ptrm = 200 mbar and Qc = 1.5 × 10−5 m3 /s (Figure 4A). By raising the continuous phase
 viscosity, the average bubble size D0 is reduced to about 50 µm due to effects on increasing
 the shear force and potentially also the (dynamic) surface tension force. The decreasing
 trend with viscosity collapses onto the same Ca−0.8 behavior (assuming a constant surface
 tension, Figure S3). For these experiments taken at larger Ca, the rather constant D0 can
 be ascribed to the fast bubble detachment process induced by shear force exerted by the
 continuous phase [24]. When the protein concentration increases to 2.5 wt %, the D0
 decreases also just slightly to approximately 51 µm. The decrease is ascribed to faster
 protein adsorption which further lowers the (dynamic) surface tension and advances the
 force balance for bubble snap-off. Moreover, because the surface tension only can be
 decreased to a limited extent, bounded by the equilibrium surface tension of the air/water
 interface stabilized by whey proteins, the influence of protein adsorption on bubble size
 is moderate. Hence, bubble formation at the membrane surface falls into a regime where
 bubble snap-off is dominated by shear force, and under the conditions studied here, mainly
 controlled by the continuous phase flow rate [10].
 1
 The bubble size distribution varies with bubble size. The histogram plot indicates that
 bubbles with higher monodispersity are formed as Qc increases, with the main peak in the
 plot shifting from right to left (Figure 4D). In addition to the effects of Qc , the bubble size
 distribution can further be narrowed by increasing the protein concentration and/or the
 continuous phase viscosity (Figure 4E,F). Bubbles with diameters in the range of 40–60 µm

Membranes 2021, 11, 710 8 of 12

 account for more than 90% of the size distributions (Figure 4E,F). The corresponding
 coefficient of variation (CV) is below 15% when the highest protein concentration and/or
 viscosity is used (Figure 4E,F). However, the average D0 can be decreased only to a
 limited extent (to approximately 50 µm), with the smallest bubbles having a diameter
 of approximately 40 µm (corresponding to the left side of the histogram plot), which is
 independent of the experimental conditions; and the bubble size distribution cannot be
 infinitely narrowed. This can be ascribed to the characteristics of protein adsorption and the
 properties of the used membrane—the pore size and the pore size distribution. Specifically,
 when bubble formation is much faster than protein adsorption, the surface tension keeps
 constant as that of a pure interface, limited by the efficiency of protein adsorption; and
 moreover, the smallest pores that have a lower holding force, produce smaller bubbles
 thus widening the bubble size distribution [17], and determine the lower boundary of
 the bubble size. In addition, interactions between bubbles can influence the bubble size
 distribution by detaching the bubbles early on [25].

 3.3. Bubble Coalescence
 To thoroughly understand the CFMF system, the bubble coalescence is also evaluated
 as a function of the same experimental parameters. Firstly, within the resolution of our
 experimental results, coalescence of bubbles growing at adjacent active pores is rarely
 visually observed. Instead, coalescence often happens upon collision amongst flowing
 bubbles or a collision between a flowing bubble and a forming bubble. To demonstrate
 the extent of bubble coalescence, we report here the bubble size measured in the flow cell
 (Dcoal ). In addition, we compare the volumes (V0 and Vcoal ) of single and coalesced bubbles
 to estimate the number N of coalescence events a bubble has undergone: N = Vcoal /V0 − 1.
 Because V0 may show some variation across different positions at the membrane surface
 (Figures S4-1 and S4-2), due to the pressure drop in the continuous phase and the presence
 of bubbles (which further influence the local flow rate and viscosity of the continuous
 phase), the absolute values of the estimates for N are shown in Figure S5, yet general
 conclusions can be drawn and will be discussed below.
 For a given transmembrane pressure, Dcoal decreases as Qc increases (Figure 5A) and is
 always larger than its corresponding D0 . Yet, N increases as a function of Qc , which possibly
 resulted from faster bubble formation (i.e., less protein adsorption) (Figure S5). At any fixed
 Qc , Dcoal as well as N increase with Ptrm due to increasing bubble crowdedness (Figure S5),
 and higher propensity to coalescence. Furthermore, as function of the protein concentration,
 Dcoal decreases strongly, much more strongly than D0 (see Figure 5B). With the highest
 protein concentration tested (2.5 wt %), Dcoal is very similar to D0 , and the coalescence is
 effectively suppressed with N ≈ 0 (Figures S5 and S6). When a sufficiently high protein
 concentration is used, more proteins are able to adsorb to the bubble interface before
 bubble–bubble interactions take place, thus preventing the bubble coalescence [26,27].
 Lastly, Dcoal also decreases and converges to D0 when a higher continuous phase viscosity
 is used (see Figure 5C), which can be explained by the slower movement of bubbles [5]
 and the slower drainage process of the liquid thin film (between bubbles) [28], delaying
 (or diminishing) bubble coalescence. To summarize, the continuous phase properties
 (namely, protein concentration and phase viscosity) show vastly different influence on
 either bubble formation or coalescence: (1) they can control the size at bubble formation
 (D0 ) only to a very limited extent, with Qc the dominating factor; (2) they significantly
 suppress coalescence and thus the formation of larger bubbles (Dcoal ).
 The coefficient of variation (CV) is used to characterize the bubble size distribution
 (see Figure 5D–F). The CV is always higher for the coalesced bubbles than for the initially
 formed bubbles. The CV can only be reduced to a limited extent when we increase the
 continuous phase flow rate, and we obtain a minimum CV of 20% and 34% for D0 and
 Dcoal , respectively. The CV does decrease strongly down to 14% and 17%, respectively,
 when measures are taken to enhance stabilization of the freshly-created interfaces, namely
 by raising the protein concentration, or increasing the continuous phase viscosity. In both

Membranes 2021, 11, 710 9 of 12

 cases a smaller average bubble size is accompanied by a smaller CV as the bubble size
 distribution is narrowed on the upper end. These results indicate that to tightly control
 the properties of bubbles in the end product, irrespective of membrane properties, it is
 crucial to manipulate the operation conditions and the fluid properties to control bubble
 formation and, especially, to prevent bubble coalescence by sufficiently
 Membranes 2021, 11, x fast
 FOR stabilization
 PEER REVIEW of
Membranes
Membranes
Membranes 2021,
 2021,
 2021, 11,
 Membranes
 11,
 11, x
 x
 x FOR
 2021,
 FOR
 FOR PEER
 11,
 PEER
 PEERx REVIEW
 FOR PEER
 REVIEW
 REVIEW
 Membranes 2021, 11, x FOR PEER REVIEW the
 REVIEWfreshly-created interface and by slowing down the approaching bubbles, 9and
 99 of
 9 12
 of
 of thus
 12
 12
 of 9 of the
 12 12
 film drainage process.

 Figure 5. The size
 Figure 5. Figure
 Figure
 The size5. and
 5. The size
 size and size
 size
 distribution distribution
 distribution
 of of
 of
 coalesced, coalesced,
 coalesced,
 stabilized stabilized
 stabilized
 bubbles. bubbles.
 bubbles.
 Bubble Bubble
 Bubble
 size ( size
 size
 , ( (D
 presented, presented
 coal , presented
 with filled circle
 Figure
 Figure 5. 5.
 The
 The size and
 size andsize
 sizedistribution
 distribution of of
 coalesced,
 coalesced, stabilized
 stabilized bubbles.
 bubbles. Bubble
 Bubble size
 size( ( , presented
 ,(C)
 presented
 with filledwith
 with filled
 filled
 circle) circle)
 circle)
 under under
 under
 the thethe
 effects effects
 effects
 of: (A)of: of:
 (A)
 shear (A) shear
 shear
 flow; flow;
 (B)flow;
 (B) (B) protein
 protein
 protein concentration;
 concentration;
 concentration; (C) (C) continuous
 continuous
 continuous phase
 with filled
 with filled circle) under the effects of: (A) shear flow; (B) protein concentration; (C) continuous phase viscosity.
 phasecircle) under
 viscosity. In the
 (A), effects
 the of: of
 effect (A)shear
 shear flow;
 flow
 onis(B) protein
 investigated concentration;
 is investigated (C)toequal
 forequal continuous
 to ),100 ( ),
 phase
 phase viscosity.
 viscosity.
 viscosity.
 phase 200 viscosity. In
 InIn(A),
 (A),
 (A),
 In( (A),the
 thethe effect
 effect
 effect
 the400effectof
 of shear
 of shear
 shear flow
 flow
 flow on
 onon D is investigated
 sizeisofinvestigated
 is investigated for
 for
 for P
 for( ) measured
 equal to 100
 100 (
 ( ( ),= 200 300 ( ) a
 ), 200 ( ),
 ) of shear flow onthe equal toat100
 coal trm
 ( )),and300 ) and ( In mbar. Inthe
 (A–C), initial bubbles = 
 200
 200 (
 ( ),
 ), 300
 300
 300
 200 ( ),mbar (
 (( ) and
 300 (is )plotted400
 400
 and 400for(
 ( )
 ) mbar.
 mbar.
 ( comparisonIn
 In (A–C),
 (A–C),
 (A–C),
 ) mbar. In (A–C), the
 the size
 size
 size of
 of
 of initial
 initial
 initial bubbles
 bubbles
 bubbles ( 
 ( (D )
 ) measured
 measured
 ) measured at
 at 
 at P = =200
 trmof=variation
 200 200 mbar
 mbar is plotted
 and isthe size of initial
 presented bubbles circle
 with unfilled ( 0 ( ). Coefficient
 mbar
 mbar
 mbar is plotted
 is is
 plotted
 plotted for comparison
 forfor
 comparison
 comparison and
 and andis presented
 is is
 presented
 presented with
 with
 with unfilled
 unfilled
 unfilled circle
 circle (( ).
 circle (). Coefficient
 Coefficient
 ). Coefficient
 Coefficient of
 of ofvariation
 variation
 of variation
 variation (CV)
 (CV)correspond
 (CV) corresponding to and measured at = 200 mbar shown in (A–C) is presented in
 (CV)
 (CV)
 (CV)corresponding
 corresponding
 corresponding
 corresponding to 
 Dand
 to to
 to andand
 and 
 D coalmeasured
 measured
 measured
 measured at
 atat 
 P trm=
 at ==200
 =
 200 mbar
 200
 200 mbar
 mbar shown
 shown
 shown in
 inin(A–C)
 (A–C)
 in (A–C) is
 isispresented
 presented
 is presented in
 inin (D–F).
 in The unfill
 (D–F). The unfilled 0and filled bars represent the CV of mbar shown
 initially formed (A–C)
 and presented
 coalesced bubbles, (D–F).
 re-
 (D–F).
 (D–F).
 (D–F). The
 The unfilled
 unfilled
 The unfilled and
 andand filled
 filled bars
 bars
 filled barsrepresent
 represent
 represent the
 the CV
 CV
 the CV of
 of initially
 initially
 of initiallyformed
 formed
 formed and
 and and coalesced
 coalesced
 coalesced bubbles,
 bubbles,
 bubbles, re-
 re- re-spectively.
 The unfilled and filled bars represent the CV of initially formed and coalesced bubbles, respectively.
 spectively.
 spectively.
 spectively.
 spectively.
 3.4. Bubble Formationof Dynamics—Timescales The coeffi
 The coefficient variation (CV) is used to characterize the bubble size distribution
 The
 TheThe coefficient
 coefficient
 coefficient of
 of ofvariation
 variation
 variation (CV)
 (CV)(CV) is
 is used
 used
 is used to
 to tocharacterize
 characterize
 characterize the
 the bubble
 thebubble
 bubble size
 sizesize distribution
 distribution
 distribution (see Figure 5D–
 Within5D–F).
 (see Figure our experimental
 The CV is always resolution,higherwe forobserve
 the coalesced that bubble
 bubblesformationthan for the can be sep-
 initially
 (see
 (see
 (seeFigure
 Figure
 Figure 5D–F).
 5D–F).
 5D–F). The
 TheThe CV
 CV CV is
 is always
 always
 is always higher
 higher
 higher for
 for the
 forthe thecoalesced
 coalesced
 coalesced bubbles
 bubbles
 bubbles than
 than
 than for
 for forthe
 thethe initially
 initially
 initially formed bubble
 arated
 formedinto two stages:
 bubbles. The CVa can bubble onlygrowing
 be reduced stage to anda limited an interval
 extent stage.when we Theincrease
 latter stage the
 formed bubbles. The toCV can only be reduced to aa limited extent when we increase the
 formed
 formed bubbles.
 bubbles.
 corresponds
 continuous TheThe
 phaseCVaCV can
 period
 flowcan onlyonly
 of time
 rate, be be
 and reduced
 reduced
 between
 we obtain tothe
 to aalimited
 limited
 moment
 minimum extent
 extent
 that
 CVone when
 ofwhen we
 bubble
 20% we
 and increase
 34% forthe
 increase
 detaches continuous
 the
 and that
 and pha
 continuous
 continuous
 continuous phase
 phase flow
 flow rate,
 rate, and
 and we
 we obtain
 obtain a minimum
 a aminimum CV
 CV of 20%
 ofof20% and
 and 34%
 34% for
 for 
 for growing
 and
 and , respectiv
 next
 the , phase
 bubble flow
 respectively. rate,
 appears.The and
 CVThe we
 doestwo obtain minimum
 corresponding
 decrease strongly CV
 timescales
 down 20%
 to are
 14% and
 theand 34%
 bubble
 17%, and time
 respectively,
 ,, respectively.
 respectively.
 ,(red
 respectively.
 symbols The
 The
 inThe CVCV
 FigureCV does
 doesdoes
 6A) decrease
 decrease
 decrease
 and the strongly
 strongly
 strongly
 interval down
 down
 time down(grey to
 to 14%
 to14%14%
 symbolsand
 andand 17%,
 17%,
 in 17%,
 Figurerespectively,
 respectively,
 respectively,
 6A). For awhen
 givenmeasures
 when measures are taken to enhance stabilization of the freshly-created interfaces, namely
 when
 when
 when measures
 measures
 measures
 transmembrane are
 are taken
 aretaken
 taken to
 to enhance
 enhance
 to
 pressure, enhance the stabilization
 stabilization
 stabilization
 bubble growing of
 of the
 ofthethe freshly-created
 freshly-created
 time freshly-created
 significantly interfaces,
 interfaces,
 interfaces,
 decreases namely
 namely
 namely
 from by
 1.64 raising
 to the p
 by raising the protein concentration, or increasing the continuous phase viscosity. In both
 by
 bybyraising
 raising
 raising the
 the
 the protein
 protein
 protein concentration,
 concentration,
 as Qc increasesconcentration, or
 or increasing
 orincreasing
 increasing the
 the thecontinuous
 continuous
 continuous phase
 phase
 phase viscosity.
 viscosity.
 viscosity. In
 In both
 Inbothboth cases a smaller
 0.13
 casesms a smaller average(Figure bubble 6A). size This is because with
 is accompanied smaller CVQas
 by aincreasing c thetheshearbubble forcesize in-
 cases
 cases
 cases aa creases,
 smaller
 asmaller
 smaller average
 average
 and average
 the bubble
 bubble
 bubble bubble issize
 size
 size
 snapped is accompanied
 is is
 accompanied
 accompanied
 off faster. The by
 byby aa smaller
 asmaller
 smaller
 corresponding CV
 CV CV as
 asasthe
 the
 interval the bubble
 bubble
 bubble
 time size
 size
 only sizedistribution is
 slightly
 distribution is narrowed on the upper end. These results indicate that to tightly control
 distribution
 distribution
 distribution
 decreases is narrowed
 isis
 the propertiesnarrowed
 narrowed
 and converges on
 onon
 of bubbles the
 thethe upper
 upper theend.
 inupper
 towards end.
 end.
 the
 end These
 These
 These
 bubble
 product, results
 results
 results
 growing indicate
 irrespectiveindicate
 indicate
 time of that
 that
 for Qcto
 that to>
 membrane totightly
 tightly
 tightly
 1.5 control
 10 − 5 m3 /s.
 control
 ×properties,
 control theit Weproperties
 is
 the
 the properties
 theproperties
 highlight
 properties
 crucial to of
 ofofbubbles
 bubbles
 that both in
 bubbles
 manipulate in the
 inthe
 timescales
 the end
 end
 theoperationproduct,
 endproduct,
 can decrease
 product, irrespective
 irrespective
 conditions to hundreds
 irrespectiveand the of membrane
 ofoffluid
 membrane
 of microseconds.
 membrane
 properties properties,
 properties,
 properties, itit it
 Muijlwijk
 to control is crucial
 isbubble
 is and to mani
 crucial
 crucial
 crucial to
 to manipulate
 tomanipulate
 co-authors
 manipulate
 formation (2017)
 and, the
 the
 the operation
 operation
 [29]
 especially, reported
 operation toconditions
 conditions
 that inbubble
 conditions
 prevent a and
 1andwt
 and the
 the
 % the fluid
 fluid
 coalescence fluid properties
 properties
 β-lactoglobulin properties to
 toto
 system,
 by sufficiently control
 control fastbubble
 which
 control bubbleis theformation
 bubble
 stabilization main and,
 formation
 formation
 formation and,
 and,
 component and, especially,
 especially,
 of whey
 especially, to
 to prevent
 prevent
 protein,
 to prevent bubble
 bubble
 bubbles bubblearecoalescence
 coalescence
 stable
 coalescence
 of the freshly-created interface and by slowing down the approaching bubbles, and thus against by
 by by sufficiently
 sufficiently
 coalescence
 sufficiently fast
 fast
 onlyfaststabilization
 stabilization
 if a 100-millisecond
 stabilization of the freshly-c
 of the
 ofofthethefreshly-created
 freshly-created
 duration
 freshly-created
 the (within
 film drainage interface
 interface
 the
 interface
 process. and
 and
 experimental
 and by
 byby slowing
 slowing down
 down
 resolution)
 slowing down the
 the
 isthe approaching
 approaching
 allowed
 approaching bubbles,
 bubbles,
 for protein bubbles, and
 and
 adsorption
 and thus
 thusthus the
 beforefilm draina
 the
 the film
 thefilmfilm drainage
 drainage process.
 drainageprocess.
 bubble–bubble interactions occur. Additionally, in a 5 wt % whey protein system, we
 process.
 recently
 3.4. Bubble demonstrated that micrometer-sized bubbles can be sufficiently stabilized
 Formation Dynamics—Timescales 3.4.atBubble
 a Form
 3.4.
 3.4.
 3.4.Bubble
 Bubble
 Bubble Formation
 Formation
 timescale Formation Dynamics—Timescales
 largerDynamics—Timescales
 than 1 millisecond;
 Dynamics—Timescales and at a timescale of ~0.01–1 millisecond, bubble Within ou
 Within our experimental resolution, we observe that bubble formation can be sepa-
 formation
 Within
 Within
 ratedour
 Within our co-exists
 experimental
 ourexperimental
 into two with finite
 resolution,
 stages: aresolution,
 experimental bubble
 resolution,bubble we
 we
 growing coalescence
 observe
 weobserve
 stage and
 observe that
 that [30].
 that bubble
 anbubble Therefore,
 interval
 bubble formation
 formation the
 stage. The
 formation similar
 can
 cancan be observations
 sepa-
 bebesepa-
 latter stage
 sepa- rated
 cor- into two
 rated
 rated
 rated of
 into
 into bubble
 two
 two
 responds
 into two formation
 stages:
 stages: aa bubble
 to a period
 stages: abubbleand
 bubble controllable
 growing
 growing
 of time between
 growing stage
 stagebubble
 the
 stage and
 and and coalescence
 an
 anan
 moment interval
 intervalthat one
 interval in the
 stage.
 stage.
 stage. current
 The
 The
 bubble The latterCFMF
 latter
 detaches
 latter stage
 stage system
 and
 stage cor-
 cor-that
 cor- can
 responds
 the be to a p
 responds
 responds
 responds explained
 nextto abubble
 totoa period by
 aperiod
 period the
 of
 ofof
 appears. intersecting
 time
 time
 time between
 between
 The between timescales
 the
 the
 two corresponding
 themoment
 moment
 moment of bubble
 that
 that one
 one
 timescales
 that formation
 one bubble
 bubble
 are the
 bubble and
 detaches
 detaches protein
 bubbleand
 detaches and adsorption
 growing
 and that
 that
 that the
 the
 time
 thenext[30].
 (redbubble ap
 next
 next bubble
 bubble
 symbols appears.
 appears.
 in The
 The
 Figure two
 two
 6A) corresponding
 corresponding
 and the interval timescales
 timescales
 next bubble appears. The two corresponding timescales are the bubble growing time (red time (greyare
 are the
 the
 symbols bubble
 bubble in growing
 growing
 Figure time
 6A).time For(red
 (red a symbols
 given in Fig
 symbols
 symbols in
 symbolsininFigure Figure
 transmembrane
 Figure6A)6A) and
 pressure,
 6A)and the
 andthe interval
 the
 theinterval bubble
 intervaltimetime (grey
 growing
 time(grey symbols
 (greysymbols time in Figure
 significantly
 symbolsininFigure 6A).
 Figure6A). decreasesFor
 6A).For a given
 from
 Fora agiven given 1.64 to
 transmembrane
 transmembrane
 transmembrane0.13 ms as
 transmembrane increases
 pressure,
 pressure,
 pressure, the
 thethe bubble
 (Figure
 bubble
 bubble growing
 6A).
 growing
 growingThis time
 time
 time significantly
 is because
 significantly
 significantly decreases
 with increasing
 decreases
 decreases from
 from
 from the 1.64shear
 1.64
 1.64 to
 toto forcems as 
 0.13
 0.13
 0.13 ms
 0.13ms ms as 
 asas increases
 increases, increases
 increases (Figure
 and the(Figure bubble6A).
 (Figure 6A).is
 6A). This
 snapped
 This is because
 off
 Thisisisbecause faster.
 because with
 with increasing
 Theincreasing
 with corresponding
 increasing the
 the shear
 interval
 the shear force
 shearforce time
 force only
 increases, and
 increases,
 increases,
 increases, and
 slightly
 andandthe
 thethebubble
 decreases
 bubble
 bubble is
 isissnapped
 and converges
 snapped
 snapped off faster.
 offoff faster.The
 towards
 faster. The the
 The corresponding
 bubble growing
 corresponding
 corresponding interval
 interval timetime
 interval for
 time only
 timeonly
 only 1.5 ×
 slightly decrea
 slightly
 slightly
 slightly 10 m /s. We
 decreases
 decreases
 decreases and
 andand converges
 highlight
 converges
 converges thattowards
 both
 towards
 towards the
 timescales
 thethebubble can decrease
 bubble
 bubble growing
 growing
 growing to time timefor
 hundreds
 time forfor of 1.5
 microseconds.
 1.5 ×
 1.5×× 10 m /s. We

adsorption before bubble–bubble interactions occur. Additionally, in a 5 wt % whey pro-
 tein
 teinsystem,
 system,wewerecently
 recentlydemonstrated
 demonstratedthatthatmicrometer-sized
 micrometer-sizedbubbles
 bubblescancanbebesufficiently
 sufficiently
 stabilized
 stabilized at a timescale larger than 1 millisecond; and at a timescale of ~0.01–1millisec-
 at a timescale larger than 1 millisecond; and at a timescale of ~0.01–1 millisec-
 ond,
 ond,bubble
 bubbleformation
 formationco-exists
 co-existswith
 withfinite
 finitebubble
 bubblecoalescence
 coalescence[30].
 [30].Therefore,
 Therefore,the
 thesimilar
 similar
 observations of bubble formation and controllable bubble coalescence in
 observations of bubble formation and controllable bubble coalescence in the current the current
Membranes 2021, 11, 710 CFMF 10 of 12
 CFMF system
 system can
 can be
 be explained
 explained by
 by the
 the intersecting
 intersecting timescales
 timescales of
 of bubble
 bubble formation
 formation andand
 protein
 proteinadsorption
 adsorption[30].
 [30].

 Figure
 Figure6.
 Figure 6.6.Two
 Two timescales
 Twotimescales
 timescalesfor for bubble
 forbubble formation
 bubbleformation
 formationat atatthe
 the membrane
 themembrane surface.
 surface.(A)
 membranesurface. (A) Bubble
 (A)Bubble growing
 Bubblegrowing time
 growingtimetime
 (Ο)
 (Ο)and
 (O) andthe
 and theinterval
 the intervaltime
 interval time(( ))as asaafunction
 functionof
 function ofthe
 of thecontinuous
 the continuousphase
 continuous phase
 phase flow
 flow
 flowrate.
 rate. (B)
 rate.(B) Average
 (B)Average
 Averagevolume
 volume
 volume of
 of
 initial
 initialbubbles
 bubbles as
 asa afunction
 function of
 ofthe
 the bubble
 bubble growing
 growing time
 time for
 forthe
 theeffects
 effects of
 of (Ο),
 (Ο), (Ο),
 (Ο), (Ο)
 (Ο)
 of initial bubbles as a function of the bubble growing time for the effects of Qc (O), Ptrm (O), c (O)
 andη (O).
 and
 and
 (Ο). The
 (Ο).The
 The bubble
 bubble
 bubble
 volumes
 volumes
 volumes
 correspond
 correspond
 correspond
 to
 tothat
 to that that presented
 presented
 presented
 in
 inFigure
 in FigureFigure 4A–C.
 4A–C.
 4A–C.
 The two
 The The
 two two
 timescales
 timescales
 timescales are
 are
 arederived
 derived based
 based on
 on 3030bubble
 bubble formation
 formation events,
 events, focusing
 focusing on
 on bubble
 bubble formation
 formation from
 from three
 three positions
 positions
 derived
 in based on 30 bubble formation events, focusing on bubble formation from three positions in
 inthe
 thefield
 fieldofofview
 viewof ofthe
 themembrane
 membranein inthe
 thevideo
 videorecorded
 recordedatataaframeframerate rateofof20,000
 20,000frames
 framesper per
 the field
 second. of view of the membrane in the video recorded at a frame rate of 20,000 frames per second.
 second.
 The final bubble size reflects a balance between bubble formation and bubble coa-
 The
 Thefinal bubble
 bubblesize
 finalprobability sizereflects
 reflects aabalance
 balance between
 between bubble
 bubble formation
 formationwhen and
 andbubble
 bubble coales-
 coales-
 lescence. The of bubble coalescence is steeply decreasing a monolayer
 cence.
 cence. The
 The probability
 probability of
 of bubble
 bubble coalescence
 coalescence isissteeply
 steeply decreasing
 decreasing when
 when aamonolayer
 monolayer sur-
 sur-
 surface coverage is achieved. When the protein concentration or the continuous phase
 face
 face coverage
 coverage is
 is achieved.
 achieved. When
 When the
 the protein
 protein concentration
 concentration or
 or the
 the continuous
 continuous phase
 phase vis-
 vis-
 viscosity is manipulated, and both Qc and Ptrm are fixed, bubbles are likely to grow at a
 cosity is
 cositysurface manipulated,
 is manipulated, and both 
 both a fixed and 
 and period are fixed, bubbles are likely to grow at a
 fixed expansion and rate within areoffixed,
 time, bubbles
 ranging mostly are likely from to 0.13
 grow upattoa
 fixed
 fixedmssurface
 surface expansion
 expansion rate
 rate within
 withinbubblea fixed period
 a fixedstabilization of
 period of time,time, ranging
 ranging mostly
 mostly from 0.13 up to
 0.23 (see Figure 6B). To explain within the 2.5 wt %from whey0.13 up to
 protein
 0.23
 0.23 msms (see
 (see Figure
 Figure 6B).
 6B). To
 To explain
 explain bubble
 bubble stabilization
 stabilization within
 within the
 the 2.5
 2.5 wtwt % % whey
 whey
 Lv c
 protein
 protein
 system, we introduce a dimensionless Péclet number (Pe, defined as Pe = D , where D
 system,
 issystem, weweintroduce
 the diffusion introduce aadimensionless
 coefficient dimensionless Péclet
 Pécletnumber
 and L is a characteristic ( é,
 numberlength),( é,defined
 defined
 which as é é== , ,where
 asdescribes where
 the isis
 relative
 the diffusion
 importance
 the diffusion coefficient
 of coefficient
 convectionand and is a characteristic
 is a characteristic
 and diffusion during transport length),
 length), which
 of which
 proteins. describes
 We firstthe
 describes the relative
 relativeim-
 calculated the
 im-
 portance
 diffusion of convection
 portance coefficient
 of convection and diffusion
 of β-lactoglobulin
 and diffusion during during transport
 (as the transport
 representativeof proteins.
 component
 of proteins. We first
 We first calculated
 of whey the
 protein)
 calculated the
 diffusion
 using the coefficient
 Stoke–Einstein of β-lactoglobulin
 equation and (as
 thenthe representative
 obtained Pe
 diffusion coefficient of β-lactoglobulin (as the representative component of whey protein)  component
 1 (S7). of
 Therefore, whey theprotein)
 above-
 using
 usingthe
 mentioned theStoke–Einstein
 surprisingly high
 Stoke–Einstein equation
 bubble
 equation and
 and then
 thenobtained
 stability é
 can be ascribed
 obtained é≫ ≫11to (Figure
 high bulk
 (Figure S7).
 S7).Therefore,
 Therefore,the
 concentration the
 above-mentioned
 above-mentioned surprisingly high bubble stability can be ascribed to highbulk
 and bulk convection surprisingly
 (enhanced high
 mass bubble
 transport stability
 of can
 proteins). be ascribed
 Additionally, to high
 given bulktheconcen-
 bubble
 concen-
 tration
 size
 tration and
 and bulk
 encountered bulkconvection
 in this study,
 convection (enhanced
 the highly
 (enhanced masscurved
 mass transport
 surface
 transport of proteins).
 ofcan Additionally,
 also accelerate
 proteins). Additionally, given
 the protein
 given
 the
 thebubble
 bubblesize
 adsorption sizeencountered
 process in
 inthis
 and thus contribute
 encountered thisstudy, to the
 study, the
 the highly
 high bubble
 highly curved surface
 stability
 curved [31].can
 surface canalso
 alsoaccelerate
 accelerate
 the
 theprotein
 proteinadsorption
 adsorptionprocessprocessand andthusthuscontribute
 contributeto tothe
 thehigh
 highbubblebubblestability
 stability[31]. [31].
 4. Conclusions
 4.4.Conclusions
 In the cross-flow membrane foaming (CFMF) system, bubble formation is studied
 Conclusions
 usingInwhey protein as the surfactant. At a (sub)millisecond timescale, bubbles continuously
 In thethe cross-flow
 cross-flow membrane
 membrane foaming foaming (CFMF) (CFMF) system, system, bubble
 bubble formation
 formation isis studied
 studied
 grow
 using at the pores and snap off based on a force balance mechanism. The snap-off bubble
 usingwhey wheyprotein
 proteinas asthe
 thesurfactant.
 surfactant.At Ataa(sub)millisecond
 (sub)millisecondtimescale, timescale,bubbles bubblescontinu-
 continu-
 size (Dgrow
 ously 0 ) is dominated
 at by the snap
 continuous phase shear force; theremechanism.
 is almost no dependency
 ously grow atthe
 thepores
 poresand and snapoff offbased
 basedon onaaforce
 forcebalance
 balance mechanism.The Thesnap-off
 snap-off
 on the transmembrane
 bubble pressure. The final bubble phasesize (Dshear
 coal ) isforce;
 also determined by bubble
 size ( 
 bubble size ( ) is dominated by the continuous phase shear force; there is almostno
 ) is dominated by the continuous there is almost node-de-
 coalescence,
 pendency on and
 the it is greatly
 transmembrane reduced at
 pressure. higherThe protein
 final concentration
 bubble size ( and/or
 ) is also higher contin-
 determined
 pendency on the transmembrane pressure. The final bubble size ( ) is also determined
 uous
 by phase viscosity. The Dcoal can be almost equal to D0 , and the coefficient of variation
 by bubble
 bubble coalescence,
 coalescence,and and itit isis greatly
 greatlyreduced
 reducedat at higher
 higher protein
 proteinconcentration
 concentration and/or and/or
 (CV) can be well controlled below 20%. This means that in an ideal CFMF system where
 higher
 highercontinuous
 continuousphase phaseviscosity.
 viscosity.The The can
 canbe bealmost
 almostequal equalto to , ,and
 andthe thecoeffi-
 coeffi-
 bubbles
 cient of can be directly
 variation (CV) stabilized,
 can be well acontrolled
 foam product below composed
 20%. This ofmeans
 monodisperse
 that in an bubbles
 ideal with
 CFMF
 cient of variation (CV)
 targeted size can be produced. can be well controlled below 20%. This means that in an ideal CFMF
 To further understand and optimize the CFMF system, several aspects such as mem-
 brane properties and dimensionless analysis of membrane foaming systems, etc., can be
 investigated in-depth in a future work. For example, as was reported for membrane emul-
 sification, specifically small membrane pores allow the formation of monodisperse and
 small droplets, which have a higher storage stability; meanwhile, smaller pore size may
 screen out the effects of other tested parameters during emulsification [11]. Hence, it is also
 interesting to explore the effect of the small pore size and unravel the potential competitive
 effects of small pore size and continuous phase shear on the formation mechanism and the
 probability of coalescence of bubbles. This could either be studied for a range of membranes