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Universal equations for the coalescence probability and long-term size stability of phospholipid-coated monodisperse microbubbles formed by flow-focusing Tim Segers, Detlef Lohse, Michel Versluis, and Peter Frinking Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02547 • Publication Date (Web): 05 Sep 2017 Downloaded from http://pubs.acs.org on September 6, 2017

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Universal equations for the coalescence probability and long-term size stability of phospholipid-coated monodisperse microbubbles formed by flow-focusing Tim Segers,∗,† Detlef Lohse,‡ Michel Versluis,‡ and Peter Frinking† †Bracco Suisse S.A., Route de la Galaise 31, 1228 Geneva, Switzerland ‡Physics of Fluids group, MIRA Institute for Biomedical Technology and Technical Medicine, MESA+ Institute for Nanotechnology, University of Twente, Postbus 217, 7500 AE Enschede, The Netherlands E-mail: [email protected]

Abstract Resonantly driven monodisperse phospholipid-coated microbubbles are expected to substantially increase the sensitivity and efficiency in contrast-enhanced ultrasound imaging and therapy. They can be produced in a microfluidic flow-focusing device but questions remain as to the role of the device geometry, the liquid and gas flow, and the phospholipid formulation on bubble stability. Here, we develop a model based on simple continuum mechanics equations that reveals the scaling of the coalescence probability with the key physical parameters. It is used to characterize short-term coalescence behavior and long-term size stability as a function of flow-focusing geometry, bulk viscosity, lipid co-solvent mass fraction, lipid concentration, lipopolymer molecular weight and lipopolymer molar fraction. All collected data collapse on two master curves given by universal equations for the coalescence probability and the long-term size stability. This work is therefore a route to a more fundamental 1

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understanding of the physicochemical monolayer properties of microfluidically formed bubbles and their coalescence behavior in a flow-focusing device.

Introduction An ultrasound contrast agent (UCA) typically consists of a suspension of phospholipid coated microbubbles with radii ranging from 1 to 5 µm. The bubbles oscillate non-linearly in response to a driving ultrasound pulse thereby generating strong harmonic echoes that allow for the visualization and quantification of organ perfusion. 1 However, the acoustic response is strongly dependent on the coupling between microbubble size and ultrasound driving frequency through resonance. Since clinical ultrasound scanners typically operate over a narrow frequency bandwidth, only a small fraction of the bubbles in a polydisperse agent resonate to the driving ultrasound pulse. Thus, the sensitivity of contrast-enhanced ultrasound imaging, and more particularly that of single bubble molecular imaging, 2 may be substantially increased through the use of monodisperse bubbles that are resonant to the driving ultrasound pulse. 3 Moreover, in the context of therapeutic applications, the delivery of drugs and genetic material (e.g., mRNAs or siRNAs) to target cells using functionalized microbubbles and ultrasound 4–8 is expected to be more efficient and more precise using a suspension of monodisperse bubbles through its highly controlled and uniform acoustic response. Monodisperse bubble suspensions can be obtained by mechanical filtration, 9 decantation, 10 and centrifugation 11 of a polydisperse agent. Recently, it has been demonstrated that polydisperse bubbles can be sorted with high precision in microfluidic devices, e.g. microbubbles can be sorted to size in a pinched microchannel 12 and they can be sorted to their acoustic property using the primary radiation force. 13 Microfluidics can also be used to produce monodisperse bubbles directly, e.g. in a flow-focusing device, a proven versatile tool for the highly controlled production of monodisperse bubbles. 14–16 In a flow-focusing device, a gas thread is focused between two liquid flows through an orifice where the gas

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thread destabilizes and pinches off to release monodisperse bubbles. To stabilize the freshly formed monodisperse bubbles against coalescence and dissolution, surfactant molecules are added to the co-flows. However, for biocompatible phospholipids, in contrast to simple short chain surfactants such as Tween 17 and the detergent Dreft, 18 it has been shown that only very specific mixtures at high concentrations are able to sufficiently stabilize the freshly formed bubbles against coalescence, 19 especially when produced at high production rates. 20 Surprisingly, at a high lipid concentration and a low degree of bubble coalescence, not more than 0.1% of the total lipid concentration in the fluid is adsorbed to the bubble interface. 3 Lowering the lipid concentration was reported to result in severe bubble coalescence in the outlet of the flow-focusing device. 3,19,21 The explanation for the low coating efficiency, and at the same time, the need for a high lipid concentration in the liquid may be twofold. First, as previously suggested, 21 a high lipid concentration may increase the adsorption rate by increasing the average liposome-to-microbubble collision frequency. The resulting increased lipid surface packing density may stabilize bubbles more efficiently against coalescence, e.g., through an increased steric repulsion force. 22 Second, the free liposomes within the thin liquid film between colliding bubbles may play a role in preventing bubble coalescence through colloidal and surface forces 22–28 resulting in an increase of the effective viscosity in the thin film. 29 However, to date, a quantitative explanation is still missing. Recently, it has been shown that freshly formed lipid-coated microbubbles formed by flowfocusing are inherently unstable, and prone to Ostwald ripening, until they dissolve to their final size. 20 The shrinking bubble mechanically compresses the lipid monolayer and it thereby increases the surface pressure until it balances the surface tension, thereby stabilizing the bubble against further Laplace pressure-driven dissolution. During stabilization, the total number of lipid molecules on the bubble surface remains unchanged. 20 Therefore, a freshly formed bubble with a lower lipid packing density will dissolve to a smaller final bubble size than a bubble of the same size with a higher lipid packing density. Thus, the size ratio between the initially formed bubble and the stable bubble provides the relative amount of

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lipids on the surface of freshly formed bubbles produced under different conditions, e.g. a different lipid concentration in the co-flow. R formulation, propylene glycol and glycerol are commonly added Inspired by the Definity

to lipid dispersions employed for the production of monodisperse bubbles in a flow-focusing device. 19–21,30,31 Propylene glycol is a co-solvent that increases the solubility of lipids in water. It is therefore expected to have an effect on lipid adsorption and subsequent bubble stabilization. The addition of glycerol increases the bulk viscosity which directly affects the size of the formed bubbles. 32,33 On top of that, liquid viscosity has been observed to have an effect on the degree of bubble coalescence in the outlet of a flow-focusing device. 21 Nevertheless, the effects of propylene glycol and glycerol on coalescence and stabilization of microbubbles formed by flow-focusing was never systematically studied or understood. The design of phospholipid formulations for the successful production of monodisperse bubble populations requires a fundamental understanding of the role of the different components present in a typical lipid formulation, i.e. on the short-term, the coalescence behavior, and on the long-term, the stabilization process of freshly formed microbubbles. Moreover, for further optimization of the flow-focusing technique it is of key importance to understand the role of the microfluidic channel geometry on bubble coalescence and stabilization. Here, we investigate the parameter space that allows for the production of stable monodisperse bubbles formed by flow-focusing. First, we derive a coalescence model to allow for the quantitative comparison of coalescence experiments performed under different experimental conditions, e.g., at different gas and liquid flow-rates. The model is based on simple continuum equations and it reveals the scaling of the coalescence probability with the key physical parameters. The model is validated for flow-focusing geometries with different channel heights, different expanding angles of the nozzle, and for a range of liquid bulk viscosities. Subsequently, the model is used to characterize the scaling of the coalescence probability with the physicochemical properties of the liquid co-flow, i.e., lipid concentration, lipid co-solvent mass-fraction, lipopolymer chain length, and lipopolymer molar fraction. The scaling results are then em-

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ployed to derive two universal equations, one for the coalescence probability and one for the long-term size stability of microfluidically formed phospholipid-coated microbubbles.

Bubble coalescence in a flow-focusing device Bubble coalescence can be described as a probabilistic process governed by two characteristic time scales, i.e. the drainage time τd and the contact time τc , as follows: 34

P = exp(−τd /τc ),

(1)

where P is the coalescence probability. The drainage time τd is the time required for the thin film between two bubbles, forced together under an external force F , to thin down from an initial thickness hi to a critical thickness hc (typically 10-100 nm 22 ) at which it destabilizes and ruptures, 35 see Fig. 1A. The relatively high Laplace pressure of freshly

A

B

Figure 1: (A) Two bubbles forced together under an external force F coalesce when the thin film between the bubbles, initially of thickness hi , has thinned down to a critical thickness hc at which it ruptures. (B) Thin film thinning is affected by the PEGylated liposomes present in the thin film between the PEGylated monomolecular bubble coatings.

formed microbubbles (surface tension σ ≈ 66 mN/m 20 ) and their viscoelastic shell resist deformation. Therefore, the drainage time is approximated by that of two equally sized non-

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deformable bubbles with rigid interfaces. It is found by integrating the approach velocity of two hydrodynamically interacting rigid spheres: 22,36 3πηe R2 τd = ln 2F

hi hc

,

(2)

where ηe is the effective viscosity in the thinning film and F is the net force, comprising a compressive force FD minus a surface force Fs originating from intermolecular interactions. Biocompatible surfactant dispersions employed for microfluidic bubble synthesis typically consist of an aqueous dispersion of a mixture of phospholipids and PEGylated phospholipids. 19,37,38 Before use, the lipid mixture is sonicated 20,30,31,39 to decrease the size of the lipid aggregates, i.e. to form small liposomes with diameters ranging from 20 to 70 nm. The interactions between these PEGylated liposomes, and that between PEGylated liposomes and the PEGylated monomolecular film around the bubbles, see Fig. 1B, result in surface forces, including van der Waals forces, electrostatic forces, steric forces and oscillatory structural forces. 22 These interactions are complex and no analytical models are available for the deformable polymer surface grafted liposomes considered here. Rather than modeling the discrete liposome-liposome and liposome-monolayer interactions, their interactions were modeled by a simple continuum mechanics approach. Viscosity effects resulting from the presence of liposomes in the elongation flow of a thinning film were captured by an elongational viscosity term ηE as follows: ηe = η0 + ηE , 29 with η0 the bulk viscosity of the medium. In order to find an expression for the compressive force, F in Eq. 2, the velocity of the bubbles was compared to the mean fluid velocity in the expanding nozzle of a typical flowfocusing device, 40 see Fig. 2A for the dimensions. The bubble velocity was measured from high-speed recordings captured at a frame-rate of 225,000 frames/s for various flow-rates, each time averaged over at least 100 individually tracked bubbles (data from Segers et al. 20 ). Figure 2B shows a typical example of the bubble velocity in the x-direction; it decreases

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stepwise with increasing downstream position. The gray area in Fig. 2B indicates the error; it shows the average of half the difference in bubble velocity between two neighbouring grid points. Before the first collision of a freshly formed bubble at x = xc , it translates at approximately the mean fluid velocity (blue curve) that is given by:

U (x) ≃

Qt 2Hx tan θ

for w ≪ x,

(3)

where θ is the expanding half angle of the nozzle, w the nozzle width, H the channel height, and Qt the sum of the liquid flow-rate Ql and the gas flow-rate Qg . After collision, the bubble train, a single bubble diameter in width, travels at a velocity approximately equal to the mean fluid velocity at downstream position xL . Note that at xL , the bubble train separates to form a bubble train of 2 bubble diameters in width. From the above analysis it follows that there is a net fluid flow around the bubbles which results in a drag force that compresses the bubbles and that, therefore, drives bubble coalescence. At x = xc , the difference between the mean fluid velocity and the bubble velocity is at maximum and therefore, bubble coalescence is most likely induced in the bubble train that is a single bubble diameter in width. This was confirmed by high-speed imaging of coalescence events, see Fig. 2C. The interface of the bubbles is fully immobilized by surfactants (verified a posteriori) and as the Reynolds numbers are low, O (Re) = 1, therefore, the compressive force at x = xc is approximated by Stokes drag: 41 F = 6πaw η0 R∆U,

(4)

where R the bubble radius, and ∆U = U (xc ) − U(xL ), with U(xc ) the mean fluid velocity at xc and U (xL ) that at xL . The bubbles are in close proximity to the channel top and bottom walls which results in an increased drag force 42,43 that is accounted for by a constant aw , for simplicity. The drag force F is assumed to be only dependent on the bulk viscosity η0 since it has been shown that sterically stabilized particles 44,45 and macromolecules, e.g. polymers, dissolved at low concentrations can dramatically increase the apparent viscosity

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C

B

coalescence

Figure 2: (A) Schematic drawing of a typical flow-focusing geometry. (B) Measured bubble velocity in x-direction (red) and the calculated mean fluid velocity (blue). The error is indicated by the gray area. The inset shows a frame from the high-speed movie from which the bubble velocity was measured with θ = 17.5◦ , H = 14 µm, Ql = 16 µL/min, T = 250 µm, L = 790 µm. (C) Coalescence event. The green arrows represent the velocity vector of each bubble.

ηe in a thinning film, and, at the same time, have a negligible effect on the bulk viscosity η0 . 29 The downstream location at which a bubble with a volume of Qg /Prate = 34 πR3 produced at a production rate Prate collides with its predecessor can be estimated from a volume conservation argument; the bubble collides at the downstream location xc where the volume element containing the total volume per bubble Qt /Prate = 4xc RH tan θ has a width that is equal to the bubble diameter. The ratio of these two expressions results in the following

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relation: xc H tan θ Qt ≃ , R2 Qg

(5)

from which the collision location xc can be calculated. Using the same argument, the downstream location xL can be derived to be xL = 2xc . The bubbles are continuously moving past each other during their downstream travel, see velocity vectors in Fig. 2C, thereby entrapping fresh liquid in the inter-bubble film that prevents it from thinning down. The cone that the bubbles occupy during their downstream translation is limited by the channel walls. In this cone, the larger bubbles are in mutual contact over a longer distance than the smaller bubbles. Since the bubbles do not pass each other in the z-direction, the relative distance over which the bubbles are in contact scales as the ratio of the cross-sectional area of the bubble to the total area of the expanding nozzle: πR2 /T L. This can be multiplied by the average retention time of the bubble in the expanding nozzle: HT L/Qt , to find the contact time:

τc ≃ ac

πR2 H , Qt

(6)

where ac is a proportionality constant. By combining Eqs. 1-6 and by using xL = 2xc , it is straightforward to obtain that the coalescence probability is given by: R Qt , P ≃ exp −Φr β H Qg

(7)

where Φr = 1 + ηE /η0 is the relative viscosity and β = (πaw ac )−1 ln(hi /hc ), which is assumed to be approximately constant and it will be determined in the Results section. Equation 7 allows for the comparison of coalescence experiments performed at different flow rates, different bubble sizes, and in different flow-focusing geometries. It is not possible to speculate on the exact form of Φr for a lipid system a priori since no data nor model is available for

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the effective viscosity of an aqueous dispersion of PEGylated liposomes in a thinning film between PEGylated interfaces. Therefore, Eq. 7 is used to characterize Φr experimentally from microfluidic coalescence experiments, as a function of lipid concentration, propylene glycol content, PEG molecular weight, and PEG molar ratio.

Materials and methods Phospholipid formulations R like formulation used by Segers et al. 20 were In this work, 12 variations of the Definity

studied for at least 4 different total phospholipid concentrations. DPPC, DPPA, and DPPEPEG were mixed at molar fractions of: 1 8 (1 − φP EG ) : (1 − φP EG ) : φP EG , 9 9

(8)

respectively, were φP EG is the molar DPPE-PEG fraction. The molecular weight Mw of the PEG chain was varied at 1000, 2000, 3400, and 5000 gmol−1 and φP EG was varied at 0.05, 0.10, 0.15, and 0.20. The mass fractions of the additives glycerol λG and propylene glycol λP G were varied at 0.05, 0.15, 0.25 and 0, 0.05, 0.10, and 0.15, respectively. An overview of the studied formulations is shown in table 1. Lipids in powder form (Corden Pharma, Liestal, Switzerland) were mixed and dissolved in a 50 mL round bottom flask, containing a 2:1 v/v mixture of chloroform and methanol, mounted on a rotavapor (Buchi R-205, V-800, and B-490) operated at ambient pressure, a temperature of 60◦ C and at a rotation rate of 60 RPM for 30 min. Then, the pressure was reduced to 100 mbar for 60 min to evaporate the solvent. The lipid film was further dried overnight in a vacuum oven at a pressure of 100 mbar. The next day, the lipids were rehydrated in a 10 mL mixture of 20 mM TRIS (Sigma Aldrich) buffered water (Milli-Q, Millipore Corp., Billerica, MA, USA) at a pH of 7, propylene glycol, and glycerol (GPW

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mixture) using the same rotavapor operated at 60◦ C and 60 RPM for 30 min. Directly after rehydration, the 60◦ C lipid dispersion was sonicated for 5 min using a tip sonicator (Branson Sonifier 250) at a continuous output power of 20 W. After sonication, the dispersion was cooled down to room temperature. A Zetasizer (Malvern, ZetaSizer, Nano ZSP) was employed to measure the liposome size distribution using dynamic light scattering (DLS); 10 µL of the concentrated lipid suspension was diluted in 1 mL of pure Milli-Q water before the measurement. The Zetasizer was also employed to measure the viscosity of the pure GPW mixtures before the addition of lipids. This was done by using its rheology measurement feature which tracks the random motion of calibrated 730 nm polystyrene particles through which the viscosity is calculated. Table 1: Studied phospholipid formulations formulation DPPC/DPPA/DPPE-PEG1000 DPPC/DPPA/DPPE-PEG2000 DPPC/DPPA/DPPE-PEG3400 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000 DPPC/DPPA/DPPE-PEG5000

φP EG 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.05 0.15 0.20

λG 0.05 0.05 0.05 0.05 0.15 0.25 0.05 0.05 0.05 0.05 0.05 0.05

λP G legend Fig. 7 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.10 0.15 0.05 0.05 0.05

Flow-focusing geometry and chip fabrication Three different flow-focusing devices were used, see schematic drawing in Fig. 2A for the dimensions. All devices had a 5 µm nozzle (w) that expanded into a 500 µm wide outlet channel (2T ). The expanding half-angle θ of the nozzle and the overall channel height H of

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device A were θ=17.5◦ and H=14 µm, those of device B were θ=17.5◦and H=28 µm, and those of device C were θ=45.0◦and H=14 µm, see table 2. Table 2: Employed flow-focusing geometries chip A B C

w [µm] θ 5.0 ±0.5 17.5 ±0.1 5.0 ±0.5 17.5 ±0.1 5.0 ±0.5 45.0 ±0.1

H 14 28 14

[µm] ±0.5 ±1.0 ±0.5

T [µm] 250 ±1 250 ±1 250 ±1

L [µm] 790 ±2 790 ±2 250 ±2

The molds for the polydimethylsiloxane (PDMS) chips were fabricated using standard soft-lithography techniques. 46 In short, a layer of SU-8 photoresist was spin-coated on a polished silicon wafer, the channel features were UV-exposed through a mask (MESA+, University of Twente, Enschede, The Netherlands), and the wafer was developed to be ready for replica molding. PDMS (Sylgard 184, Dow Corning) was mixed in a 1:10 ratio, poured over the mold, cured for 1 h at 60◦ C, then cut to size. Fluidic ports were punched through the PDMS chip after which it was plasma bonded (Harrick Plasma, Model PDC-002, Ithaca, NY, USA) to a microscope slide to close the channels. The channels were filled with water within 5 min after bonding to maintain their hydrophilicity. The liquid and gas were supplied through teflon tubing (PEEK, Upchurch). The outlet of the flow-focusing device was not connected to tubing; during bubble production a drop of bubble suspension formed at the outlet port.

Imaging setup The imaging system consisted of an inverted microscope (Olympus IX50) equipped with three magnifying objectives (10×, 20× and 40×, Olympus LCPlanFl) connected to a CCD camera (Lumenera, LM165M) with a pixel size of 6.45 × 6.45 µm2 . To minimize motion blur, illumination was provided by a high-intensity LED (Everlight, EHP-C52C) that produced a single 300 ns flash per frame. 12


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Coalescence and stability measurement A

B

50 µm

C

D

100 µm

E

F

20 µm

Figure 3: (A) Images of the nozzle region were analyzed to measure the initial bubble size Ri . (B) The initial bubble size was determined from the mode of the normalized number N distribution. The rectangular outlet channel was imaged (C) to measure the coalescence probability (D).The detected bubbles are outlined by the blue circles. The final bubble size was measured in a flow-cell (E) to determine the final bubble size Rf (F).

For every lipid formulation, starting at the highest concentration, microbubble coalescence and stability were measured for a range of bubble sizes produced at different flow rates and gas pressures. The bubbles were produced at room temperature, in a lab controlled at a temperature of 21◦ C ± 1◦ C. The liquid flow-rate was controlled via a syringe pump (Harvard Apparatus, PHD 4400, Holliston, MA, USA) and the C4 F10 gas-pressure was controlled using a pressure regulator (Omega, PRG101-25). For each specific lipid formulation, 13


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the flow rate and gas pressure were varied such that both the minimum and the maximum possible coalescence percentages were covered. After setting the flow-rate and gas pressure, the bubble formation was left to stabilize for at least 3 min. Then, the liquid on top of the outlet port was removed and 100 images of the nozzle region (Fig. 3A) were captured at a frame-rate of 15 frames/s and at a spatial resolution of 323 nm per pixel to measure the initial size of the freshly formed bubbles. Subsequently, the field of view was enlarged and moved in order to visualize the full width of the rectangular outlet channel of which a second set of 100 images was captured, at a spatial resolution of 645 nm, to measure the coalescence percentage, see Fig. 3C. Finally, the bubble suspension that formed on top of the outlet port during the measurements was pipetted and transferred to one of the ten 7.0 × 4.0 × 0.1 mm3 compartments of a flow-cell. The flow-cell was fabricated using double sided tape (3M Scotch, 665 Permanent) and two microscope slides. After 10 repeated measurements, each at different flow-rates, and after an additional stabilization time of 30 mins., 100 microscope images were captured at a resolution of 160 nm per pixel from each of the 10 flow-cell compartments, located at different locations within the compartment, to measure the final bubble size (Fig. 3E). Thus, a complete measurement series consisted of 10 initial bubble size measurements, 10 coalescence percentages, and 10 final bubble size measurements. After a completed series of experiments, the total lipid concentration was lowered through dilution, using the corresponding GPW mixture, and the measurement series was repeated, for at least 4 different concentrations per lipid mixture.

Image processing The images were processed with a semi-automated image analysis algorithm programmed in MATLAB (The Mathworks, Natick, MA). The size of the initially formed bubbles and that of the final bubbles were measured from the inflection point on the intensity profile of at least 500 bubbles per size distribution. 13 The initial bubble size Ri (Fig. 3B) and the final bubble size Rf (Fig. 3D) were determined from the mode of the size distribution. Even 14


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at high coalescence percentages, the final bubble size could be easily obtained since the coalesced bubbles, with a lower Laplace pressure, act as a sink for the gas diffusing out of the smaller bubbles during their stabilization 20 thereby highly increasing the size difference between coalesced and non-coalesced bubbles, see Figs. 3E. The size distribution of the bubbles in the rectangular outlet channel was measured using the imfindcircles function in MATLAB. In the function, the object polarity option was set to ’dark’, the sensitivity was set to 0.89, and the minimum and maximum detectable bubble size were manually adjusted to the produced bubble size. To demonstrate the accuracy of the method, the detected bubbles are outlined by blue circles in Fig. 3C. In contrast to the inflection point method, this sizing method is sensitive to a background intensity variations within the image and between images. 47 On the other hand, it allows for the detection of all bubbles within an image, see Fig. 3C. From the obtained size distribution, the coalescence probability (value between 0 and 1) was calculated as follows:

P =

Pn

nNn , Ntot 2

(9)

where n is the number of the n-th peak in the size distribution (Fig. 3D), Nn the number of P bubbles within the nth peak, and Ntot the total number of bubbles: Ntot = n1 nNn . The gas flow-rate Qg was calculated as follows:

Qg =

Ntot VB Ql , 2T FL H − Ntot VB

(10)

where VB is the volume of the initially formed bubble VB = 4/3πRi3, Ntot VB the total amount of gas per image, 2T FL H the total volume of the outlet channel within the image with FL the length of the imaged part of the rectangular outlet channel, see Fig. 3C. Equations 5 and 6 were validated experimentally. The locations xc and xL were directly measured from images of the nozzle region captured during the coalescence experiments in the three different devices. The scaling of the contact time τc was validated by track15


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ing bubble pairs, right after their formation, in high speed movies previously recorded at 225,000 frames/s 20 in device A. The contact time was determined from the moment of first contact until the moment where the centerline between both bubbles had rotated over a relative angle of 45◦ . Bubble tracking was performed in MATLAB. First, for every high-speed movie frame, the bubbles were detected using the imfindcircles function. The resulting position matrix was processed using a tracking algorithm 48 to track individual bubbles over the frames and to find their velocity vector.

Results and discussion Model validation Flow-focusing geometry The initial bubble size, the coalescence probability, and the final bubble size were measured for bubbles produced in devices A, B, and C using the same lipid formulation: DPPC, DPPA, and DPPE-PEG5000 mixed according to Eq. 8 at a DPPE-PEG molar fraction φP EG of 0.1. The total lipid concentration was varied at 0.5, 1.0, 2.0, 4.1, 6.1, and 8.1 mmol/L and the propylene glycol and glycerol mass fractions were both 0.05 resulting in a bulk viscosity of 1.2 mPas. Equation 5 was validated by measuring xc and xL from images of the nozzle region captured during the coalescence experiments in the three different devices. Figure 4A shows that, indeed, xc ≃ Qt R2 (Qg H tan θ)−1 and that xL /xc = 2.0 ± 0.2. The measured contact time τc is plotted in Fig. 4B as a function of πR2 HQ−1 t . The proportionality constant in Eq. 6, was obtained from a linear best fit, ac = 6 ± 0.5. Using this, and using a wall correction factor of aw = 5, 49 the dimensionless constant β in Eq. 7 was calculated to be β ≈ 0.024 ± 0.007. In this calculation, the initial film thickness hi was set to 1 µm and the final film thickness was set to hf = 100 nm. The choice for these values

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Figure 4: Measured collision location xc plotted as a function of the total flow-rate to gas flow-rate ratio. (B) Measured contact time. (C) Percentage of coalesced bubbles plotted as a function βRQt (HQg )−1 (see Eq. 7) for different total lipid concentrations. The data collapse on exponential curves (solid lines) validating correct scaling with bubble size and flow rates. (D) Relative viscosity Φr obtained from the exponential fits for the 3 different flow-focusing devices employed here. The data collapse onto a single curve confirming correct scaling of Eq. 7 with the channel geometry. (E) Φr decreases inversely proportional with bulk viscosity, as predicted by the model. (F) Final bubble size Rf plotted as a function of initial bubble size Ri for different bulk viscosities and lipid concentrations (inset) from which the ratio Ri /Rf was obtained. The error bars represent the root mean square (RMS) of the fitting residuals. The ratio Ri /Rf is independent of the lipid concentrations employed in this study.

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was based on literature. 22,50 Note that β is a prefactor and it does not affect the obtained scaling results. The measured percentage of coalesced bubbles in flow-focusing device A is plotted in Fig. 4C for different lipid concentrations as a function of βRQt (HQg )−1 , see Eq. 7. The data points per lipid concentration collapse on exponential curves which confirms the correct scaling of Eq. 7 with bubble size and flow-rates. The relative viscosity Φr was obtained by fitting an exponential function (y = exp(−ax) × 100%) to the data points per lipid concentration, see Fig. 4D. Φr (c∞ ) was obtained in the same way for devices B and C, see also Fig. 4D. Note that Φr − 1 is plotted on a double-log scale; it shows that Φr − 1 ∝ c2∞ . The probability data, as shown in Fig. 4C, for devices B and C will be shown later in a single master plot. Fig. 4D shows that, the measured Φr are completely independent of the device geometry, which was expected from the model since Φr was measured for the exact same lipid formulation. Thus, the scaling of the exponent in Eq. 7 with the inverse of the flow-focusing channel height is valid and, indeed, the coalescence probability is independent of the expanding nozzle angle θ. Varying the bulk viscosity All following experiments were performed in flow-focusing device A. Equation 7 predicts that the degree of coalescence increases with an increase in bulk viscosity through an decrease of the relative viscosity. To verify this, the bulk viscosity of water was increased through the addition of glycerol. Coalescence was measured at bulk viscosities of 1.2, 1.6 and 2.2 mPas. The propylene glycol mass fraction was always 0.05 and the lipid mixture was mixed according to Eq. 8 at φP EG = 0.1. Fig. 4E shows that, indeed, Φr − 1 is inversely proportional to the bulk viscosity, the solid lines show functions of the form: Φr − 1 ∝ c2∞ /η0 . The formed bubbles were left to stabilize in the flow cell. The final bubble size Rf is plotted in the inset of Fig. 4F as a function of the initial bubble size Ri for all concentrations and bulk viscosities. The ratio Ri /Rf was obtained by fitting a linear function to the data

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Figure 5: (A) The relative viscosity Φr decreases with an increasing propylene glycol mass fraction λP G through a bulk viscosity η0 increase as is shown by the solid lines representing functions of the form: Φr − 1 ∝ c2∞ /η0 . (B) The ratio Ri /Rf increases with λ2P G as does the root mean square (RMS) of the fitting residuals represented by the errorbars (C) Φr for different PEG molecular weights Mw . The solid lines represent the functions:Φr − 1 ∝ c2∞ Mw4 /η0 . (D) The ratio Ri /Rf scales linearly with Mw . (E) Φr increases with the PEG molar fraction cubed φ3P EG as shown by the solid lines of the form: Φr − 1 ∝ c2∞ Mw4 φ3P EG /η0 . (F) The ratio Ri /Rf scales linearly with φP EG .

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per lipid concentration and per bulk viscosity, see Fig. 4F. The error bars represent the root mean square (RMS) of the fitting residuals. A unique bulk viscosity and lipid concentration independent relation is found between Ri and Rf where the final bubble size is always found to be 2.3 times smaller than the initial bubble size, independent of bulk viscosity and of lipid concentration. Thus, the gas-liquid interface of the freshly formed bubbles is fully saturated with lipids, even at the lowest concentrations used here since a lower lipid packing density would have resulted in a higher Ri /Rf ratio. Therefore, the observed decrease in coalescence probability with an increase in lipid concentration indicates that the liposomes present in the thin film between colliding bubbles hamper bubble coalescence and that bubble coalescence at low lipid concentrations is not due to limited lipid adsorption. The ratio Ri /Rf of a factor of 2.3 obtained in this work is different from the factor of 2.55 previously obtained for the same lipid mixture. 20 It has been observed by the authors of this work that the ratio Ri /Rf is sensitive to the amount of ions in the lipid dispersion. Therefore, the lower dissolution ratio found in this work is most likely a result of the addition of the TRIS buffer in contrast to the pure water that was used by Segers et al. 20

Relative viscosity and stability characterization Varying the propylene glycol mass fraction The role of the co-solvent propylene glycol on coalescence and bubble stabilization was measured for a lipid system mixed according to Eq. 8 with φP EG = 0.1. The glycerol mass fraction was kept constant at 0.05. The propylene glycol mass fraction λP G was varied at 0, 0.05, 0.10, and 0.15 with resulting bulk viscosities of 1.05, 1.23, 1.43, and 1.62 mPas, respectively. Figure 5A shows Φr − 1 plotted as a function of the lipid concentration. The addition of propylene glycol results in a bulk viscosity increase and thereby in a decrease of Φr . The decrease is following the inverse proportionality of Φr with the bulk viscosity as can be observed from the solid lines that represent the function: Φr − 1 ∝ c2∞ /η0 , as before. Thus, 20


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apart from the relatively small decrease of Φr through a bulk viscosity increase, no other significant influence on microbubble coalescence was observed from the addition of propylene glycol. The formed bubbles were left to stabilize in a flow-cell. The ratio Ri /Rf is plotted in Fig. 5B as a function of the propylene glycol mass fraction λP G . Since the ratio Ri /Rf was concentration independent (see Fig. 4F), no distinction between the different lipid concentrations was made in the figure. Fig. 5B shows that, the difference between the initial bubble size and the final bubble size increases quadratically with the propylene glycol mass fraction λP G for 0 ≤ λP G ≤ 0.15. The error bars in Fig. 5B represent the root mean square (RMS) of the fitting residuals. Note that the error bars increase in magnitude with increasing λP G . The increase of Ri /Rf with increasing propylene glycol mass fraction can be explained as follows. The state of the PEG chain depends on the affinity of the polymer with the medium. In a poor solvent, a PEG chain collapses and in a good solvent it swells; increasing its excluded volume to above that of a PEG chain conformed as a Gaussian coil in pure water. 51,52 The addition of the co-solvent propylene glycol increases the affinity of the PEG chain with the subphase, thereby increasing its excluded volume, through which the average area per molecule in the shell of a freshly formed bubble increases. As a result, the relative area decrease during bubble stabilization increases in order for the monomolecular film to reach the same highly compressed state of the stable bubble. Varying the PEG molecular weight The role of the PEG chain length on coalescence and stabilization was studied at PEG molecular weights Mw of 1000, 2000, 3400, and 5000 for lipid formulations mixed according to Eq. 8 with φP EG = 0.1. The propylene glycol mass fraction and the glycerol mass fraction were both kept constant at 0.05. Figure 5C shows Φr − 1 for the different PEG molecular weights. The relative viscosity is highly dependent on the PEG molecular weight, it increases with Mw4 which is shown by 21


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A

B

Figure 6: (A) Normalized number count N as a function of the liposome diameter for PEG molecular weights of 1000, 2000, 3400, and 5000. (B) The liposome size decreases with an increase in PEG molar fraction. The inset shows that the liposome concentration, which is proportional to the inverse of the average bilayer area per liposome, increases linearly with the PEG molar fraction.

the solid lines that represent the function Φr − 1 ∝ c2∞ Mw4 /η0 . To date, to the best of the author’s knowledge, no rheological data is available on an aqueous dispersion of PEGylated liposomes in an extensional flow. However, rheological studies are available on sterically stabilized nanoparticles, 44 nanoparticles suspended in an aqueous polyethylene oxide (PEO) solution 24 (PEO is chemically equivalent to PEG), and aqueous PEO solutions. 53–56 Generally speaking, shear thickening and large extensional viscosities are reported, up to 1000 times larger than the bulk viscosity. 24 However, the effect of the molecular weight of the PEG chain on the extensional viscosity was not reported. It can be speculated that the scaling of Φr results from the steric interaction between the liposomes and the monomolecular film around the bubbles, however, in principle the steric 3/2

force scales with Mw which is very different from what is observed here. 57 Modeling the full liposome-monolayer and liposome-liposome interactions during the drainage of a thin film, by Monte Carlo 58 or Molecular Dynamics 59 simulations, may reveal the underlying physics of the observed scaling. 22


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Figure 5D shows the ratio Ri /Rf as a function of the PEG Mw ; it is directly proportional to the PEG chain length. The extrapolation of the ratio Ri /Rf to zero PEG chain length shows that bubbles formed without any PEG attached to the DPPE molecule dissolve to a final size a factor of 1.4 times smaller the initial size. Varying the PEG molar ratio The relative viscosities for lipid systems mixed according to Eq. 8 at PEG molar fractions φP EG of 0.05, 0.10, 0.15, and 0.20 are plotted in Fig. 5E as a function of the lipid concentration. Φr − 1 increases with φ3P EG as is shown by the solid lines that represent functions obeying: Φr − 1 ∝ c2∞ Mw4 φ3P EG /η0 . When the total amount of PEG would be the only important factor in Φr , then, Φr is expected to scale as (c∞ φP EG )2 . However, the scaling exponent of c∞ is different from that of φP EG . The difference can be explained from the observation that the liposome size decreases with increasing PEG molar fraction, see Fig. 6B. Such a decrease in liposome size with an increase in PEG molar fraction is commonly observed. 60,61 On the other hand, the liposome concentration is inversely proportional to the bilayer surface area per liposome. It was calculated following 62 and it was found to increase linearly with φP EG (inset Fig. 6B), which then explains the increase of Φr with φ3P EG . Thus, the total amount of PEG and the liposome concentration are both important parameters in microbubble coalescence. The formed bubbles were left to stabilize as before. Figure 5F shows that the ratio Ri /Rf increases linearly with φP EG; the PEG chains strongly influence the size decrease during bubble stabilization. Bubbles formed at a PEG molar ratio of 0.20 did not stabilize to a monodisperse bubble population and therefore, the data is not shown in Fig. 5F. It has been shown that the monolayer rigidity decreases with an increasing amount of lipopolymer; 63 the monolayer buckles at lower compression which may result in lipid shedding. 64,65 This may explain the observed instability of bubbles coated by a shell containing PEG at a molar fraction of 0.2.

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Universal stabilization and coalescence equations Using the empirically obtained scaling exponents, a universal equation for the relative viscosity Φr was obtained, as follows:

Φr = 1 +

Kc2∞ φ3P EG Mw4 , η0

(11)

where K = 1.58×10−13 mol2 m5 kg−1 s−2 is a fitting constant. Figure 7A shows all coalescence probability data from which Φr in Figs. 4 and 5 was obtained, plotted as a function of Φr βRQt (HQg )−1 with Φr given by Eq. 11. All data collapse on a single master curve. Thus, for a DPPC, DPPA, and DPPE-PEG lipid system, Eqs. 7 and 11 can be used to predict the percentage of bubbles that coalesce in the outlet of a flow-focusing device. A second universal equation for the ratio of the initial bubble size to the final bubble size was derived using the empirically obtained stabilization data: Ri = 1.4 + α(1 + γλ2P G )Mw φP EG Rf

(12)

where α = 1.6 × 10−3 mol/g and γ = 30 are fitting constants. All stabilization data is plotted in Fig. 7B rescaled according to Eq. 12 and they all collapse on a single master curve. Thus, for an aqueous DPPC, DPPA, and DPPE-PEG lipid system, Eq. 12 predicts the final bubble size as a function of the propylene glycol mass fraction, the PEG molecular weight, the PEG molar mixing ratio and the initial on-chip bubble size. Equation 12 shows that microfluidically formed bubbles without a PEG chain grafted to the DPPE lipid, or without any DPPE-PEG lipid at all, dissolve to a final size that is a factor of 1.4 times smaller than the initial size, corresponding to a surface area decrease by a factor of 2. It is known that DPPC molecules in the subphase equilibrate with an air-water interface to form a liquid-expanded phase monolayer with a surface pressure ≈ 6 mN/m at 20 ◦ C. 66 Lozano and Longo 67 showed that, for a pure DPPC monolayer, the surface area per molecule

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Figure 7: (A) Master plot of all coalescence probability data measured in this study. (B) Master plot of all bubble stabilization data measured in this work.

at a surface pressure of 6 mN/m equals 0.7 nm2 . The surface tension of a DPPC monolayer approaches zero at an area of 0.35 nm2 per molecule. This is in excellent agreement with the decrease in surface area by a factor of 2 found in our experiment. Moreover, the surface pressure of a pure DPPA and a pure DPPE monolayer are also at maximum at a surface area per molecule of 0.35 nm2 confirming that no DPPE in the shell, or DPPE without PEG, result both in an area decrease by a factor of 2 during stabilization. 68,69 Using the present lipid system, Eq. 12 shows that microfluidically formed bubbles always dissolve before their final size is reached. Thus, when a low aqueous solubility microbubble 25


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filling gas is used, foam formation though Ostwald ripening is inevitable. 20 However, the size difference between the stable bubbles and the foam bubbles, that have taken up the gas that diffused out of the stable bubbles, is large 20 (Fig. 3E) allowing for their separation through decantation. 20 Nevertheless, there is a tradeoff between on-chip bubble coalescence and the amount of foam in a microfluidically formed bubble population, and Eqs. 11 and 12 now allow for the optimization within the boundaries of the selected phospholipid formulation. In this study, perfluorobutane was used as microbubble filling gas. It has been shown that perfluorocarbon gases can increase the rate of lipid adsorption to a gas-liquid interface with respect to air. 70,71 However, this was measured for static conditions in the absence of flow. For microfluidically formed bubbles no difference was observed in the dissolution ratio of air-filled bubbles with respect to perfluorobutane-filled bubbles. 20 Therefore, the filling gas is also not expected to have an effect on the results presented in this work. We speculate that the degree of lipid saturation of the gas interface in a microfluidic flow-focusing device before bubble pinch-off is due to the shear flow along this gas-thread. Equations 11 and 12 can also be written in terms of the number of monomers per PEG chain N since N ∝ Mw resulting in different units of the constant K and a dimensionless constant α. Further investigation is needed to reveal the exact nature of K and α. However, it can be speculated that K is temperature dependent since steric- and structural forces are temperature dependent, as well as the apparent viscosity of polymer solutions. 22 It has been shown that the conformation of a PEG chain in an aqueous medium is temperature dependent, 51 therefore, α is also expected to be temperature dependent. In this work, the bubble formation temperature varied through room temperature fluctuations by ± 1◦ C. However, this is not expected to have a significant effect on the presented results since the variation in the apparent viscosity of polymer solutions and that of the conformation of PEG is relatively small over a variation of only 2◦ C. 22,51 It has been shown that the drag force on a sphere between two infinite parallel plates increases with the size of the sphere. 42,43,49 In the expanding nozzle, the flow is diverging and

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it is most likely disturbed by the formed bubbles. These disturbances are affected by the bubble production rate, i.e. by the shape of the bubble train, see the cone in Fig. 2A versus the line in Fig. 3A. Therefore, the actual drag force is expected to be more complex than originally stated in Eq. 4, where all resulting uncertainties are captured by wall correction factor aw . Here, we showed that sterically stabilized liposomes between colliding bubbles prevent their coalescence. This knowledge may be used to develop lipid formulations with an additional compound that takes over the function of the liposomes, e.g. through the use of polymers or nanoparticles, in order to decrease the total lipid concentration. This is not only interesting for economic reasons but also for the control over the resonance frequency and non-linear acoustic behaviour, which is expected to be higher for lower amounts of lipopolymer in the microbubble shell. 20

Conclusions A model was developed for the coalescence probability of microbubbles in a flow-focusing device. The key physical parameters are the bubble size, the microfluidic channel height, the gas and liquid flow rates, and the viscosity of the fluid in the thinning film between colliding bubbles relative to the bulk viscosity. Experiments showed that an increase in the bulk viscosity results in a relative viscosity decrease through which the coalescence probability increases, quantitatively predicted by the model. The addition of propylene glycol results in a slightly increased coalescence probability through an increased bulk viscosity. It was found that the free liposomes present between colliding bubbles hinder bubble coalescence. The bubble interface was found to be fully saturated with lipids already at lipid concentrations down to 0.5 mmol/L. The coalescence model was successfully employed to characterize the effective viscosity of DPPC, DPPA, and DPPE-PEG lipid mixtures and for a range of molar PEG fractions and PEG molecular weights. The results show that the coalescence probability

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strongly decreases with lipid concentration, PEG molecular weight and PEG molar fraction and that the relative viscosity can be described by a power law of fully independent variables. The size stability was found to be independent of the flow-focusing geometry. It was shown that microfluidically formed bubbles using an aqueous DPPC, DPPA, DPPE-PEG lipid system always decrease in size during their stabilization. The size difference between the freshly formed bubble and the stable bubble increases with PEG molecular weight, PEG molar fraction, and the propylene glycol mass fraction. The coalescence probability and long-term size stability can be predicted by universal equations. This work therefore provides a basic framework of bubble coalescence and physicochemical monolayer properties and it provides practical scaling laws that allow for the optimization of lipid formulations and flow-focusing geometries. Based on the present work, it can be concluded that additives that increase the bulk viscosity are better left out of the phospholipid formulation employed for the formation of monodisperse bubbles since they increase the coalescence probability. The detrimental effect of the commonly used co-solvent propylene glycol is even larger; it increases the amount of foam volume with λ6P G . No benefits were found for the addition of propylene glycol; phospholipids could also be dispersed in pure water using the tip sonicator. All in all, this work shows that propylene glycol and glycerol should not be added to a lipid formulation employed for monodisperse microbubble synthesis in a flow-focusing device.

Acknowledgements We kindly acknowledge Anne Lassus for the preparation of the lipid dispersions. We also thank Anne Lassus, Philippe Bussat, Emmanuel Gaud, and Samir Cherkaoui for fruitful discussions. Finally, we would like to thank Thierry Bettinger for his general support to the project.

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References (1) Lindner, J. R. Microbubbles in medical imaging: current applications and future directions. Nat. Rev. Drug Disc. 2004, 3, 527–533. (2) Klibanov, A. L. Microbubble Contrast Agents: Targeted ultrasound imaging and ultrasound-assisted drug-delivery applications. Invest. Radiol. 2006, 41, 354–362. (3) Segers, T.; de Jong, N.; Versluis, M. Uniform scattering and attenuation of acoustically sorted ultrasound contrast agents: Modeling and experiments. J. Acoust. Soc. Am. 2016, 140, 2506–2517. (4) Tsutsui, J. M.; Xie, F.; Porter, R. T. The use of microbubbles to target drug delivery. Cardiovasc. Ultrasound 2004, 2, 23. (5) Hernot, S.; Klibanov, A. L. Microbubbles in ultrasound-triggered drug and gene delivery . Adv. Drug Deliv. Rev. 2008, 60, 1153–1166. (6) Deelman, L. E.; Declèves, A. E.; Rychak, J. J.; Sharma, K. Targeted Renal Therapies through Microbubbles and Ultrasound. Adv. Drug Deliv. Rev. 2010, 62, 1369–1377. (7) Carson, A. R.; McTiernan, C. F.; Lavery, L.; Grata, M.; Leng, X.; Wang, J.; Chen, X.; Villanueva, F. S. Ultrasound-targeted microbubble destruction to deliver siRNA cancer therapy. Cancer Res. 2012, 72, 6191–6199. (8) Dewitte, H.; Vanderperren, K.; Haers, H.; Stock, E.; Duchateau, L.; Hesta, M.; Saunders, J. H.; De Smedt, S. C.; Lentacker, I. Theranostic mRNA-loaded Microbubbles in the Lymphatics of Dogs: Implications for Drug Delivery. Theranostics 2015, 5, 97–109. (9) Emmer, M.; Vos, H. J.; Goertz, D. E.; van Wamel, A.; Versluis, M.; de Jong, N. Pressure-dependent attenuation and scattering of phospholipid-coated microbubbles at low acoustic pressures. Ultrasound Med. Biol. 2009, 35, 102–111.

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(10) Goertz, D. E.; de Jong, N.; van der Steen, A. F. W. Attenuation and size distribution measurements of Definity and manipulated Definity populations. Ultrasound Med. Biol. 2007, 33, 1376–1388. (11) Feshitan, J. A.; Chen, C. C.; Kwan, J. J.; Borden, M. A. Microbubble size isolation by differential centrifugation. J. Coll. Interf. Sci 2009, 329, 316–324. (12) Kok, M. P.; Segers, T.; Versluis, M. Bubble sorting in pinched microchannels for ultrasound contrast agent enrichment. Lab. Chip 2015, 15 . (13) Segers, T.; Versluis, M. Acoustic bubble sorting for ultrasound contrast agent enrichment. Lab. Chip 2014, 14, 1705–1714. (14) Ga˜ nán-Calvo, A. M.; Gordillo, J. M. Perfectly Monodisperse Microbubbling by Capillary Flow Focusing. Phys. Rev. Lett. 2001, 87, 274501. (15) Anna, S. L.; Bontoux, N.; Stone, H. A. Formation of dispersions using ”flow focusing” in microchannels. Appl. Phys. Lett. 2003, 82, 364–366. (16) Garstecki, P.; Stone, H. A.; Whitesides, G. M. Mechanism for Flow-Rate Controlled Breakup in Confined Geometries: A Route to Monodisperse Emulsions. Phys. Rev. Lett. 2005, 94, 164501. (17) Castro-Hernández, E.; van Hoeve, W.; Lohse, D.; Gordillo, J. Microbubble generation in a co-flow device operated in a new regime. Lab. Chip 2011, 11, 2023–9. (18) Dollet, B.; van Hoeve, W.; Raven, J. P.; Marmottant, P.; Versluis, M. Role of the Channel Geometry on the Bubble Pinch-Off in Flow-Focusing Devices. Phys. Rev. Lett. 2008, 100, 034504. (19) Hettiarachchi, K.; Talu, E.; Longo, M. L.; Dayton, P. A.; Lee, A. P. On-chip generation of microbubbles as a practical technology for manufacturing contrast agents for ultrasonic imaging. Lab. Chip 2007, 7, 463–468. 30


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(20) Segers, T.; de Rond, L.; de Jong, N.; Borden, M.; Versluis, M. Stability of monodisperse phospholipid-coated microbubbles formed by flow-focusing at high production rates. Langmuir 2016, 32, 3937–3944. (21) Talu, E.; Lozano, M.; Powell, R.; Dayton, P.; Longo, M. Long-term stability by lipid coating monodisperse microbubbles formed by a flow-focusing device. Langmuir 2006, 22, 9487–9490. (22) Danov, K. In Fluid Mechanics of Surfactant and Polymer Solutions; Starov, V., Ivanov, I., Eds.; Springer-Verlag Wien, 2004; Chapter 1. (23) Trokhymchuk, D., A. Henderson; Nikolov, A.; Wasan, D. A Simple Calculation of Structural and Depletion Forces for Fluids/Suspensions Confined in a Film. Langmuir 2001, 17, 4940–4947. (24) Khandavalli, S.; Rothstein, J. Extensional rheology of shear-thickening fumed silica nanoparticles dispersed in an aqueous polyethylene oxide solution. Journal of Rheology 2014, 58, 411–431. (25) Wagner, N.; Brady, J. Shear thickening in colloidal dispersions. Physics Today 2009, 62, 27–32. (26) Chellamuthu, M.; Arndt, E.; Rothstein, J. Extensional rheology of shear-thickening nanoparticle suspensions. Soft Matter 2009, 5, 2117–2124. (27) Wasan, D.; Nikolov, A. Thin liquid films containing micelles or nanoparticles. Curr. Opin. Colloid Interface Sci. 2008, 13, 128–133. (28) Bergeron, V. Forces and structure in thin liquid soap films. J. Phys.: Condens. Matter 1999, 11, R215–R218. (29) Barnes, H.; Hutton, J.; Walters, F. An introduction to rheology; Elsevier, Amsterdam, 1989; Vol. 3. 31


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Graphical TOC Entry coalescence

lipid concentration increase

stabilization

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flow-rate increase no coalescence

coalescence

8.1 mmol/L

1.0 mmol/L

coalescence

8.1 mmol/L

25 µm

monolayer compression

Ri

Rf formed bubble

stable bubble

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Universal Equations for the Coalescence ... - ACS Publications

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