Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility

The effect of bulk-soluble surfactants on the dynamics of a drop translating through a cylindrical tube under low-Reynolds-number conditions is investigated. Interfacial surfactant adsorption/desorption is modeled according to the Frumkin adsorption framework, and the bulk-insoluble surfactant limit is recovered as the rate of surfactant sorption becomes large compared to that of bulk diffusion. As the equilibrium surface coverage is increased, the mechanism by which drop mobility is reduced changes from uniform retardation at low surface coverage to the formation of a stagnant cap at high surface coverage. For large capillary numbers, the drop does not achieve a steady shape, and eventually it breaks up either through the formation of a penetrating viscous jet of suspending fluid, or by continuous elongation and pinch-off. Surfactants have a destabilizing effect on transient drop shapes by accelerating the formation and development of the penetrating viscous jet that leads to drop breakup. The critical conditions for drop breakup, as well as the mode of breakup, depend on the manner in which the strength of the flow (i.e., the capillary number) is increased.     

Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up

This article describes the process of formation of droplets and bubbles in microfluidic T-junction geometries. At low capillary numbers break-up is not dominated by shear stresses: experimental results support the assertion that the dominant contribution to the dynamics of break-up arises from the pressure drop across the emerging droplet or bubble. This pressure drop results from the high resistance to flow of the continuous (carrier) fluid in the thin films that separate the droplet from the walls of the microchannel when the droplet fills almost the entire cross-section of the channel. A simple scaling relation, based on this assertion, predicts the size of droplets and bubbles produced in the T-junctions over a range of rates of flow of the two immiscible phases, the viscosity of the continuous phase, the interfacial tension, and the geometrical dimensions of the device.     

CFD Simulation of Droplet Formation in a Wide-Type Microfluidic T-Junction

Droplet formation in a wide-type microfluidic T-junction was studied using the computational fluid dynamics (CFD) method. Two distinct regimes of droplet formation were confirmed: dripping and jetting; and, at both regimes, droplet size decreases with an increase in capillary number. CFD simulation demonstrated that droplet formation in the T-junction can be divided into three steps: droplet emergence and growing up; separation with the disperse phase; and detachment from the channel wall. The wettability of the channel wall significantly affects the process of droplet detachment from the channel wall; also, the simulation clearly showed that droplets can be formed only when the continuous phase fluid preferentially wets the channel wall, that is, its contact angle on the wall is smaller than 90°. Finally, the CFD study verified that the disperse phase flow rate can significantly affect the droplet size as well as the mechanism of droplet formation.     

Air-bubble-triggered drop formation in microfluidics

In microfluidic devices, droplets are normally formed using T-junction or flow focus mechanisms. While both afford a high degree of control over drop formation, they are limited in maximum production rate by the jetting transition. Here, we introduce a new drop formation mechanism that is not limited by jetting, allowing much faster drop production.     

Interfacial aspects of water drop formation at micro-engineered orifices

The formation of emulsions with micro-engineered silicon based arrays of micro-orifices is a relatively new technique. Until now, only the preparation of oil-in-water emulsions was studied due to the hydrophilic nature of silicon. This work evaluates the emulsification of water into n-hexadecane with hydrophobized arrays of micro-orifices. We have studied the drop formation rate, the number of active pores and the drop size. In contrast to conventional macroporous membranes used for membrane emulsification, we observed high dispersed phase fluxes up to 4600 L h(-1) m(-2) bar(-1) while all pores being active at applied pressures below 2 times the critical pressure. The drop diameter was independent from the applied pressure difference. We observed a pressure dependent lag time between drop formations at low emulsification pressures. The lag time is related to the rate of surfactant diffusion to the water-oil interface causing a reduction of the interfacial tension. A significant influence of the used hydrophobization agents, perfluorinated octyltrichlorosilane (FOTS) and octyltrichlorosilane (OTS), was found for the resulting drop sizes and the number of active pores.     

Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions

The combination of short-range repulsive and long-range attractive forces in many-body dissipative particle dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid is evidenced. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread; correctly, no pinch-off occurs below the cutoff wavelength. Moreover, in an example that illustrates the cascade of fluid dynamics behaviors from potential to inertial-viscous to stochastic flow, the dynamics of the jet radius is consistent with the power law predictions of asymptotic analysis. To model interaction with a solid wall, MDPD is augmented by a set of bell-shaped weight functions; hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. The dynamics of droplets entering an inverted Y-shaped fracture junction is shown to be correctly captured in simulations parametrized by the Bond number, confirming the flexibility of MDPD in modeling interface-dominated flows.     

Systematic investigation of droplet generation at T-junctions

Droplet microfluidics has attracted much attention in recent years. For many droplet-based applications, researchers want to predict the size of the droplets in a certain experimental condition. To meet this need, van Steijn and colleagues proposed an elegant theoretical model that predicts the volume of droplets generated in a common channel configuration for forming a steady-state, continuous stream of droplets, the T-junction geometry. To determine the accuracy of this model in predicting droplet volume, we performed a systematic experimental study over two orders of magnitude in capillary number. We found that this model, albeit elegant, has a limited range of interfacial tension over which it can predict accurately the droplet volume. Our experimental results, together with fluid dynamic simulations, allowed us to highlight the importance of physical fluid properties when employing theoretical models.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

The drop size in membrane emulsification determined from the balance of capillary and hydrodynamic forces

Here, we investigate experimentally and theoretically the factors that determine the size of the emulsion droplets produced by membrane emulsification in "batch regime" (without applied crossflow). Hydrophilic glass membranes of pore diameters between 1 and 10 mum have been used to obtain oil-in-water emulsions. The working surfactant concentrations are high enough to prevent drop coalescence. Under such conditions, the size of the formed drops does not depend on the surfactant type and concentration, on the interfacial tension, or on the increase of viscosity of the inner (oil) phase. The drops are monodisperse when the working transmembrane pressure is slightly above the critical pressure for drop breakup. At higher pressures, the size distribution becomes bimodal: a superposition of a "normal" peak of monodisperse drops and an "anomalous" peak of polydisperse drops is observed. The theoretical model assumes that, at the moment of breakup, the hydrodynamic ejection force acting on the drop is equal to the critical capillary force that corresponds to the stability-instability transition in the drop shape. The derived equations are applied to predict the mean size of the obtained drops in regimes of constant flow rate and constant transmembrane pressure. Agreement between theory and experiment is established for the latter regime, which corresponds to our experimental conditions. The transition from unimodal to bimodal drop size distribution upon increase of the transmembrane pressure can be interpreted in terms of the transition from "dripping" to "jetting" mechanisms of drop detachment.     

Geometry-driven wetting transition

Wetting states are quantitatively described by the number of inflection points on the liquid-vapor interface and by the macroscopic contact angle. The number of inflection points required for complete, partial, and pseudopartial wetting is determined for geometries with positive, zero, and negative capillary pressures. The wetting state of a material system is not always independent of the magnitude of the capillary pressure; for example, the wetting state of a fluid inside a capillary tube may depend on the capillary radius. In particular, a fluid that pseudopartially wets the inside of a tube exhibits a transition to partial wetting (or complete wetting) as the capillary radius is decreased.     

流动聚焦型微流控体系中的液滴的图案化排列和转变模式

流体在微流通道中形成剪切流场（低雷诺数）．不同于宏观体系,由于剪切力和表面张力的竞争作用,产生的液滴在微尺度下的微流通道中形成特殊的排列现象---周期性类似“晶格”排列现象．设计了新型流动聚焦型微流控芯片,分析研究在微流体系中液滴周期性图案化排列和转变机理性,液滴排列模式受两方面因素影响：水油两相的流速比值和微通道尺寸．当微通道宽度为250或300 μm时,液滴形成单层分散,双层和单层挤压排列．当微通道宽度为350 μm 时,液滴会形成单层分散到三层排列到双层挤压最后到单层挤压排列．当出口通道宽度增加到400 μm时,甚至出现了液滴四层排列的现象．同时研究了各个液滴排列模式的“转变点”.     

Hydrodynamic interaction between spheres coated with deformable thin liquid films

In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.     

Drop Coalescence during Emulsion Formation in a High-Pressure Homogenizer for Tetradecane-in-Water Emulsion Stabilized by Sodium Dodecyl Sulfate

The present study investigates the effects of homogenizer pressure, surfactant concentration, ionic strength, and dispersed phase fraction on the coalescence rate of tetradecane-in-water emulsions during their formation in a high-pressure homogenizer. Experiments were conducted in a recirculating system consisting of a Rannie laboratory-scale single-stage homogenizer and a stirred vessel for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS). The initial evolution of the number concentration of droplets in the stirred tank was measured when subjected to a negative stepchange in the homogenizer pressure. The average drop coalescence rate constant in the homogenizer was inferred by fitting the experimental evolution of the number concentration of drops to a simple model accounting for the coalescence in the homogenizer under the assumption of a quasi steady state in the homogenizer. The residence time of the emulsion in the homogenizer was evaluated from the analysis of radial turbulent flow between disks. The step down homogenizer pressure was varied in the range 20.7-48.3 MPa, the drop size in the range 174-209 nm, the dispersed phase fraction in the range 5%-15%, SDS concentration in the range 0.0033-0.25 wt%, and ionic strength in the range 0.01-0.1 M. The coalescence rate constants were found to be in the range from 3.34x10(-17) to 2.43x10(-16) m(3) s(-1). The coalescence rate constant was found to be higher for higher homogenizer pressures, smaller drop sizes, lower dispersed phase fractions, and lower SDS concentrations and was insensitive to variations in ionic strength. Copyright 2001 Academic Press.     

Effect of Intersection Angle of Input Channels in Droplet Generators

In this paper, we studied the effects of the intersection angle between the inlet channels on the droplet diameter using a COMSOL Multiphysics^® simulation. We employed the level-set method to study the droplet generation process inside a microfluidic flow device. A flow-focusing geometry was integrated into a microfluidics device and used to study droplet formation in liquid–liquid systems. Droplets formed by this flow-focusing technique are typically smaller than the upstream capillary tube and vary in size with the flow rates. Different intersection angles were modeled with a fixed width of continuous and dispersed channels, orifices, and expansion channels. Numerical simulations were performed using the incompressible Navier–Stokes equations for single-phase flow in various flow-focusing geometries. As a result of modeling, when the dispersed flow rate and the continuous flow rate were increased, the flow of the continuous flow fluid interfered with the flow of the dispersed flow fluid, which resulted in a decrease in the droplet diameter. Variations in the droplet diameter can be used to change the intersection angle and fluid flow rate. In addition, it was predicted that the smallest diameter droplet would be generated when the intersection angle was 90°.     

Experimental investigation of bubble and drop formation at submerged orifices

The aim of this study was to investigate bubble/drop formation at a single submerged orifice in stagnant Newtonian fluids and to gain qualitative understanding of the formation mechanism. The effects of various governing parameters were studied. Formation behavior of bubbles and drops in Newtonian aqueous solutions were investigated experimentally under different operating conditions with various orifices. The results show that the volume of the detached dispersed phase (bubble or drop) increases with the viscosity of the continuous phase (or dispersion medium), surface tension, orifice diameter, and dispersed phase flow rate. A PIV system was employed to measure the velocity flow field quantitatively during the bubble/drop formation, giving interesting information useful for the elucidation of the fundamental formation process at the orifice. It was revealed that the orifice shape strongly influences the size of the bubble formed. Furthermore, based on a simple mass balance, a general correlation successfully predicting both bubble and drop sizes has been proposed.     

Retention in coupled capillary column supercritical fluid chromatography with lipids as model compounds

Summary We have investigated to which extent retention data, acquired on single capillary columns, can be used for predicting retention factors in a coupled column system. For this purpose we utilized a model mixture of 18 lipid components with widely different vapor pressures and polarities. The sample was chromatographed on two columns, SB-biphenyl-30 (70% methyl-30% biphenylpolysiloxane) and SB-cyanopropyl-50 (50% methyl-50% cyanopropylsiloxane). Experimental retention factors, acquired in coupled column systems with two columns connected in different order, were thus compared with values calculated from runs on each single column. The agreement between calculated and experimental values generally was better than 5% without any pressure drop correction.To study the possibility of predicting retention behavior in a wide pressure range from a limited number of experiments, we also investigated the relation between solute retention and mobile phase density. We found that all data could be fitted to second order equations, which gives the possibility to optimize the resolution with respect to pressure from a limited number of runs at different pressures.     

Determining the mechanical response of particle-laden fluid interfaces using surface pressure isotherms and bulk pressure measurements of droplets

The mechanical response of particle-laden fluid interfaces is determined by measuring the internal pressures of particle-coated drops as a function of the drop volume. The particle monolayers undergoing compression-expansion cycles exhibit three distinct states: fluid state, jammed state, and buckled state. The P-V curves are compared to the surface pressure isotherms Pi-A that are measured using a Langmuir trough and a Wilhelmy plate on a flat water-decane interface covered with the same particles. We find that in the fluid and jammed states, the water drop in decane can be described by the Young-Laplace equation. Therefore in these relatively low compression states, the bulk pressure measurements can be used to deduce the interfacial tension of the droplets and yield similar surface pressure isotherms to the ones measured with the Wilhelmy plate. In the buckled state, the internal pressure of the drop yields a zero value, which is consistent with the zero interfacial tension measured with the Wilhelmy plate. Moreover we find that the compressibility in the jammed state does not depend on the particle size.     

Oscillating drop/bubble tensiometry: effect of viscous forces on the measurement of interfacial tension

The oscillating drop/bubble technique is increasingly popular for measuring the interfacial dilatational properties of surfactant/polymer-laden fluid/fluid interfaces. A caveat of this technique, however, is that viscous forces are important at higher oscillation frequencies or fluid viscosities; these can affect determination of the interfacial tension. Here, we experimentally quantify the effect of viscous forces on the interfacial-tension measurement by oscillating 100 and 200 cSt poly(dimethylsiloxane) (PDMS) droplets in water at small amplitudes and frequencies ranging between 0.01 and 1 Hz. Due to viscous forces, the measured interfacial tension oscillates sinusoidally with the same frequency as the oscillation of the drop volume. The tension oscillation precedes that of the drop volume, and the amplitude varies linearly with Capillary number, Ca=DeltamuomegaDeltaV/gammaa(2), where Deltamu=mu(D)-mu is the difference between the bulk Newtonian viscosities of the drop and surrounding continuous fluid, omega is the oscillation frequency of the drop, DeltaV is the amplitude of volume oscillation, gamma is the equilibrium interfacial tension between the PDMS drop and water, and a is the radius of the capillary. A simplified model of a freely suspended spherical oscillating-drop well explains these observations. Viscous forces distort the drop shape at Ca>0.002, although this criterion is apparatus dependent.     

Drop deformation dynamics and gel kinetics in a co-flowing water-in-oil system

Drop deformation and superimposed gel kinetics were studied in a fast continuous-flow process for a water-in-oil system. Highly monodisperse drops were generated in a double capillary and then deformed passing through a narrowing rectangular channel geometry. Nongelling deformation experiments were used to establish the process and compare it with existing theories. Thereafter, temperature induced drop gelation was included to study its effect on deformation and gel kinetics on short timescales and at high temperature gradients. The disperse phase was a kappa-carrageenan solution with additional sodium and potassium ions for gelation experiments. Sunflower oil was used for the continuous phases. Nongelling experiments showed that shear forces are able to deform drops into ellipsoids. A comparison with the small deformation theory by Taylor was surprisingly good even when drop deformation and flow conditions were not in steady state. Superimposed gelation on the deformation process showed clearly the impact of the altered rheological properties of the dispersed and continuous phase. Deformation first increased on cooling the continuous phase until the onset of gel formation, where a pronounced decrease in deformation due to increasing droplet viscosity/viscoelasticity was observed. Drop deformation analyses were then used to detect differences in gelation kinetics at high cooling rate within process times as short as 1.8 s.     

Molecular dynamics simulations of capillary rise experiments in nanotubes coated with polymer brushes

The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying molecular mechanism differs for wettable and nonwettable walls. For wettable walls, fluid imbibition is compatible with the Lucas-Washburn mechanism whereby the total influx of matter drops steadily with growing chain length N and the meniscus speed goes through a minimum at intermediate chain lengths. Moreover, because of flow, the polymer brush reorganizes its structure by forming a dense plug of chain segments under the meniscus that follows the meniscus in its motion. When the tube wall does not wet, one observes no meniscus formation for short chains although the fluid seeps through the wet brush. For a brush coating with longer chains, axial segregation between the brush segments and the fluid occurs by a kind of diffusive spreading, reminiscent of invasion percolation transport in a random medium, leading to the formation of a moving meniscus. For even longer chains that reach the tube axis, the rise of a meniscus with vanishing curvature-like imbibition in a porous medium is observed to take place.