Transient and steady-state deformations and breakup of dispersed-phase droplets of immiscible polymer blends in steady shear flow

Transient and steady-state deformations and breakup of viscoelastic polystyrene droplets dispersed in viscoelastic high-density polyethylene matrices were observed in a simple steady shear flow between two transparent parallel disks. By separately varying the elasticities of the individual blend components, the matrix shear viscosity, and the viscosity ratio, their effects on the transient deformation, steady-state droplet size, and the breakup sequence were determined. After the startup of a steady shear flow, the viscoelastic droplet initially exhibits oscillations of its length in the flow direction, but eventually stretches preferentially in the vorticity direction. We find that at fixed capillary number, the oscillation amplitude decreases with increasing droplet elasticity, while the oscillation period depends primarily on, and increases with, the viscosity ratio. At steady-state, the droplet length along the vorticity direction increases with increasing capillary number, viscosity ratio, and droplet elasticity. Remarkably, at a viscosity ratio of unity, the droplets remain in a nearly undeformed state as the capillary number is varied between 2 and 8, apparently because under these conditions a tendency for the droplets to widen in the vorticity direction counteracts their tendency to stretch in the flow direction. When a critical capillary number, Ca_c, is exceeded, the droplet finally stretches in the vorticity direction and forms a string which becomes thinner and finally breaks up, provided that the droplet elasticity is sufficiently high. For a fixed matrix shear stress and droplet elasticity, the steady-state deformation along the vorticity direction and the critical capillary number for breakup both increase with increasing viscosity ratio.     

A framework for interpreting the coarsening and structural evolution of two co‐continuous immiscible viscous fluids

Experimental data from multiple studies show the coarsening of co‐continuous, high interfacial tension fluid systems is driven by capillary instabilities. Coarsening of low interfacial tension systems follows viscosity ratio dependence consistent with the pinch‐off of suspended short filaments although there is uncertainty of this interpretation. The attenuation of coarsening rates for both types follows a common dependence on phase volume fraction and viscosity ratio. Dimensional analysis provides an interpretation of the transition from linear coarsening to slower nonlinear coarsening as a balance of interfacial tension driven flow and a critical level of interconnectivity. The slowdown of coarsening is consistent with the formation of discrete domains which subsequently coexist with the remaining co‐continuous structure. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4140–4156, 2016     

Coalescence dynamics of two droplets of different viscosities in T-junction microchannel with a funnel-typed expansion chamber

The coalescence behavior of two droplets with different viscosities in the funnel-typed expansion cham-ber in T-junction microchannel was investigated experimentally and compared with droplet coalescence of the same viscosity.Four types of coalescence regimes were observed:contact non-coalescence,squeeze non-coalescence,two-droplet coalescence and pinch-off coalescence.For droplet coalescence of different viscosities,the operating range of non-coalescence becomes narrowed compared to the droplet coalescence of same viscosity,and it shrinks with increasing viscosity ratio η of two droplets,indicating that the difference in the viscosity of two droplets is conducive to coalescence,especially when 1 ＜ η＜ 6.Furthermore,the influences of viscosity ratio and droplet size on the film drainage time (Tdr) and critical capillary number (Cac) were studied systematically.It was found that the film drainage time declined with the increase of average droplet size,which abided by power-law relation with the size dif-ference and viscosity ratio of the two droplets:Tdr ～ (ld)0.25±0.04 and Tdr ～ (η)-0.1±002.For droplet coales-cence of same viscosity,the relation of critical capillary number with two-phase viscosity ratio and dimensionless droplet size is Cac =0.48λ0.26l-2.64,while for droplet coalescence of different viscosities,the scaling of critical capillary number with dimensionless average droplet size,dimensionless droplet size difference and viscosity ratio of two droplets is Cac =0.11 η-0.07ls-2.23ld0.16.     

Liquid‐liquid two‐phase flow patterns in a new helical microchannel device

Flow patterns of liquid‐liquid two‐phase fluids in a new helical microchannel device were presented in this paper. Three conventional systems were considered: kerosene‐water, n‐butyl acetate‐water, and butanol‐water. Six different flow patterns, slug flow, continuous parallel flow, discontinuous deformation parallel flow, discontinuous deformation parallel‐droplet flow, droplet‐slug flow, and filiform‐droplet flow, were observed. The influence of interfacial tension, microchannel structure, and rotation rate on two‐phase flow patterns were studied, and a universal flow pattern map was presented and discussed. The systems without mass transfer (0.1 g/g (10 %) tri‐n‐butyl phosphate (TBP)‐water, 0.2 g/g (20 %) TBP‐water, and 0.8 g/g (80 %) TBP‐water) and the system with mass transfer (0.8 g/g (80 %) TBP‐0.62 g/g (62 %) H₃PO₄) were used to verify the validity of the proposed universal flow pattern map in predicting flow patterns. The results showed that the former compared with the latter can be predicted more accurately by the universal flow pattern map.     

十字聚焦型微通道内弹状液滴在黏弹性流体中的生成与尺寸预测

利用高速摄像仪对十字聚焦微通道内液滴在黏弹性流体中的生成过程进行了实验研究。微通道截面为600μm×600 μm 的正方形结构,采用硅油作为分散相,含0.3%表面活性剂十二烷基硫酸钠(SDS)的聚环氧乙烷(PEO)水溶液(质量分数分别为0.1%,0.3%,0.6%)为连续相。实验观察到了弹状流、滴状流和喷射流3 种流型。对弹状流型下液滴生成过程的颈部动力学进行了研究,考察了两相流率、连续相毛细数及弹性数对液滴尺寸的影响。结果表明:弹状液滴尺寸随连续相流率、毛细数及弹性数的增加而减小,随分散相流率的增加而增加,连续相弹性对液滴尺寸的影响相对较小。以油水两相流率比和连续相的毛细数及Reynolds 数为变量建立了弹状液滴尺寸的预测关联式,预测值与实验值吻合良好。     

Y聚焦型微通道内磁流体液滴的生成与调控

利用高速摄像仪研究了截面为400 μm×400 μm Y聚焦型微通道内磁流体液滴在矿物油中的生成过程。以水基磁流体EMG 807为分散相,含4%表面活性剂Span-20的矿物油为连续相。实验观察到了3种流型：弹状流、滴状流和喷射流。分别考察了两相流量、连续相毛细数及磁感应强度对液滴尺寸及生成过程的影响。结果表明：可通过改变两相流量及磁场调控液滴尺寸。当分散相流量不变时,液滴尺寸随着两相流量比的增加而减小。液滴尺寸随着连续相毛细数及磁感应强度的增加而减小,随着分散相流量的增加而增加。以两相流量比、连续相毛细数和磁Bond数为参数提出了一个液滴尺寸的关联式,预测值与实验值吻合良好。     

Bubble/droplet formation and mass transfer during gas–liquid–liquid segmented flow with soluble gas in a microchannel

Microchannels have great potential in intensification of gas–liquid–liquid reactions involving reacting gases, such as hydrogenation. This work uses CO₂–octane–water system to model the hydrodynamics and mass transfer of such systems in a microchannel with double T‐junctions. Segmented flows are generated with three inlet sequences and the size laws of dispersed phases are obtained. Three generation mechanisms of dispersed gas bubbles/water droplets are identified: squeezing by the oil phase, cutting by the droplet/bubble, cutting by the water–oil/gas–oil interface. Based on the gas dissolution rate, the mass transfer coefficients are calculated. It is found that water droplet can significantly enhance the transfer of CO₂ into the oil phase initially. When bubble‐droplet cluster are formed downstream the microchannel, droplet will retard the mass transfer. Other characteristics such as phase hold‐up, bubble velocity and bubble dissolution rate are also discussed. The information is beneficial for microreactor design when applying three‐phase reactions. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1727–1739, 2017     

Three‐Dimensional Simulation of Bubble Formation Through a Microchannel T‐Junction

Three‐dimensional simulations of bubble formation in Newtonian and non‐Newtonian fluids through a microchannel T‐junction are conducted by the volume‐of‐fluid method. For Newtonian fluids, the critical capillary number Ca for the transition of the bubble breakup mechanism is dependent on the velocity ratio between the two phases and the microchannel dimension. For the power law fluid, the bubble diameter decreases and the generation frequency increases with higher viscosity parameter K and power law index n. For a Bingham fluid, the viscous force plays a more important role in microbubble formation. Due to the yield stress τ_y, a high‐viscous region is developed in the central area of the channel and bubbles deform to a flat ellipsoid shape in this region. The bubble diameter and generation frequency are almost independent of K.     

正弦型微通道内液-液两相流型及流动特性实验研究

采用实验的方法对不混溶的液液两相流体在不同入口结构下的正弦微通道(直通道正弦、波峰正弦和波中正弦)内液滴的流动特性进行了分析。硅油作为离散相,含有0.5% SDS的蒸馏水作为连续相,观测到弹状流、滴状流和射状流。分析了两相流动参数及不同的微通道入口结构对流型和液滴长度的影响。流型受微通道入口结构影响较大,波峰正弦微通道能够生成最大范围的稳定的流型。液滴长度随离散相体积流量和离散相与连续相体积流量之比的增大而增大,随连续相的体积流量和毛细数的增大而降低。微通道入口结构对液滴长度有影响,直通道的正弦微通道内液滴长度最短,更有利于液滴的形成。三种通道生成的液滴中,最大的液滴尺寸是最小的液滴尺寸的1.15~1.39倍,但正弦流动段对液滴速度几乎没有影响。     

Effect of viscoelasticity on drop dynamics in 5:1:5 contraction/expansion microchannel flow

Recently, we reported how viscoelasticity affects drop dynamics in a microchannel flow using the finite element-front tracking method (FE-FTM). In this work, we investigate drop dynamics for a wider range of parameters: viscosity ratio between droplet and medium (χ), capillary number (Ca), droplet size, and fluid elasticity. The Oldroyd-B model is adopted as the constitutive equation for the viscoelastic fluid. We observe that the drop deformation in a microfluidic channel is dependent on Ca, which is more pronounced for smaller χ values. The present work shows that viscoelasticity plays an important role in drop dynamics with increasing χ values for Newtonian droplet in viscoelastic medium, which can be attributed to high normal stress developed in narrow film thickness between droplet and channel for higher χ values. We also study circulation problem inside droplets, which is important in practice, such as in droplet reactor application. The present work shows that circulation intensity is enhanced with decreasing χ values. We find that the relevance of viscoelastic effects on internal circulation is dependent on χ values, and the circulation intensity is distinctively decreased with increasing elasticity for high χ values for Newtonian droplet in viscoelastic medium. We expect that the present work be helpful not only in controlling droplets but also to improve our physical insight on drop dynamics in microchannel flows.     

T型微通道内液滴尺寸的实验测定与关联

利用高速摄像仪对不同深宽比的T型微通道内液滴尺寸进行了实验研究。分别采用3种不同尺寸(深度×宽度)的微通道:400 μm×400 μm、400 μm×600 μm、400 μm×800 μm。以环己烷为分散油相,含0.3%表面活性剂十二烷基硫酸钠(SDS)的蒸馏水-甘油(质量分数分别为20%、40%、60%)溶液为连续相。考察了弹状流、过渡流和滴状流流型下微通道尺寸、两相流率、物性对液滴尺寸的影响。结果表明:液滴尺寸随微通道深宽比、连续相流率、黏度和毛细数的增加而减小,随分散相流率的增加而增加。用毛细数、两相流量比和通道深宽比对微通道内液滴尺寸进行了关联和预测,预测值与实验结果吻合良好。     

Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Simulations of microfluidic droplet formation using the two-phase level set method

Microdroplet formation is an emerging area of research due to its wide-ranging applications within microfluidic based lab-on-a-chip devices. Our goal is to understand the dynamics of droplet formation in a microfluidic T-junction in order to optimize the operation of the microfluidic device. Understanding of this process forms the basis of many potential applications: synthesis of new materials, formulation of products in pharmaceutical, cosmetics and food industries. The two-phase level set method, which is ideally suited for tracking the interfaces between two immiscible fluids, has been used to perform numerical simulations of droplet formation in a T-junction. Numerical predictions compare well with experimental observations. The influence of parameters such as flow rate ratio, capillary number, viscosity ratio and the interfacial tension between the two immiscible fluids is known to affect the physical processes of droplet generation. In this study the effects of surface wettability, which can be controlled by altering the contact angle, are investigated systematically. As competitive wetting between liquids in a two-phase flow can give rise to erratic flow patterns, it is often desirable to minimize this phenomenon as it can lead to a disruption of the regular production of uniform droplets. The numerical simulations predicted that wettability effects on droplet length are more prominent when the viscosity ratio λ (the quotient of the viscosity of the dispersed phase with the viscosity of the continuous phase) is O(1), compared to the situation when λ is O(0.1). The droplet size becomes independent of contact angle in the superhydrophobic regime for all capillary numbers. At a given value of interfacial tension, the droplet length is greater when λ is O(1) compared to the case when λ is O(0.1). The increase in droplet length with interfacial tension, σ, is a function of with the coefficients of the regression curves depending on the viscosity ratio.     

Experimental and computational study of microfluidic flow‐focusing generation of gelatin methacrylate hydrogel droplets

This work presents the experimental and computational study of droplet generation for hydrogel prepolymer solution in oil using a flow‐focusing device. Effects of different parameters on hydrogel droplet generation and droplet sizes in a flow‐focusing device were investigated experimentally and computationally. First, three dimensional (3D) computational simulations were conducted to describe the physics of droplet formation in each regime and mechanism of three different regimes: squeezing, dripping, and jetting regime of hydrogel were investigated. Subsequently, the effects of viscosity, inertia force, and surface tension force on droplet generation, and droplet size were studied through these experiments. The experiments were carried out using different concentration of gelatin methacrylate (GelMA) hydrogel (5 wt % and 8 wt %) as the dispersed phase and two different continuous phase liquids (light mineral oil and hexadecane) with various concentrations of surfactant (0 wt %, 3 wt %, and 20 wt %). All experimental data was summarized by capillary number of dispersed phases and the continuous phases to characterize the different regimes of droplet generation and to predict the transition of dripping to a jetting regime for GelMA solution in flow‐focusing devices. It is shown that the transition of dripping to a jetting regime for GelMA happens at lower capillary numbers compared to aqueous solutions. Moreover, by increasing the viscous force of continuous phase or decreasing the interfacial force, the size of GelMA droplets was decreased. By controlling these parameters, the droplet sizes can be controlled between 30 μm and 200 μm, which are very suitable for cell encapsulation. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43701.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part I: Droplet dispersion and coalescence—a review

The theoretical and experimental data on the breakup of droplets are reviewed. Several factors influence development of droplets: flow type and its intensity, viscosity ratio, elasticity of polymers, composition, thermodynamic interactions, time, etc. For Newtonian systems undergoing small, linear deformation, both the viscosity ratio and the capillary number control deformability of drops. On the other hand, the breakup process can be described by the dimensionless breakup time and the critical capillary number. Drops are more efficiently broken in elongational flow than in shear, especially when the viscosity ratio λ ? 3. The drop deformation and breakup seems to be more difficult in viscoelastic systems than in Newtonian ones. There is no theory able to describe the deformability of viscoelastic droplet suspended in a viscoelastic or even Newtonian medium. The effect of droplets coalescence on the final morphology ought to be considered, even at low concentration of the dispersed phase, ?_d ? 0.005. Several drop breakup and coalescence theories were briefly reviewed. However, they are of little direct use for quantitative prediction of the polymer blend morphology during compounding in a twin-screw extruder. Their value is limited to serving as general guides to the process modeling.     

Droplet splitting in multi-furcating microchannel: A three-dimensional numerical simulation study

This work investigates the splitting of a droplet in a multi-furcating microfluidic channel for a two-phase system employing 3D simulation. The simulations were performed using an explicit volume of fluid (VOF) method and have been validated using experimental data taken from the literature. The width ratio of the branch channel to the main channel is set to 0.25 for five branches of the multi-furcating microchannel, as it is the width ratio at which multiple splitting takes place. Simulations have been carried out at different oil velocities (V_o) ranging from 0.12 to 0.22 m/s and at different water velocities (V_w) ranging from 0.002 to 0.10 m/s. Oil fraction data in the main channel has been recorded and compared with the homogenous model. The average difference between the homogeneous model and the 3D simulations is 22.68%. Analysis of dimensionless droplet length in ±0°, ± 40°, and 90° branch channels has been done. α (length of the droplet in branch channel/width of the main channel) increases up to a flow rate ratio of 0.38, and then decreases, whereas β (length of the droplet in the main channel/width of the main channel) increases with an increase in flow rate ratio. A flow pattern map has been developed to identify the various droplet breakup regimes at the junction. Frequency (counts per unit time) of droplet generation increases with capillary number for all the branch channels except for the 0° branch channel, where the regime is that the droplet passes through three branch channels. The volume distribution ratio (λ) decreases at first, then increases with an increase in capillary number for 0°:90° and 40°:90° angle branch channels for the regime where the droplet passes through five branch channels. For the regime where the droplet passes through three branch channels, the trend is likely linear with λ = 0.3 ± 0.04. The dimensionless mother droplet length increases with an increase in capillary number for V_o = 0.13 and 0.16 m/s, but for V_o = 0.19 and 0.22 m/s, the dimensionless mother droplet length becomes constant after capillary number = 0.26 and 0.30 respectively. The droplet breakup time (t) for regime (a), where the droplet passes through three branch channels, is 0.002 s; for regime (b), where the droplet passes through five branch channels, it is 0.001 s; and for regime (c), where multi-furcation and coalescence of the droplet occurs, it is 0.0005 s. Multiple splitting is a topic covered in this paper that can be applied to upcoming microfluidic platform-based devices.     

Study on the transient interfacial tension in a microfluidic droplet formation coupling interphase mass transfer process

In two‐phase dispersion coupling interphase mass transfer process, the variation of interfacial tension is an important factor affecting the dispersion. In this study, we described a microfluidic method for the determination of the transient interfacial tension (TIFT). The method has the advantage of determining TIFT during the whole droplet formation process, rather than only at the rupture moment as reported in previous studies. The TIFTs of several systems were determined. In certain systems, it has been found that the droplet size decreased with the increase of the dispersed phase flow rate, which is obviously different from the constant interfacial tension system. It has also been found that TIFT was mainly affected by two‐phase flow rates, solute type and concentration, and droplet size. A semiempirical equation was finally established to predict TIFT. It has the potential to be used in a variety of industrial equipment with dispersion–mass transfer coupling process. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2542–2549, 2016     

Bivariate population balance model of ethanol‐fueled spray combustors

We present a bivariate population balance‐based formulation of the performance of well‐mixed adiabatic combustors fed by ethanol (EtOH)‐containing sprays of prescribed droplet size distribution (DSD) and composition. Our historically interesting example is the fuel‐cooled V‐2 chemical rocket—using 75 wt % EtOH + H₂O solution, and oxidizer O₂(L). Of special interest are the predicted combustion “intensity” (GW/m³) and efficiency (EtOH fraction vaporized) at each ratio of combustor mean residence time to feed‐droplet characteristic vaporization time. Our formulation exploits a quasi‐steady, gas‐diffusion‐controlled individual droplet evaporation rate law, and the method‐of‐characteristics to solve the associated first‐order population balance partial differential equation governing the joint distribution function n(m₁, m₂) of the fuel spray exiting such a chamber, where m₁ = EtOH mass/droplet, and m₂ = H₂O mass/droplet. Besides the combustor efficiency and intensity, this bivariate distribution function enables predictions of corresponding unconditional DSD, and the joint distribution function(diam., droplet temperature)—perhaps measurable. Our numerically exact formulation/results also provide valuable test cases for convenient approximate methods (bivariate moment and spectral/weighted residual) to predict these “correlated” bivariate distribution functions in more complex situations. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

A rheological and optical properties investigation of aliphatic (nylon 66, PγBLG) and aromatic (kelvar,nomex) polyamide solutions

An experimental study of shear viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}), principal normal stress difference N₁(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}), storage modulus G′(ω), dynamic viscosity η′(ω), and filament elongation to break L_B is reported for solutions of several polyamides; namely, nylon 66 in sulfuric acid (H₂SO₄) and formic acid (HCOOH), poly(γ-benzyl-L -glutamate) (PγBLG) in m-cresol, Nomex in H₂SO₄ and dimethylacetamide (DMA)/5% LiCl, and Kevlar in H₂SO₄ at 25 and 60°C. The variation of properties with concentration, polymer backbone and chain configuration, and solvent type is emphasized. The nylon 66/H₂SO₄ solutions have higher viscosity, normal stresses, and storage modulus than the HCOOH solutions of equivalent concentrations. The Nomex/H₂SO₄ solutions have higher viscosity and higher normal stresses and storage modulus than the DMA/LiCl solutions at equivalent concentrations. The significance of polymer chain backbone rigidity in forming liquid crystalline phases in Kevlar and PγBLG solutions is discussed and its influence on flow properties in indicated. These systems allow polarized light to pass through crossed polarizers and show maxima in viscosity–concentration data. The 25°C Kelvar solutions are distinctive in that they exhibit apparent yield stress values. This gives distinctive shear flow and oscillatory data. Filament elongation-to-break data show Kelvar > Nomex > nylon 66 in H₂SO₄ solutions for the order of spinnability.     

Physicochemical properties,surface active species and formation of reverse micelles in the Cyanex 923‐n‐heptane/cerium(IV)‐H2SO4 extraction system

BACKGROUND: The Cyanex^® 923 (trialkylphosphine oxides, TRPO)‐n‐heptane/cerium(IV)‐H₂SO₄ extraction system has been investigated focusing on the physicochemical properties, surface active species and interfacial phenomena. The effects of H₂SO₄ and Ce(IV) extraction on them were considered. RESULTS: Results showed that the density and refractive index reflect the mass transfer by H₂SO₄ and Ce(IV) extraction and the change of refractive index was more sensitive than density. The interfacial tension decreased on extraction of H₂SO₄ but increased on extraction of Ce(IV). The viscosity of the equilibrium organic phase increased abruptly when the extracted H₂SO₄ concentration in the organic phase reached certain high values. The formation of reversed micelles, with mean diameter of about 10 nm, at high H₂SO₄ concentrations in the organic phase, is suggested by various measurements such as viscosity, interfacial tension and dynamic light‐scattering (DLS). CONCLUSION: It is suggested that TRPO‐H₂SO₄ complexes are more surface‐active than TRPO itself and tend to aggregate into reverse micelles by self‐assembling in the organic phase but the Ce(IV)‐TRPO complexes are neutral, less surface‐active than TRPO and not helpful for reverse micelle formation. Copyright © 2008 Society of Chemical Industry