微通道内非牛顿流体中液滴生成机理研究进展

微流体技术良好的可控性为制备均一可控的微液滴提供了新的途径,而非牛顿流体因广泛的应用而受到关注。综述了近年来剪切变稀和黏弹性两类典型非牛顿流体中液滴生成机理的研究进展。围绕流动聚焦型和T型微通道两种典型微通道构型,介绍了非牛顿流体分别作为分散相和连续相时液滴生成过程的界面演化动力学,并与牛顿流体液滴生成过程进行了对比,分析了剪切变稀特性和弹性对主液滴和卫星液滴生成的影响。展望了非牛顿流体液滴生成过程待解决的关键科学问题,为进一步的模拟和实验研究提供了借鉴和参考。     

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.     

Viscoelastic surfactant fluids filtration in porous media: A pore-scale study

We investigated the flow of viscoelastic surfactant (VES) solutions, an important type of fracturing fluids for unconventional hydrocarbon recovery, through a diverging–converging microfluidic channel that mimics realistic unit in porous media. Newtonian fluid and viscoelastic hydrolyzed polyacrylamide (HPAM) solution were used as control groups. We vary Deborah numbers (De) up to 61.2, and found that the flow patterns of HPAM and VES solutions become very different once De ≥ 6.12. This is attributed to different generation mechanisms of viscoelasticity, thus different responses to extensional rates at pore-throats, for HPAM and VES solutions. It results in significantly smaller pressure drop of VES solutions through the microchannel compared to HPAM solution. It interprets higher filtration loss of VES solution than HPAM in core experiments and in field observations. The set-up can be generalized as a prototype to effectively evaluate the filtration of fracturing fluids.     

Visualization study of emulsion droplet formation in a coflowing microchannel

An experimental visualization study is conducted to investigate the hydrodynamic characteristics of emulsion droplet formation in a coflowing microchannel. Both monodisperse and polydisperse patterns of drop formation are observed, including dripping regime, jetting regime (widening jetting and narrowing jetting). Especially, two dripping-to-jetting transition regimes and wavy regime with no individual droplet produced are captured and analyzed. A corresponding phase diagram is provided to characterize the transitions between different emulsification patterns through the control of flow rate of continuous phase. In addition, the dependence of generated droplet size on the Capillary number of the continuous phase (Ca) and the Weber number of the dispersed phase (We) is presented. It is indicated that, when Ca is below 3, the generated droplet size is sensitive to the viscous force and the drop formation regime is widening jetting and dripping. However, when Ca exceeds 3, the generated droplet size is approximately independent of Ca, and the droplet formation regime is thinning jetting.     

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.     

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。     

Determination of the interfacial tension of low density difference liquid-liquid systems containing surfactants by droplet deformation methods

The interfacial tension, σ, between two low density difference liquids containing a surfactant was determined using drop deformation method with a computer-controlled parallel bands apparatus. This device applies a linear homogeneous shear flow field to a fluid matrix in which a droplet of another immiscible and buoyancy-free fluid is immersed. The flow induces topological changes on the initially spherical drop, which deforms into an ellipsoid and orients respect to the flow direction. The time evolution of the sheared droplets was recorded with two CCD cameras (placed along the x and z directions) for extended times, allowing the steady state of the drops to be achieved accurately, and further digitally analyzed. Appropriate theories corresponding to each flow-induced mechanism of the droplet under shear (steady-state deformation and orientation) were employed for determining the interfacial tension, under the basis of reaching equilibrium states of deformation of the sheared drop. The calculated σ values via the drop deformation theories were checked for a wide range of viscosity ratios of binary systems conformed by silicon oils as droplets and a water solution of polyvinylpyrrolidone as continuous phase (both Newtonian), being found that σ is independent on λ. These values were compared with measurements carried out in a conventional tensiometer, using the drop volume method. The comparison showed a very good agreement between both techniques.     

Gas-assisted displacement of a viscoelastic fluid in capillary geometries

The effect of fluid viscoelasticity on the fraction of liquid deposited on the walls of capillary geometry and the pressure drop at the capillary static region are theoretically investigated using the Criminale-Ericksen-Filbey (CEF) constitutive equation to describe a non-Newtonian fluid displaced by the pressurized gas in a capillary. The singular perturbation method is used to determine the residual liquid film thickness of a viscoelastic fluid on the walls of a circular tube or a rectangular channel when displaced by another immiscible fluid. Inner and outer expansions are developed in terms of both a small parameter Ca^1/3 and a small parameter De/Ca^1/3. The method of matched asymptotic expansion is used to match the inner and outer solutions by means of a transition region between the advancing meniscus and the entrained film where the fluid rheology has its greatest effect. A detailed analysis indicates that the residual liquid film thickness of the viscoelastic fluid tends to decrease and the pressure drop across the bubble front tends to increase as the fluid becomes more viscoelastic. The theoretical results presented in this paper are in agreement with some of the experimental data and theoretical analyses available in the literature.     

Drop Deformation and Breakup Mechanisms in Viscoelastic Model Fluid Systems and Polymer Blends

This paper reviews the dispersion mechanisms in viscoelastic systems under relatively high shear rate conditions. In particular, two non‐Newtonian deformation and breakup mechanisms were revealed by flow visualization in a transparent Couette shearing setup. The first one is the dispersed droplet elongation perpendicular to the flow direction. This was observed only for viscoelastic drops and had been associated to normal force buildup in the droplet. The second deformation/breakup mechanism was observed in very high viscosity ratio polymer systems. It consists in erosion at the drop surface. Clouds of very small ribbons and sheets were developed around the drop then stretched and finally broken into very small droplets, rapidly distributed in the matrix.     

Development of fibrillar morphology in immiscible PP/PS blends under shear flow

The formation dynamics of fibrillar morphology in dilute immiscible polypropylene (PP)/polystyrene blends under simple shear flow is investigated using optical‐shear technique. Two strategies in generating fibrillar droplets under shear flow, namely temperature quench and shear jump, are studied. It is found that the shear‐induced deformation of PP droplets is closely related to the total shear strain and changes of rheological properties of components during the temperature quench or shear‐jump process. The shape evolution of fibrillar droplets under shear flow displays large deviation to the prediction of affine deformation theory based on Newtonian fluids and that of three deformation models, which consider the viscoelastic properties of components. The possible effect of droplet coalescence, breakup, and interfacial slip on the deviation between the experimental data and the prediction values for droplet deformation are discussed. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Influence of elasticity on dispersed‐phase droplet size in immiscible polymer blends in simple shearing flow

The influence of elasticity of the blend constituent components on the size and size distribution of dispersed‐phase droplets is investigated for blends of polystyrene and high density polyethylene in a simple shearing flow. The elasticities of the blend components are characterized by their first normal stress differences. The role played by the ratio of drop to matrix elasticity at fixed viscosity ratio was examined by using high molecular weight polymer melts, high density polyethylene and polystyrene, at temperatures at which the viscosity ratios roughly equaled each of three different values: 0.5, 1, and 2. The experiments were conducted by using a cone‐and‐plate rheometer, and the steady‐state number and volume‐mean averages of droplet diameters were determined by optical microscopy. After steady‐state shearing, the viscoelastic drops were larger than the Newtonian drops at the same shearing stress. From the steady‐state dispersed‐phase droplet diameters, the steady‐state capillary number, Ca, defined as the ratio of the viscous shearing stress over the interfacial tension stress, was calculated as a function of the ratio of the first normal stress differences in the droplet and matrix phases. For the blend systems with viscosity ratio 0.5, 1 and 2, the values of steady‐state capillary number were found to increase with the first normal stress difference ratio and followed a power law with scaling exponents between 1.7 and 1.9.     

Retarded relaxation and breakup of deformed PA6 droplets filled with nanosilica in PS matrix during annealing

The effect of hydrophilic silica nanoparticles (SiO₂) on the relaxation and breakup dynamics of selectively filled polyamide (PA6) droplets with different degrees of deformation in polystyrene (PS) matrix during quiescent annealing were in situ investigated. It was found that, with the increase of silica content, the relaxation process of PA6 droplets was slowed down gradually and the relaxation mode was changed correspondingly. The critical break aspect ratios (AR_cr) of PA6 droplets were also improved with the increase in SiO₂ nanoparticle contents. Comparisons of the experimental values of AR_cr, characteristic relaxation time (τ_d) and breakup time (t_b) of the SiO₂-filled PA6 droplets with corresponding theoretical values were made. The results of comparison were discussed in terms of viscoelasticity and interfacial tension. It was proposed that the alternation of the viscoelastic properties of PA6 droplets in stead of the interfacial tension change of the blends was responsible for the phenomena observed.     

Numerical simulations of drop impact and spreading on horizontal and inclined surfaces

The phenomenon of drop spreading is important to several process engineering applications. In the present work, numerical simulations of the dynamics of drop impact and spreading on horizontal and inclined surfaces were carried out using the volume of fluid (VOF) method. For the horizontal surfaces, the dynamics of impact and spreading of glycerin drops on wax and glass surfaces was investigated for which the experimental measurements were available [Šikalo, Š., Tropea, C., Ganic, E.N., 2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29, 795-802; Šikalo, Š., Tropea, C., Ganic, E.N., 2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286, 661-669]. The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. The dynamics of drop impact and spreading on inclined surfaces and the different regimes of drop impact and spreading process were also investigated. In particular, the effects of surface inclination, surface wetting characteristics, liquid properties and impact velocity on the dynamics of drop impact and spreading were investigated numerically and the results were verified experimentally. It was found that the SCA model can predict the drop impact and spreading behavior in quantitative agreement with the experiments for less wettable surfaces (SCA>90^°). However, for more wettable surfaces (SCA<90^°), the DCA observed at initial contact times were order of magnitude higher than SCA values and therefore the DCA model is needed for the accurate prediction of the spreading behavior.     

A study on polymer blending microrheology: Part 1

In order to achieve a better understanding of polymer blending processes some experimental work has been carried out on the deformation and break-up behavior of liquid droplets in simple shearing matrices. For Newtonian systems good agreement was obtained with existing theories. For non-Newtonian systems trends were established regarding the influence of fluid elasticity on droplet deformation and break-up.     

A level set method for simulating wrinkling of extruded viscoelastic sheets

When a polymer is extruded freely from a rectangular die of large cross-sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress-driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix-logarithm-based formulation of the conformation tensor and the single-phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width-to-thickness ratio of the die exit cross section, χ, to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1 , wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σ_c, for the onset of wrinkling of an elastic sheet scales like σ_c~1/χ² , with a significant drop for χ >> 1 . As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ (σ_c being small), in accordance with numerical predictions.     

Formation of viscoelastic droplets in a step-emulsification microdevice

In this article, polyethylene oxide glycerin aqueous solution is used as the dispersed phase, and cyclohexane is used as the continuous phase to study the formation mechanism of viscoelastic fluid droplets in a step-emulsification microdevice. The formation process of viscoelastic droplets mainly includes three stages: two-dimensional expansion stage, necking stage, and pinch-off stage. The elasticity has basically no effect on the two-dimensional expansion stage, but it can delay the process of the necking stage and cause the beading phenomenon of droplets in the pinch-off stage. The results show that the effect of elasticity on the droplet size is weak, but it cannot be ignored. Moreover, the elasticity will be coupled with the viscous force to reduce the operating range of the dripping regime. Finally, the influence of the elasticity on the formation of satellite droplets is analyzed, and the method to prevent the influence of satellite droplets is proposed.     

Depletion of cross‐stream diffusion in the presence of viscoelasticity

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T‐sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one‐dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015     

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR=2.4, 4, 8 and 12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streak line photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at De≈200, 300, 70 and 450 for CR=2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments.     

Microdrop impact on soft substrates at low Weber numbers

In this work, we experimentally investigate the impact of microdrops on diverse soft substrates at low Weber numbers. We show that the dynamic behaviors of the impinging microdrops are very different from that of macroscopic droplets reported in the literature. Whereas various impact phenomena have been identified for millimeter-sized water droplets in previous studies, we only observed regular deposition for droplets of a few tens of micrometers in the experiment. In contrast to the significant slowdown of the receding millimeter-sized droplets, no effects of substrate stiffness on the impact process have been identified at microscale. These different dynamics are explained by the different dynamic response of soft viscoelastic materials during droplet impact over different timescales. Finally, the analysis of the post-impact droplet oscillation with the theory for damped harmonic oscillators reveals that the damping coefficient is also size-dependent while the spring constant is not. A simple scaling argument was proposed to understand this finding.