Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Abnormal rotation of a deformed liquid crystal droplet immersed in an isotropic fluid after transient flow

The morphology evolution of liquid crystal droplets immersed in an isotropic fluid in flow field is found to be different from flexible polymer droplets. In this paper, we investigated the retraction of a liquid crystal droplet after transient flow. It is found that the liquid crystal droplet will rotate during the shape recovery, which has never been observed for an isotropic droplet. The factors that influence the rotational angle of a single liquid crystal droplet during retraction progress were studied, including the temperature, the dimension of the droplets, the time of shear flow, the shear rate, the flow type, and the properties of liquid crystal molecules. The rotation of liquid crystal droplet during shape recovery is ascribed to both the bulk elasticity of liquid crystal droplets and the anisotropic properties of the interface between liquid crystal and isotropic fluid.     

组装式微流控系统制备双重包裹微液滴的方法研究

介绍了一种组装式微流控系统制备单、双重包裹微液滴的方法。微系统中用三通接头构成T型微流体通道,使得分散相在连续相强烈的剪切力和压力差作用下断裂形成单个微米级液滴。在制备单个微液滴基础上,用毛细管将两个三通接头串联,通过调控三相流量,可产生双重包裹液滴。结合实验结果,分析了流体粘度比对液滴大小的影响,并得出液滴的尺寸与流量比之间的关系式,为制备不同尺寸的液滴提供了参考依据。对制备的样品进行统计分析,结果显示,液滴的多分散性指数均小于3.2%,表明微液滴的高度均匀性。此外,通过调节三相液体的流量不仅可以控制内外层液滴的大小,还可以调节内层包裹液滴的个数。本文提出的制备方法,设备组装拆卸简便,不需表面亲疏水性处理,装置利用率高,产生的单、双重包裹微液滴可满足高通量的测量分析要求。     

Investigating the effects of shear rate on the collapse time in a gas–liquid system by lattice Boltzmann

In order to evaluate the effects of shear rate on the time of collapse process in a two-phase; one component system, a free energy lattice Boltzmann model is developed. Considering a system consists of two droplets in the surrounding vapor it is observed that, for various physical and geometrical conditions, imposing shear flow has similar effects on the collapse time. Actually, for each case there is an optimum shear rate of collapse that is corresponded to highest collapse rate and smallest time. In all test cases, for shear rates smaller than the optimum value, increasing the shear rate raise collapse rate and reduce its time. But for higher shear rates, increasing the shear rate has reverse effect and decreases the collapse rate. The results also show that, higher droplet radius ratio, viscosity ratio, surface tension and interface thickness lead to a higher optimum shear rate of collapse while higher density ratio of liquid and vapor decreases that.     

Convective heat transfer from molten salt droplets in a direct contact heat exchanger

This paper presents a new predictive model of droplet flow and heat transfer from molten salt droplets in a direct contact heat exchanger. The process is designed to recover heat from molten CuCl in a thermochemical copper–chlorine (Cu–Cl) cycle of hydrogen production. This heat recovery occurs through the physical interaction between high temperature CuCl droplets and air. Convective heat transfer between droplets and air is analyzed in a counter-current spray flow heat exchanger. Numerical results for the variations of temperature, velocity and heat transfer rate are presented for two cases of CuCl flow. The optimal dimensions of the heat exchanger are found to be a diameter of 0.13 m, with a height of 0.6 and 0.8 m, for 1 and 0.5 mm droplet diameters, respectively. Additional results are presented and discussed for the heat transfer effectiveness and droplet solidification during heat recovery from the molten CuCl droplets.     

平面激波冲击并排液滴的三维数值模拟研究

采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.      

The periodicity of droplets emanating from interconnected orifices

The periodicity of droplets emanating from a single and from two orifices with a common fluid reservoir between them was investigated. Experiments were conducted in which the effects of variations in mass flow rate, orifice diameter and common reservoir volume were determined. The results reported herein indicate that dripping from an orifice at relatively low mass flow rates is singly periodic and that the period between droplets is inversely proportional to the imposed mass flow rate. A simple model of the singly periodic droplet emission process is developed and supported by the experimental results. Period doubling initiates and continues to develop with further increases in the mass flow rate. It is marked by the introduction of additional, smaller diameter droplets that are interspersed temporally among the larger, primary droplets. The presence of a common fluid reservoir volume between two orifices of the same diameter is shown for the singly periodic regime not to alter the droplet emission rate of either orifice as compared to its single orifice counterpart. The volume of the reservoir, however, does affect the mass flow rate per orifice necessary for initial period doubling, with this mass flow rate being lower for a smaller reservoir volume.     

Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Using a counter rotating parallel plate shear flow cell, the shape relaxation of deformed droplets in a quiescent matrix is studied microscopically. Both the effects of geometrical confinement and component viscoelasticity are systematically explored at viscosity ratios of 0.45 and 1.5. The flow conditions are varied from a rather low to a nearly critical Ca number. Under all conditions investigated, viscoelasticity of the droplet phase has no influence on shape relaxation, whereas matrix viscoelasticity and geometrical confinement result in a slower droplet retraction. Up to high confinement ratios, the relaxation curves for ellipsoidal droplets can be superposed onto a master curve. Confined droplets with a sigmoidal shape relax in two stages: the first consists of a shape change to an ellipsoid with a limited amount of retraction, and the second is the retraction of this ellipsoid. The latter stage can be described by means of one single relaxation time that can be obtained from the relaxation of initially ellipsoidal droplets. The experimental results are compared to the predictions of a recently published phenomenological model for droplet dynamics in confined systems with viscoelastic components (Minale et al., Langmuir 26:126–132, 2010). However, whereas the model predicts additive effects of geometrical confinement and component viscoelasticity, the experimental data reveal more complex interactions.     

A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.     

Specific rheology – morphology relationships for some blends containing LCPs

For the blend melts of isotropic polysulfone (PSF) and LC polyester (PES), differing in viscosity more than 10 times, the flow curves with maxima were observed in cone and plate geometry. The low shear rate branch is located near the PSF flow curve, and the high shear rate branch is close to the PES flow curve. At high strains, the formation of the ring-like morphology of the blend sample, accompanied by appearance of maximum on flow curve, was registered. The scaling analysis of the reasons for the ring morphology formation was based on stretching of the large, low-viscous LC droplet, embedded to the high-viscous polymer matrix, in a homogeneous shear field. It was shown that, if the critical Taylor radius is not exceeded, the droplet may form the closed torus. Under strong flows, the PSF melt manifests the “spurt effect”, consisting of a drastic increase of the shear rate when the critical value of the shear stress is reached. The pattern of the blend flow curves with maxima may be explained by a vanishing PSF input to the total shear stress, inherent for blends, while the PES melt continues to be in a liquid state and, consequently, is responsible for the blend viscosity at the high shear rates. The presence of regular heterogeneities in the blend in the form of LC rings may initiate the rupture of the entanglements network of the matrix PSF (close to LC rings) under strong shear flows. The appearance of the low-viscous “cracks” at the critical shear stress will diminish the contribution of the PSF to the blends rheological response. Received: 20 April 1999 Accepted: 28 January 2000     

Droplet combustion experiments in varying forced convection using microgravity environment

A new microscopic model of the interaction between droplet flames and fine vortex tubes which compose a coherent structure of turbulence was developed. Three non-dimensional numbers were introduced to extend the length scale and time scale so as to be suitable for microgravity experiments using droplets of combustion of about 1 mm in diameter. An experimental apparatus for combustion of a single droplet and that of an array of two droplets in varying airflow was developed, and experiments were performed in microgravity and normal gravity at pressures up to 2.0 MPa for n-nonane and ethanol as fuels. Variations of the instantaneous burning rate constant, K_i, in response to the varying flow velocity was successfully observed. At high pressure, the effects of droplet Reynolds number Re on K_i was clearly seen, while the effects of natural convection, which increases K_i with Re, was seen in normal gravity even in the forced airflows. As for the experiments on combustion of an array of two droplets, K_i reduction of the downstream droplet became weak when the flow direction was varied. However, the K_i reduction of the downstream droplet for flow direction variations was clearly seen for n-nonane droplets but almost not for ethanol droplets. The interaction mechanism between upstream and downstream droplets is considered to result from the elimination of oxidizer supply to the downstream droplet, indicating strong interaction effects of n-nonane droplets for a stoichiometric oxygen-fuel ratio of n-nonane (i.e., 14.0) greater than that of ethanol (i.e., 3.0).     

Large eddy simulation and experiment of shear breakup in liquid-liquid jet: Formation of ligaments and droplets

Understanding the shear breakup in jet flows and the formation of droplets from ligaments is important to determine the final droplet size distribution (DSD). The initial droplet size, which affects the final DSD, is considered to be generated by the shear breakup. Large eddy simulation (LES) was performed to investigate the shear breakup in liquid-liquid jet flows. The explicit Volume of Fluid (VOF) model with the geometric reconstruction scheme was used to capture the oil-water interface. The estimated oil distribution including wave peaks, ligaments, droplets and water streaks were compared to the experiments with a good agreement. The estimated DSD matched with the measurements favorably well. In the simulation, the formation of droplets with a smooth and curved surface from ligaments or sheet-like structures was obtained. Different mechanisms were observed along with the shear layer including the formation of droplets from ligament through the capillary forces, breakage of a droplet into smaller ones and attachment of a droplet to a ligament. The destructive shear forces and resisting surface tension forces were quantified on stretching and retracting ligaments. The influence of internal viscous force was found to be negligible due to low oil viscosity. The critical capillary number was found to be larger than 5.0 for ligaments breaking with the shear breakup. The capillary number was below unity for retracting ligaments. The coalescence of two equal-sized droplets was obtained in the shear breakup region. The shear stress magnitude at the contact region increased more than two folds. The total surface area decreased nearly 20% after the coalescence.     

Deformation and orientation of single droplets during shear flow: combined effects of confinement and compatibilization

Combined effects of geometrical confinement and compatibilization on the deformation and orientation of single droplets during steady-state shear flow are investigated in a counter-rotating cell by means of microscopic observations. The model system consists of polydimethylsiloxane droplets of varying sizes and viscosities in a polyisobutylene matrix. To this system, a premade polyisobutylene–polydimethylsiloxane block copolymer is added as compatibilizer in different concentrations. For each droplet, the equilibrium interfacial tension is determined by comparing droplet axes with the predictions of the confined Minale model for uncompatibilized droplets at the appropriate degree of confinement. Although large reductions in interfacial tension are seen for all compatibilized droplets, it is shown that the effect of compatibilization on droplet deformation and orientation can efficiently be taken into account in the equilibrium capillary number. This way, for all viscosity ratios and confinement ratios, steady-state data for compatibilized and uncompatibilized droplets coincide, and agree well with the predictions of the confined Minale model at sub-critical conditions. For near-critical capillary numbers, compatibilization slightly reduces droplet deformation and postpones breakup, irrespective of the degree of confinement.     

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.     

Low-Reynolds-number droplet motion in a square microfluidic channel

In this study, we investigate computationally the low-Reynolds-number droplet motion in a square micro-channel, a problem frequently encountered in microfluidic devices, enhanced oil recovery and coating processes. The droplet deformation and motion are determined via a three-dimensional spectral boundary element method for wall-bounded flows. The effects of the flow rate, viscosity ratio and droplet size on the interfacial dynamics are identified for droplets smaller and larger than the channel size and for a wide range of viscosity ratio. Owing to the stronger hydrodynamic forces in the thin lubrication film between the droplet interface and the solid walls, large droplets exhibit larger deformation and smaller velocity. Under the same average velocity, a droplet in a channel shows a significantly smaller deformation and higher velocity than in a cylindrical tube with the same size, owing to the existence of the corners’ area in the channel which permits flow of the surrounding fluid. A suitable periodic boundary implementation for our spectral element method is developed to study the dynamics of an array of identical droplets moving in the channel. In this case, the droplet deformation and velocity are reduced as their separation decreases; the reduction is influenced by the flow rate, viscosity ratio and more significantly the droplet size.     

Self-propelling,coalescing droplets

This work proposes and explores a new propulsion mechanism for sessile droplets which could be of interest for microfluidic applications. This mechanism relies on the Marangoni stresses resulting from the surface tension gradient arising when two droplets of different surface tensions coalesce. We argue that the tendency of the fluid to flow towards regions of higher surface tension is sufficient to displace the droplet. The coalescence of two miscible, partially wetting droplets with different surface tensions is investigated theoretically in this paper and modeled in the lubrication approximation framework. The problem is described by a set of three highly non-linear, coupled partial differential equations which is solved with a commercial finite element code. The analysis reveals two important dimensionless numbers which govern the flow characteristics, one related to the strength of the surface tension gradient and the other to the diffusion time scale. The numerical results confirm the occurrence of the self-propulsion behavior and a parametric study is performed to explore the role of the two dimensionless numbers on the propulsion speed and the total displacement. Unsurprisingly, self-propulsion is enhanced for larger values of the surface tension contrast between the two droplets and smaller values of the diffusion time scale which results in more time for the surface tension gradient to act.     

煤油液滴直径对两相旋转爆轰发动机流场的影响

为探究煤油液滴不同初始直径对气液两相旋转爆轰发动机流场的影响,假设初始注入的煤油液滴具有均匀直径,考虑雾化破碎、蒸发等过程,建立了非定常两相爆轰的Eulerian-Lagrangian模型,进行了液态煤油/高温空气爆轰的非预混二维数值模拟。结果表明：在初始液滴直径为1～70μm的工况范围,燃烧室内均形成了单个稳定传播的旋转爆轰波;全局当量比为1时,爆轰波前的空气区域大于液滴煤油的蒸气区域,导致波前燃料空气混合不均匀,波前均存在富油区和贫油区,两相速度差导致分离出的空气形成低温条带;当煤油液滴的初始直径较小时,波前的反应物混合过程主要受蒸发的影响,爆轰波可稳定传播;当直径减小至1μm时,煤油液滴在入口处即蒸发,旋转爆轰波表现为气相传播的特性,爆轰波结构平整;当煤油液滴的初始直径较大时,波前的反应物混合过程主要受液滴破碎的影响;对于相同的燃料质量流量,在不同初始煤油液滴直径工况下,煤油液滴最大的停留时间均占爆轰波传播时间尺度的80%以上;爆轰波前燃料预蒸发为气相的占比越高,爆轰波的传播速度越高;初始液滴直径为10～70μm的工况范围内,爆轰波的速度随初始直径的增大先升高后降低。     

Droplet dynamics in sub-critical complex flows

A newly designed eccentric cylinder device has been used to study the deformation and orientation of single Newtonian droplets immersed in an immiscible Newtonian liquid in a controlled complex flow field. Optical microscopy coupled with image acquisition analysis allows monitoring the dynamics of droplets flowing in the gap between the eccentric cylinders. Throughout the experiments, the flow intensity was kept below the critical conditions for droplet break-up. The experimental results are compared with predictions which are obtained using the transient form of the phenomenological model of Maffettone and Minale (J Non-Newtonian Fluid Mech 78:227–241, 1998; J Non-Newtonian Fluid Mech 84:105–106, 1999), incorporating a flow type parameter that accounts for the relative amount of elongational effects in the flow field and adapting the capillary number to mixed flows. For all the sub-critical flows studied here, good agreement was found between model predictions and experimental data, providing, for the first time, a quantitative assessment of drop shape predictions in complex flows.     

Effects of coalescence and breakup on the steady-state morphology of an immiscible polymer blend in shear flow

The steady-state morphology of an immiscible polymer blend in shear flow has been investigated by optical microscopy techniques. The blend is composed by poly-isobutylene (PIB) and poly-dimethylsiloxane (PDMS) of comparable viscosity. Experiments were performed by means of a home-made transparent parallel plate device. The two plates can be independently counterrotated, so that sheared droplets of the dispersed phase can be kept fixed with respect to the microscope point of view, and observed for long times. The distribution of drops and their average size were measured directly during flow at different shear rates and for different blend compositions. It was found that the average drop size in steady-state conditions is a decreasing function of the applied shear rate, and does not depend on blend composition for volume fractions up to 10%. Experiments have proved that, in the shear rate range which could be investigated, the stationary morphology is controlled only by coalescence phenomena, droplet breakup playing no role in determining the size of the dispersed phase. More generally, it has been shown that the steady-state morphology is a function not only of the physical parameters of the blend and of the shear rate, but also of the initial conditions applied to the blend. The steady-state results reported in this paper constitute the first direct experimental confirmation of theoretical models which describe the mechanisms of shear-induced drop coalescence.