Critical Capillary Number Research Articles

Aperture Field Anisotropy Control on Immiscible Displacement Patterns in Rough Fractures

AbstractTwo‐phase flow displacement in rock fractures is crucial for various subsurface mass transfer processes and engineering applications. In fractures, the displacement of a less viscous fluid by a more viscous one (i.e., viscosity ratio M > 1) involves viscous forces help stabilizing the displacement front in presence of capillary pressure fluctuations. Although previous studies have reported displacement patterns in isotropic fractures, the impact of anisotropic fractures on displacement patterns has not been systematically examined. In this study, we conducted flow‐rate‐controlled drainage experiments to examine how anisotropic aperture fields affect displacement patterns. We observed the transition of displacement patterns from capillary fingering (CF) to crossover zone (CZ) to compact displacement pattern (CD) based on variations in transverse pore‐filling event (TPFE) frequency, which characterizes the competition between capillary and viscous forces. Increasing aperture correlation length in the transverse direction leads to increased TPFE frequency at a low flow rate, destabilizing displacement front. While the increasing aperture correlation length in longitudinal direction suppressed TPFE frequency, stabilizing displacement front. Therefore, the critical capillary number (CaCF‐CZ), which indicates the onset of the CF‐CZ transition, decreases as the aperture field varies from transversely to longitudinally correlated. At high flow rates, TPFEs almost disappeared, indicating that anisotropy did not affect CZ‐CD transition (CaCZ‐CD). Furthermore, we modified theoretical models of CaCF‐CZ and CaCZ‐CD by incorporating the aperture anisotropy factor, achieving a good fit with the experimental data. This study demonstrates the critical role of aperture field anisotropy in controlling two‐phase displacement patterns and provides a theoretical framework for predicting multiphase flow behavior in natural fractures.

Melt blending of commercial linear polyethylene with low-entangled ultra-high molecular weight polyethylene: From dispersion compatibility to viscoelastic scaling laws

This study investigates the dispersion and compatibility of low-entangled “dis-entangled” UHMWPE (dis-UH) in a high-density polyethylene (HDPE) matrix using solvent-free melt-blending conditions and compares it with entangled UHMWPE (eUH) in the same matrix. The findings reveal that dis-UH/HDPE exhibits a significantly lower viscosity ratio than eUH/HDPE (1 and 4, respectively), indicating a lower critical capillary number (Cacritical), thus enhanced dispersion and compatibility. Blends with varying dis-UH content up to 20 wt% show homogeneity, evidenced by DSC and SEM analysis, and demonstrate improved mechanical properties by 36 % in the maximum stress (σmax) and 39 % in Young's modulus (E). Linear viscoelasticity assessments reveal that higher dis-UH content slow the dynamics and increase the apparent weight average molecular weight (Mw), consistent with previous reports for linear entangled PE. The zero-shear viscosity (η0) scaling with Mw (η0∝Mn) is adjusted for high polydispersity, yielding a transitional point in the scaling exponent (n) from 3.6 to 3 at a reptation number of entanglement segments (Mr/Me) of ∼287, in line with theoretical predictions. To rationalize the success of the homogenization process, we propose a qualitative molecular picture inspired from the constraint release Rouse mechanism involved in the disorientation process of bi-disperse linear polymers. In the case of dis-UH/HDPE blends, with initially lower density of long-long entanglements within dis-UH, and the highest density of short-short entanglements within HDPE matrix, the formation of long-short entanglements between dis-UH and HDPE is facilitated, which results in successful homogenization process. In the contrary, the establishment of long-short entanglements in eUH/HDPE blends will require unwinding of the long-long entanglements, which holds a higher kinetic barrier compared to dis-UH/HDPE blends, leading to unsuccessful homogenization.

Simultaneous effects of capillary number, viscosity ratio, and contraction ratio on droplet dynamics in contraction microchannel

Abstract In droplet-based microfluidic systems, fluid properties, flow conditions, and channel geometry play crucial roles in the movement and manipulation of droplets. This study employs a three-dimensional numerical simulation method to investigate droplet dynamics in a contraction microchannel under the simultaneous influence of different factors, such as capillary number (Ca), viscosity ratio (λ), and contraction ratio (C). Specifically, a theoretical model is introduced for predicting the transition of droplets from trap to squeeze, and it is observed to be 〖Ca〗_I = f(C,λ). Meanwhile, droplet dynamics are investigated for the transition from squeeze to breakup for finding critical capillary number value (CaII). In addition, the critical viscosity ratio for the process from squeeze to breakup has been figured out by numerical results for a wide range of contraction ratios. Eventually, droplet dynamics including deformation, velocity ratio, and breakup during contraction microchannel are also quantitatively studied under the factors above.

Universal Correlation for Droplet Fragmentation in a Microfluidic T-Junction.

Despite extensive research on droplet dynamics at microfluidic T-junction, for different droplet lengths and Capillary numbers, there remains limited understanding of their dynamics at different viscosity ratio. In this study, we adopt a modeling framework in a three-dimensional (3D) configuration to numerically investigate the droplet dynamics as it passes through a symmetric T-junction with varying Capillary numbers, droplet lengths, and viscosity ratios. We present a 3D regime map for the first time to demarcate the droplet breakup and no breakup regimes. Herein, we propose a simple surface equation accounting for the critical Capillary number for breakup, in terms of viscosity ratio and dimensionless droplet length. The proposed universal relationship aligns well with experimental and computational findings from the existing literature. Furthermore, we reveal a new droplet breakup characteristic at high viscosity ratio and high Capillary number where the droplet spreads almost twice its initial value before splitting. Overall, this research provides comprehensive understanding of droplet dynamics at the T-junction and has significant implications for several related applications, including the large-scale synthesis of microdroplets using microchannel networks.

Modelling the effect of soluble surfactants on droplet deformation and breakup in simple shear flow

A hybrid lattice Boltzmann and finite difference method is applied to study the influence of soluble surfactants on droplet deformation and breakup in simple shear flow. First, the influence of bulk surfactant parameters on droplet deformation in two-dimensional shear flow is investigated, and the surfactant solubility is found to influence droplet deformation by changing average interface surfactant concentration and non-uniform effects induced by non-uniform interfacial tension and Marangoni forces. In addition, the droplet deformation first increases and then decreases with Biot number, increases significantly with adsorption number $k$ and decreases with Péclet number or adsorption depth; and among the parameters, $k$ is the most influential one. Then, we consider three-dimensional shear flow and investigate the roles of surfactants on droplet deformation and breakup for different capillary numbers and viscosity ratios. Results show that in the soluble case with $k=0.429$ , the droplet exhibits nearly the same deformation as in the insoluble case due to the balance between surfactant adsorption and desorption; upon increasing $k$ from 0.429 to 1, the average interface surfactant concentration is greatly enhanced, leading to significant increase in droplet deformation. The critical capillary number of droplet breakup $C{{a}_{cr}}$ is identified for varying viscosity ratios in clean, insoluble and soluble ( $k=0.429$ and 1) systems. As the viscosity ratio increases, $C{{a}_{cr}}$ first decreases and then increases rapidly in all systems. The addition of surfactants always favours droplet breakup, and increasing solubility or $k$ could further reduce $C{{a}_{cr}}$ by increasing average interface surfactant concentration and local surfactant concentration near the neck during the necking stage.

Bubble-induced entrainment at viscoplastic–Newtonian interfaces

The passage of single air bubbles through the horizontal interface between viscoplastic and Newtonian fluids, considering various combinations of densities and viscosities for the fluid layers, is studied computationally. The primary focus is on the quantity of liquid transferred from the lower layer (viscoplastic fluid) to the upper layer (Newtonian fluid) as a result of the bubble's ascent, a factor with significant implications for the turbidity of methane-emitting lakes and water bodies. The entrainment characteristics are observed to vary considerably with the bubble shape, within the lower layer and as the bubble approaches the interface. The results show that at Bond number $(Bo)>1$ and moderate Archimedes ( $Ar$ ), prolate-shaped bubbles crossing the interface undergo elongation in the direction of their poles. This elongation is further accentuated when the viscosity of upper layer is less than the plastic viscosity of the lower layer. The bubble is found to break up when leaving the lower layer, of a critical capillary number, $Ca_c \approx 5$ . The results show a significant reduction in the volume of entrainment compared with the Newtonian counterpart. This suggests disturbances caused by the rising bubble at the interface dissipate over a smaller region. Four distinct entrainment regimes are identified, mainly indicating the height to which the entrained fluid can be transported away from the interface. In contrast to Newtonian fluids, the volume of entrainment increases by decreasing the viscosity of the upper layer. Interestingly, the heavy viscoplastic fluid that has been dragged up into the light Newtonian fluid does not recede with time.

Geometric influence of width ratio and contraction ratio on droplet dynamics in microchannel using a 3D numerical simulation

AbstractMicrochannel geometry is an important factor in determining droplet dynamics in droplet‐based microfluidic systems, much like fluid properties and flow conditions. In this context, two important geometric parameters—the contraction ratio () and the width ratio ()—that are limited to particular value ranges are taken into consideration for evaluation. These parameters interact with the capillary number () and viscosity ratio () to affect different aspects of droplet migration and manipulation, such as trap and squeeze regimes. A theoretical model is proposed, and a three‐dimensional numerical simulation method is used in this work. This model predicts the change from trap to squeeze, which is caused by the interaction of the previously mentioned variables. Interestingly, an inverse correlation exists between the width ratio and the critical capillary number for this transition, which is determined as . Furthermore, the investigation explores the droplet elongation and velocity ratio during their passage through the microchannel. By matching input parameters with microchannel geometry, this information may be useful for the design of microfluidic systems, which would facilitate the careful control and manipulation of droplets.

Direct numerical simulations of microlayer formation during heterogeneous bubble nucleation

In this article, we present direct numerical simulation results for the expansion of spherical cap bubbles attached to a rigid wall due to a sudden drop in the ambient pressure. The critical pressure drop beyond which the bubble growth becomes unstable is found to match well with the predictions from classical theory of heterogeneous nucleation imposing a quasi-static bubble evolution. When the pressure drop is significantly higher than the critical value, a liquid microlayer appears between the bubble and the wall. In this regime, the interface outside the microlayer grows at an asymptotic velocity that can be predicted from the Rayleigh–Plesset equation, while the contact line evolves with another asymptotic velocity that scales with a visco-capillary velocity that obeys the Cox–Voinov law. In general, three distinctive regions can be distinguished: the region very close to the contact line where dynamics is governed by visco-capillary effects, an intermediate region controlled by inertio-viscous effects away from the contact line yet inside the viscous boundary layer, and the region outside the boundary layer dominated by inertial effects. The microlayer forms in a regime where the capillary effects are confined in a region much smaller than the viscous boundary layer thickness. In this regime, the global capillary number takes values much larger then the critical capillary number for bubble nucleation, and the microlayer height is controlled by viscous effects and not surface tension.

Dynamics of meniscus-bound particle clusters in extensional flow

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number Ca and meniscus volume V. Importantly, a critical capillary number Cacrit for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow.

Deformation and breakup of a ferrofluid droplet in shear flow under magnetic field

Effects of magnetic field applied perpendicular to a shear plane in shear flow on the deformation of a ferrofluid droplet are numerically investigated. The boundary integral method is employed to solve the two-phase Stokes flow under a uniform magnetic field. When the magnetic field is applied perpendicular to the shear plane, the deformation of the droplet in the shear plane decreases. The magnetic field causes the droplet to elongate in the y-direction, and its cross-sectional radius in shear plane decreases. Consequently, the apparent capillary number in the shear plane decreases, thereby suppressing the droplet deformation. Droplet breakup is also suppressed by imposing a magnetic field perpendicular to the shear plane, thereby increasing the critical capillary numbers. The critical capillary numbers for the magnetic Bond numbers Bo = 2.0 and 4.0 increase to approximately 110% and 130%, respectively, than those without magnetic field. Furthermore, an equation for the theoretical prediction of the droplet deformation under a magnetic field in shear flow is presented, which is based on the small deformation theory, the decrease in the cross-sectional radius, and the boundary conditions at the droplet interface. The theoretical prediction agrees well with the numerical results for the variation in the magnetic susceptibility of the droplet as well as the viscosity ratio between the external fluid and the ferrofluid droplet under a small deformation. The critical capillary numbers under a magnetic field can also be predicted by using the numerical results without a magnetic field.

Wetting boundary condition for three-dimensional curved geometries in lattice Boltzmann color-gradient model

A wetting boundary condition for handling contact line dynamics on three-dimensional curved geometries is developed in the lattice Boltzmann color-gradient framework. By combining the geometrical formation and the prediction-correction wetting scheme, the present wetting boundary condition is able to avoid the necessity to select an appropriate interface normal vector from its multiple solutions in the previous prediction-correction method. The effectiveness and accuracy of the wetting boundary condition are first validated by several benchmark cases, namely a droplet resting on a flat surface and on a solid sphere, and the spontaneous imbibition into a cylindrical tube. We then use the color-gradient model equipped with the developed wetting boundary condition to study the trapping behavior of a confined droplet in a microchannel with a cylindrical hole on the top surface, in which the effects of the hole radius and the droplet radius are identified for varying capillary numbers. Results show that the simulated critical capillary numbers, below which the droplet would be anchored by the hole, and the steady-state shapes of the anchored droplet generally match well with their theoretical solutions. The critical capillary number is found to decrease by either decreasing the hole radius or increasing the droplet radius, which is attributed to the weakened anchoring surface energy gradient and the enhanced driving force from outer flow, respectively. In addition, we show that the previous theoretical solutions are valid only when the initial droplet radius is greater than twice the height of the channel.

CO2-brine mass transfer patterns and interface dynamics under geological storage conditions

CO2 geological storage is a promising carbon negative technology with important application prospects. Dissolution trapping is a reliable method throughout the life cycle of a storage project, because it plays a significant role in minimizing risks. A comprehensive understanding of its mechanism is challenging due to the complex mass transfer process controlled by numerous physical and chemical factors, which needs to be clarified at different scales but still significantly limited in current research. Investigating CO2-brine interfacial mass transfer in real rock cores during imbibition provides valuable insights into the behavior of CO2 in geological formations. This study conducted a series of pore-scale CO2-brine interfacial mass transfer experiments during imbibition in three rock cores using an X-ray micro-computed tomography machine. The dissolution patterns and interface dynamics during the dissolving processes were discussed systematically. The results indicate that the overall slice-averaged and per-cluster mass transfer coefficient between CO2 and brine is in the order of 10−8 m/s, but its specific value depends on the dissolution patterns and bubble sizes. Various dissolution patterns were found in different rock cores. A core-length dissolution finger was formed in the Berea core, causing higher per-cluster mass transfer coefficients around the finger, while lower coefficients elsewhere in the dissolution experiments. The interfacial mass transfer process, coupled with gravity instability, induced remobilization of isolated CO2 bubbles at a much lower capillary number than the critical capillary number. The remobilization of CO2 bubbles can even occur at single-pore scale. CO2 remobilization also created a phenomenon similar to intermittent pathway flow. Interface dynamics of CO2 dissolving processes were revealed for the first time, giving rise to non-uniform dissolutions in CO2 singlets, ganglia, and clusters, respectively.

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

The behavior of a droplet under shear flow in a confined channel is studied numerically using a multi-phase smoothed particle hydrodynamics (SPH) method. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.

The Surfactant Role on a Droplet Passing through a Constricted Microchannel in a Pressure-Driven Flow: A Lattice Boltzmann Study.

The role of surfactants in the flow of a droplet driven by a pressure gradient through a constricted microchannel is simulated by using our recently developed lattice Boltzmann method. We first study the surfactant role on a droplet flowing through a microchannel with a shrunken square section under different surfactant concentrations and capillary numbers (i.e., imposed pressure gradients). As the surfactant concentration increases, the droplet flow regime first changes from the flow regime I of the droplet getting stuck at the entrance of the constricted channel to the flow regime II of the droplet flowing through the constricted channel with breakup, and then to the flow regime III of the droplet flowing through the constricted channel without breakup. As the capillary number increases, the surfactant role on the number of mother droplets breaking up and the time of mother droplets completely flowing through the constricted section tend to decrease, suggesting that the surfactant effects are gradually weakened. Then, a phase diagram describing how the surfactant concentration and capillary number affect the droplet flow regime is presented. As the surfactant concentration increases, the critical capillary number that distinguishes droplet flow regimes I from II gradually decreases, while the critical capillary number that distinguishes droplet flow regimes II from III first increases and then decreases.

Understanding Deformation and Breakup Tendency of Shear-Thinning Viscoelastic Drops in Constricted Microchannels.

The study of drop deformation in response to various stresses has long piqued the interest of several academics. The deformation behavior of cells, drug carriers, and even drug particles moving via microcapillaries inside the human body can be modeled using a viscoelastic drop model. A drop breakup study can also provide better design guidance for nanocarriers that can deliver on-demand burst drug releases at specific cancer sites. Thus, we attempted to investigate the deformation and breakup of a shear-thinning finitely extensible nonlinear elastic-peterlin (FENE-P) drop moving through the constricted microchannel. The computational simulation suggested that drop deformation and breakup can be manipulated by varying of parameters like channel confinement, Deborah number, solvent viscosity ratio, viscosity ratio, and capillary number. We attempted to find the critical capillary number for initiation of drop breakup. Observations from present study will give valuable insights into deformation and breakup patterns of drug carriers inside constricted microcapillaries. The simulations of the two-phase viscoelastic drop─Newtonian matrix system were performed on an open-source solver, Basilisk.

Flow patterns and dynamic mechanisms of immiscible fluids in cross junctions with different aspect ratios

The flow patterns of immiscible liquids in microscale cross junctions are experimentally studied and the influencing factors including the capillary number (3 × 10−4–6 × 10−1), flow rate ratio (0.004–60), viscosity ratio (0.04–2.8), and channel aspect ratio (1/3–1) are systematically analyzed. Evolutions of the interfacial morphologies in different flow patterns are discussed with the aid of force analysis. In the droplet group, two different breakup modes of the liquid thread are found with the symmetric mode for squeezing and the asymmetric mode for dripping, which are divided by a critical capillary number around 0.01. Two different physical models for constructing the scaling law of the droplet length are compared over large ranges of flow parameters and the universal scaling law is valid to identify the transitional boundary between squeezing and dripping regimes. In the jet group, the jet width in different channels is compared to the theoretical prediction. A detailed comparison between the experimental results in jetting and the linear instability theory is further conducted and the reason for the polydispersity of the droplet size in widening jetting is found. Finally, the flow pattern maps are built using dimensionless parameters in both the global terms and the local terms. In contrast, the local dimensionless parameters are confirmed to show a better performance in unifying the transitional boundary between two groups of flow patterns. The obtained results should be useful for the further understanding of the dynamic mechanisms of the microscale multiphase flow.

Electric-field-controlled deformation and spheroidization of compound droplet in an extensional flow

A 3-dimensional numerical model is developed by employing the electric current model and the phase-field method to investigate the electric-field-mediated compound droplet deformation and spheroidization in an extensional flow field (EFF). Based on this model, the detailed deformation morphologies of the compound droplet under different electrophysical properties are presented and the underlying electrohydrodynamics are clarified. Furthermore, the regime diagrams for quantificationally identifying different droplet deformation characteristics are summarized. In particular, the quantitative electrohydrodynamic criterion is obtained for achieving the droplet spheroidization in an EFF via the active electric field (EF) regulation. It is found that by applying a proper EF, the hydrodynamic force imposed by the EFF on the compound droplet and the flow-field-induced morphology deformation can be completely counterweighted. The deformation types and degrees of the compound droplet are determined by the fluids’ electrophysical parameters (especially the conductivity ratio R01 and permittivity ratio S01), EFF strength, and EF strength. Within the current research scope, the compound droplet can be restored to a spherical shape only when R01S01>1. Specifically, under a proper R01S01 (7≤ R01S01≤10 in the current simulation), the changing rate of the deformation of the outer droplet and inner droplet can match exactly and the two droplets can reach a spherical shape (i.e., S-S shape) simultaneously. Furthermore, the critical electric capillary number (CaE) for the compound droplet spheroidization is almost linearly related to the capillary number (Ca), which can be expressed as CaE=kCa. The factor k decreases with an increasing R01S01, so a larger R01S01 helps the compound droplet maintain its spherical shape.

Dip coating of viscous granular suspensions

A solid substrate withdrawn from a liquid bath is coated with a uniform thickness given by the Landau–Levich–Derjaguin (LLD) law. If the bath is a suspension of neutrally buoyant particles, the liquid coating can entrain particles in a process known as capillary filtration that only depends on the capillary number Ca. Experiments were performed using a custom-built dip coating apparatus and gravimetry techniques. The working liquids were monodisperse and bidisperse suspensions with larger particle diameters and higher liquid viscosity than previously reported. The single particle entrainment point for monodisperse suspensions agrees well with the critical capillary number predicted in prior literature. Bidisperse suspensions exhibit active filtration regions where only the smallest particles are entrained with the range of Ca for active filtration consistent with reported models. These experimental results both validate and enhance our understanding of capillary filtration by exploring larger particle-sized granular suspensions of higher viscosity solutions, as relevant to applications in construction, medical care, personal care products, and food science.

Deformation and breakup behaviors of a Giesekus viscoelastic droplet in Newtonian shear flow

The deformation and breakup of a Giesekus viscoelastic droplet suspended in a Newtonian matrix under simple shear flow is investigated through a lattice Boltzmann method, which uses the color-gradient model for immiscible two-phase flows while coupling a lattice advection-diffusion scheme for the Giesekus constitutive equation. The influence of the Deborah number (De) and shear-thinning mobility parameter (α) of the droplet is first explored for relatively low capillary numbers (Ca). The transient overshoot is observed before the deformation reaches the steady state, and the overshoot generally increases with De but decreases with α. With the increase of De, the steady-state deformation parameter first decreases and then increases, which is attributed to two opposite effects on the elastic force, namely the promoting effect from the increased polymer extension and the inhibiting effect caused by the deviation of the location where the maximum elastic force occurs from the droplet tips. The droplet inclination angle varies little with α but increases with De, where the latter can be explained as an increased vertical component of viscous and elastic forces in the tip regions. Upon increasing α, the steady-state deformation parameter becomes higher due to the reduced elastic force at the droplet tips. In addition, the phase diagrams of Ca-De and Ca-α are presented in which the critical capillary number Cacr characterizing the droplet breakup can be identified. It is found that Cacr varies non-monotonically with De, while Cacr is not very sensitive to α.

Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow

The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ( $Ca$ ), Weissenberg number ( $Wi$ ) and solvent viscosity ratio ( $\beta$ ). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$ , or by increasing $Wi$ or decreasing $\beta$ , where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $\beta$ , and the inhibiting effect strengthens with an increase of $Ca$ . Decreasing $\beta$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$ , and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $\beta$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$ . The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.