Multiparticle collision dynamics simulations of a squirmer in a nematic fluid.

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer's speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.

Confinement effect on electrically induced dynamics of a droplet in shear flow.

Deformation and breakup of droplets in confined shear flows have been attracting increasing attention from the research community over the past few years, as attributable to their implications in microfluidics and emulsion processing. Reported results in this regard have demonstrated that the primary effect of confinement happens to be the inception of complex oscillating transients, monotonic variation of droplet deformation, and droplet stabilization against breakup, as attributable to wall-induced distortion of the flow field. In sharp contrast to these reported findings, here, we show that a nonintuitive nonmonotonic droplet deformation may occur in a confined shear flow, under the influence of an external electric field. In addition, we demonstrate that the orientation angle of a droplet may either increase or decrease with the domain confinement under the influence of an electric field, whereas the same trivially decreases with the increase in degree of confinement in the absence of any electrical effects. Unlike the typical oscillatory transients observed in microconfined shear flows, we further bring out the possibility of an electrohydrodynamically induced dampening effect in the oscillation characteristics, as governed by a specific regime of the relevant dimensionless electrical parameters. Our results reveal that instead of arresting droplet deformation, the unique hydrodynamics of microconfined shear flow may augment the tendency of droplet breakup, and is likely to alter the droplet breakup mode from midpoint pinching to edge pinching at high electric field strength. These results may bear far reaching implications in a wide variety of applications ranging from the processing of emulsions to droplet based microfluidic technology.

Multiparticle collision dynamics for tensorial nematodynamics.

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.

Transient electroosmosis of a Maxwell fluid in a rotating microchannel.

The transient electroosmotic flow of Maxwell fluid in a rotating microchannel is investigated both analytically and numerically. We bring out the complex dynamics of the flow during the transience due to the combination of rotation and rheological effects. We show the regimes of operation under which our analysis holds the most significance. We also shed some light on the volumetric flow rate characteristics as dictated by the underlying flow physics. Mainly we show and analyze the various regimes of operation under which viscoelastic effects actuated by electroosmotic forcing dominate over Coriolis forces and vice versa, which has not been studied before. We also observe that the analytical solution compares well with the numerical solution. We believe that the results from the present study could potentially have far reaching applications in bio-fluidic microsystems where fluids such as blood, mucus and saliva may be involved.

Capillary transport of two immiscible fluids in presence of electroviscous retardation.

The transport of two immiscible electrolytes through a narrow confinement whose walls bear a finite surface potential is analyzed through a lumped model by considering the influence of a regulatory self-induced axial electric field, termed as streaming potential. The presence of a surface charge on the channel walls culminates in the aqueous solutions carrying a net charge so as to make the overall system (channel and fluid) electrically neutral. The advection due to pressure driven flow or capillarity in the absence of any externally imposed electric field causes a preferential transport of net charged species. Thus, in order to render a net zero current through the system, there is an induced electric field which also retards the flow as a consequence of the force acting on the charged segments of fluid due to the streaming electric field. It is shown through a lumped model that for the situation of two distinct segments of fluids, the rate of front penetration into the capillary is strongly dependent on the relative conductivities of the two fluids. The streaming electric field evolves in accordance to the net conductivity of the channel and is responsible for dynamic changes in the retarding influence on the segments of fluid.

Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop.

The dielectrophoretic motion and shape deformation of a Newtonian liquid drop in an otherwise quiescent Newtonian liquid medium in the presence of an axisymmetric nonuniform dc electric field consisting of uniform and quadrupole components is investigated. The theory put forward by Feng [J. Q. Feng, Phys. Rev. E 54, 4438 (1996)10.1103/PhysRevE.54.4438] is generalized by incorporating the following two nonlinear effects-surface charge convection and shape deformation-towards determining the drop velocity. This two-way coupled moving boundary problem is solved analytically by considering small values of electric Reynolds number (ratio of charge relaxation time scale to the convection time scale) and electric capillary number (ratio of electrical stress to the surface tension) under the framework of the leaky dielectric model. We focus on investigating the effects of charge convection and shape deformation for different drop-medium combinations. A perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium always deforms to a prolate shape and this kind of shape deformation always augments the dielectrophoretic drop velocity. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the shape deformation leads to either increase (for prolate shape) or decrease (for oblate shape) in the dielectrophoretic drop velocity. Both surface charge convection and shape deformation affect the drop motion for leaky dielectric drops. The combined effect of these can significantly increase or decrease the dielectrophoretic drop velocity depending on the electrohydrodynamic properties of both the liquids and the relative strength of the electric Reynolds number and electric capillary number. Finally, comparison with the existing experiments reveals better agreement with the present theory.

Droplet migration characteristics in confined oscillatory microflows.

We analyze the migration characteristics of a droplet in an oscillatory flow field in a parallel plate microconfinement. Using phase field formalism, we capture the dynamical evolution of the droplet over a wide range of the frequency of the imposed oscillation in the flow field, drop size relative to the channel gap, and the capillary number. The latter two factors imply the contribution of droplet deformability, commonly considered in the study of droplet migration under steady shear flow conditions. We show that the imposed oscillation brings an additional time complexity in the droplet movement, realized through temporally varying drop shape, flow direction, and the inertial response of the droplet. As a consequence, we observe a spatially complicated pathway of the droplet along the transverse direction, in sharp contrast to the smooth migration under a similar yet steady shear flow condition. Intuitively, the longitudinal component of the droplet movement is in tandem with the flow continuity and evolves with time at the same frequency as that of the imposed oscillation, although with an amplitude decreasing with the frequency. The time complexity of the transverse component of the movement pattern, however, cannot be rationalized through such intuitive arguments. Towards bringing out the underlying physics, we further endeavor in a reciprocal identity based analysis. Following this approach, we unveil the time complexities of the droplet movement, which appear to be sufficient to rationalize the complex movement patterns observed through the comprehensive simulation studies. These results can be of profound importance in designing droplet based microfluidic systems in an oscillatory flow environment.

Streaming potential-modulated capillary filling dynamics of immiscible fluids.

The pressure driven transport of two immiscible electrolytes in a narrow channel with prescribed surface potential (zeta potential) is considered under the influence of a flow-induced electric field. The latter consideration is non-trivially and fundamentally different from the problem of electric field-driven motion (electroosmosis) of two immiscible electrolytes in a channel in a sense that in the former case, the genesis of the induced electric field, termed as streaming potential, is the advection of ions in the absence of any external electric field. As the flow occurs, one fluid displaces the other. Consequently, in cases where the conductivities of the two fluids differ, imbibition dynamically alters the net conductivity of the channel. We emphasize, through numerical simulations, that the alteration in the net conductivity has a significant impact on the contact line dynamics and the concomitant induced streaming potential. The results presented herein are expected to shed light on multiphase electrokinetics devices.

Effect of interfacial slip on the cross-stream migration of a drop in an unbounded Poiseuille flow.

We analyze the motion and deformation of a buoyant drop suspended in an unbounded fluid which is undergoing a quadratic shearing flow at small Reynolds number in the presence of slip at the interface of the drop. The boundary condition at the interface is accounted for by means of a simple Navier slip condition. Expressions for the velocity and the shape deformation of the drop are derived considering small but finite interface deformation, and results are presented for the specific cases of sedimentation, shear flow, and Poiseuille flow with previously reported results as the limiting cases of our general expressions. The presence of interfacial slip is found to markedly affect axial as well as cross-stream migration velocity of the drop in Poiseuille flow. The effect of slip is more prominent for drops with larger viscosity wherein the drop velocity increases. The presence of significant interface slippage always leads to migration of a deformed drop towards the centerline of the channel for any drop-to-medium viscosity ratio, which is in contrast to the case of no slip at the interface, which allows drop migration towards or away from the centerline depending on the viscosity ratio. We obtain the effect of slip on the cross-stream migration time scale, which quantifies the time required to reach a final steady radial position in the channel. The presence of slip at the drop interface leads to a decrease in the cross-stream migration time scale, which further results in faster motion of the drop in the cross-stream direction. Gravity in the presence of Poiseuille flow is shown to affect not only the axial motion, but also the cross-stream migration velocity of the drop; interfacial slip always increases the drop velocities.

Transient dynamics of confined liquid drops in a uniform electric field.

We analyze the effect of confinement on the transient dynamics of liquid drops, suspended in another immiscible liquid medium, under the influence of an externally applied uniform dc electric field. For our analysis, we adhere to an analytical framework conforming to a Newtonian-leaky-dielectric liquid model in the Stokes flow regime, under the small deformation approximation. We characterize the transient relaxation of the drop shape towards its asymptotic configuration, attributed by the combined confluence of the charge-relaxation time scale and the intrinsic shape-relaxation time scale. While the former appears due to the charge accumulation process on the drop surface over a finite interval of time, the genesis of the latter is found to be intrinsic to the hydrodynamic situation under consideration. In an unbounded condition, the intrinsic shape-relaxation time scale is strongly governed by the viscosity ratio, defined as the ratio of dynamic viscosities of the droplet and the background liquid. However, when the wall effects are brought into consideration, the combined influence of the relative extent of the confinement and the intrinsic viscosity effects, acting in tandem, alter this time scale in a rather complicated and nontrivial manner. We reveal that the presence of confinement may dramatically increase the effective viscosity ratio that could have otherwise been required in an unconfined domain to realize identical time-relaxation characteristics. We also bring out the alterations in the streamline patterns because of the combinations of transient and confinement effects. Thus, our results reveal that the extent of fluidic confinement may provide an elegant alternative towards manipulating the transient dynamics of liquid drops in the presence of an externally applied electric field, bearing far-ranging consequences towards the design and functionalities of several modern-day microfluidic applications.