arXiv subjects

Shubhadeep Mandal

Publications and source records attributed to Shubhadeep Mandal.

At least 19 recordsLinked to original sources

arXiv2026

Vortex Dynamics During Pinch-off of Micro-Droplets

Micro-droplets are extensively used in chemical, biological, and medical research, primarily for conducting various tests on samples, including living organisms, using a microfluidic framework. Recent studies have shown that the physiology of bacteria can be significantly altered when subjected to shear and/or extensional stresses. With this motivation, we perform experiments to understand the vortex dynamics involved during the pinch-off process in a cross flow droplet generator, using particle image velocimetry (PIV) to visualize the vortical structures and to quantitatively measure the associated stresses developed inside droplets. The process of pinching off inherently leads to bi-directional acceleration of fluid in the rapidly thinning capillary bridge, resulting in a vortex in the separated droplet as well as in the retracting ligament. We propose scaling laws for the vortical flow inside the droplet post pinch-off and predict the maximum circulation production inside droplet. Further, we discuss the vortex dynamics inside the droplet, the retracting ligament and the advancing ligament and examine the stress fields associated with this transient phenomenon.

physics.flu-dyn↗

arXiv2026

Rheotaxis of microswimmers in colloid-laden channel flow

Microswimmers are often found in heterogeneous and crowded environments within narrow conduits under external flow conditions, enabling them to perform interesting translational and rotational maneuvers, such as swimming in the upstream direction, following walls, and oscillatory motion. Studying such systems helps us understand the motility behaviors of microswimmers (pushers, pullers, or neutrals) and develop applications such as targeted drug delivery. To study the motion of microswimmers in a channel flow with the presence of hard, monodisperse spherical colloids, we adopted the spherical squirmer model to represent the microswimmers, along with a mesoscale simulation framework, multi-particle collision dynamics (MPCD), to represent the background fluid. In the absence of colloids, a squirmer in a microchannel flow develops an increased probability of moving away from the walls and oscillates between the walls as the flow speed increases compared to the squirmer speed, with a dominant upstream orientation near the walls. However, the presence of the colloids makes the pusher swim towards the center of the channel and upstream direction, and the puller swim away from the center of the channel at low flow speeds. At high flow speeds, the flow carries all the squirmers, resulting in a dominant upstream direction in the channel center. We observe that this leads to a decrease in the local velocity of the squirmer in the flow direction for pusher, neutral, and puller-type squirmers. We also observe that, for a constant colloidal packing fraction, the local velocity magnitude of the puller along the flow direction is less than that of the pusher.

cond-mat.soft↗

arXiv2024

Flow fields around active droplets squeezing through tight confinements

Biological microswimmers, like euglena, deform their body shape to swim through tight confinements having length scales comparable to the microswimmer length scale. Recently, it was shown that self-propelling active droplets can also squeeze through tight microconfinements by elongating their shape. However, the evolution of the hydrodynamic signature, or the velocity field, generated by the active droplet, as it deforms its shape to swim through increasingly tight microconfinements, has remained scarcely studied. Using high-resolution fluorescence microscopy and $μ$-Particle Image Velocimetry (PIV) analysis, we show here that as the swimming active droplet deforms from a spherical shape to a `stadium'-like shape, and eventually to an elongated `capsule'-like shape in increasingly tighter microchannels, its hydrodynamic signature changes from a `pusher'-like velocity field to a `puller'-like velocity field, and finally to an asymmetric velocity field. We characterize such alterations in the active droplet dynamics using the distributions of the local velocity magnitude, axial and transverse components of the local flow velocity, vorticity, and the filled micelle concentration. Finally, we use finite-element based numerical simulations to explain the aforementioned evolution of the velocity field stemming from the underlying physico-chemical hydrodynamics in the presence of a thin lubrication film between the swimming active droplet and the tight microconfinement walls. The present work provides a comprehensive understanding of the chemo-hydrodynamic characteristics of active droplets navigating extreme confined spaces, which can be beneficial for many autonomous cargo-delivery applications.

cond-mat.soft↗

arXiv2019

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 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 new 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 toque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field.

cond-mat.soft↗

arXiv2019

Electrorheology of a dilute emulsion of surfactant-covered drops

The effects of surfactant coating on a deformable viscous drop under the combined action of a shear flow and a uniform electric field, are investigated by solving the coupled equations of electrostatics, fluid flow and surfactant transport. Employing a comprehensive three-dimensional solution technique, the non-Newtonian shearing response of the bulk emulsion is analyzed in the dilute suspension regime. The present results reveal that the surfactant non-uniformity creates significant alterations in the flow disturbance around the drop, thereby influencing the viscous dissipation from the flowing emulsion. This, in effect, triggers changes in the bulk shear viscosity. It is striking to observe that the balance between electrical and hydrodynamic stresses is affected in such a way that surface tension gradient on the drop surface vanishes for some specific shear rates and the corresponding effective change in the bulk viscosity becomes negligible too. This critical condition hugely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also the physical mechanisms of charge convection of surface deformation play their role in determining this critical shear rate. The charge convection instigated shear thinning or shear thickening behavior of the emulsion gets reversed due to a coupled interaction of the charge convection and Marangoni stress. In addition, the electrically created anisotropic normal stresses in the bulk rheology, get reduced due to the presence of surfactants, especially when the drop viscosity is much lesser than the continuous fluid. A thorough description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion, may provide a fundamental understanding of a more complex emulsion system.

physics.flu-dyn↗

arXiv2018

Electrohydrodynamic settling of drop in uniform electric field at low and moderate Reynolds numbers

Dynamics of a liquid drop falling through a quiescent medium of another liquid is investigated in external uniform electric field. The electrohydrodynamics of a drop is governed by inherent deformability of the drop (defined by capillary number), the electric field strength (defined by Masson number) and the surface charge convection (quantified by electric Reynolds number). Surface charge convection generates nonlinearilty in a electrohydrodynamics problem by coupling the electric field and flow field. In Stokes limit, most existing theoretical models either considered weak charge convection or weak electric field to solve the problem. In the present work, gravitational settling of the drop is investigated analytically and numerically in Stokes limit considering significant electric field strength and surface charge convection. Drop deformation accurate upto higher order is calculated analytically in small deformation regime. Our theoretical results show excellent agreement with the numerical and shows improvement over previous theoretical models. For drops falling with moderate Reynolds number, the effect of Masson number on transient drop dynamics is studied for (i) perfect dielectric drop in perfect dielectric medium (ii) leaky dielectric drop in the leaky dielectric medium. For the latter case transient deformation and velocity obtained for significant charge convection is compared with that of absence in charge convection which is the novelty of our study. The present study suggests that for both the regimes, surface charge convection tends to increase or decrease the settling speed depending upon the ratios of electrical properties. Notably, in the inertial regime, deformation and velocity are seen to be altered prominently in the existence of significant charge convection.

physics.flu-dyn↗

arXiv2018

Electrohydrodynamic migration of a surfactant-coated deformable drop in Poiseuielle flow

In this study we attempt to explore the consequences of surfactant coating on the electrohydrodynamic manipulation of a drop motion in a plane Poiseuielle flow. In addition we consider bulk insoluble surfactants and a linear dependency of the surface tension on the surfactant concentration. Subsequently a double asymptotic perturbation method is used in terms of small electric Reynolds number and capillary number in the limit of a diffusion-dominated surfactant transport mechanism. Also going beyond the widely employed axisymmetric framework, the coupled system of governing differential equations in three dimensions are then solved by adopting the `generalized Lamb solution technique'. The expressions of key variables suggest that the flow curvature of the external flow, the electric field effects and the surfactant effects are coupled in a non-trivial manner, well beyond a linear superposition. A careful investigation shows that surfactant-induced Marangoni stresses interacts with the electrohydrodynamic stresses in a highly coupled fashion. Owing to this, under different combinations of electrical conductivity and permittivity ratios, the Mason number and the applied electric field direction, the surfactants affect differently on the longitudinal as well as cross-stream migration velocity of the drop. The present results may be of utmost importance in providing a deep insight to the underlying complex physical mechanisms. Most importantly the ability of surfactants in selectively controlling the drop motion in different directions, makes them suitable for achieving a new degree of freedom in the electrical actuation of droplets in the microfluidic devices.

physics.flu-dyn↗

arXiv2018

Electric field-induced droplet deflection in microconfined flow

The deflection of liquid droplet driven through a liquid medium under the combined action of transverse electric field and pressure driven flow has been studied in the present analysis. The present experimental and numerical analysis identifies the domain confinement as a key parameter for transverse migration of the droplets in the presence of a transverse electric field. Notably, the droplet migrates at a faster rate in highly confined domain. The present analysis also illustrates that the droplet can migrate toward the wall electrode or centerline depending on the physical and electrical properties of the system. The achieved steady state transverse position is found independent of its initial positions.

physics.flu-dyn↗

arXiv2018

Effect of uniform electric field on the deformation of a 2D liquid droplet in confined simple shear flow

In the present study, we have studied the electro-hydrodynamic of a physical system where a Newtonian dielectric liquid column or droplet suspended in another Newtonian dielectric liquid medium in presence of a simple shear flow. Taking both the phases as leaky dielectric and perfect dielectric in to consideration, we have performed 2D numerical solution for capturing the essential features of droplet deformation in between the parallel plate configuration. For a perfect dielectric system, this study shows that the deformation characteristic follows a monotonic as well as non-monotonic variation with domain confinement depending on the values of electrical permittivity ratio of the droplet and the surrounding fluid. For a leaky-dielectric system, presence of small conductivity further alters the deformation characteristic and it is happened that, at low electric field strength, the deformation increases with confinement monotonically. On contrary, deformation parameter shows non-monotonic variation with the domain confinement at higher electric field strength. Furthermore, in confined domain, the transient evolution of the deformation parameter is also markedly altered by the electric field strength in terms of steady state value of the deformation parameter and steady state time. Finally, the present analysis shows that the domain confinement significantly augment the deformation parameter in presence of electric field that leads to possible droplet break up phenomenon. From the present study, it is worthy to mention that domain confinement can be used to modulate the droplet morphology that has potential applications in modern-days droplet-based micro-fluidic devices.

physics.flu-dyn↗

arXiv2018

Sedimentation of a surfactant-laden drop under the influence of an electric field

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the the combined effect electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in internal flow pattern. Such effects further result in retardation of drop settling velocity, which would have otherwise increased due to the influence of charge convection. For highly mobile surfactants (high Peclet number limit), the drop surface becomes immobilized and the charge convection effect gets completely eliminated. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the 'tip stretching' effect on the flow field. As a result, the drop deformation gets intensified with increment in sensitivity of surface tension to the local surfactant concentration. Consequently, for oblate type of deformation the elevated drag force causes further reduction in velocity. Owing to similar reasons, prolate drops experience lesser drag and settles faster than the surfactant-free case. In addition to this, with increased sensitivity of interfacial tension on the surfactant concentration, the asymmetric deformation about the equator gets suppressed.

physics.flu-dyn↗

arXiv2017

Complex Fluid-Fluid Interface may Non Trivially Dictate Droplet Deformation in an Incipient Flow

The present study theoretically predicts the effect of interfacial viscosity on the deformation of a compound drop as well as on the bulk rheology. The system at hand comprises of a dilute emulsion of concentric compound drops, laden with surfactants and suspended in a linear flow. Two types of linear flows are considered in this study, namely, a uniaxial extensional flow and a simple shear flow. Presence of surfactants along the drop surface leads to the generation of an interfacial viscosity, which is different from the bulk. This interfacial viscosity generates a viscous drag that along with bulk flow-induced nonuniform surfactant distribution on the drop surface significantly alters drop dynamics. For the present study an asymptotic approach is used to solve the flow field under the limiting case of diffusion-dominated-surfactant transport. Assuming the surfactants to be bulk-insoluble and negligible inertia to be present in fluid flow, it is shown that presence of interfacial viscosity reduces the deformation of a compound drop and enhances the stability of a dilute double emulsion. At the same time the effective viscosity of the emulsion also increases with rise in interfacial viscosity. For large values of interfacial dilatational viscosity the drop deformation is seen to increase and hence the stability of the double emulsion is questionable.

physics.flu-dyn↗

arXiv2017

Effect of Marangoni stress on the bulk rheology of a dilute emulsion of surfactant-laden deformable droplets in linear flows

In the present study we analytically investigate the deformation and bulk rheology of a dilute emulsion of surfactant-laden droplets suspended in a linear flow. We use an asymptotic approach to predict the effect of surfactant distribution on the deformation of a single droplet as well as the effective shear and extensional viscosity for the dilute emulsion. The non-uniform distribution of surfactants due to the bulk flow results in the generation of a Marangoni stress which affects both the deformation as well as the bulk rheology of the suspension. The present analysis is done for the limiting case when the surfactant transport is dominated by the surface diffusion relative to surface convection. As an example, we have used two commonly encountered bulk flows, namely, uniaxial extensional flow and simple shear flow. With the assumption of negligible inertial forces present in either of the phases, we are able to show that both the surfactant concentration on the droplet surface as well as the ratio of viscosity of the droplet phase with respect to the suspending fluid has a significant effect on the droplet deformation as well as the bulk rheology. It is seen that increase in the non-uniformity in surfactant distribution on the droplet surface results in a higher droplet deformation and a higher effective viscosity for either of linear flows considered. For the case of simple shear flow, surfactant distribution is found to have no effect on the inclination angle, however, a higher viscosity ratio predicts the droplet to be more aligned towards the direction of flow.

physics.flu-dyn↗

arXiv2017

Cross-stream migration characteristics of a deformable droplet in a non-isothermal Poiseuille Flow through Microfluidic Channel

The migration characteristics of a suspended deformable droplet in a parallel plate microchannel is studied, both analytically and numerically, under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. Any predefined transverse position in the micro channel can be attained by the droplet depending on the applied temperature gradient in the cross-stream direction or how small the droplet is with respect to the channel width. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia or thermal convection of the fluid in either of the phases. To obtain a numerical solution, we use the conservative level set method. Variation of temperature in the flow field causes a jump in the tangential component of stress at the droplet interface. This jump in stress component, which is the thermal Marangoni stress, is an important factor that controls the trajectory of the droplet. The direction of cross-stream migration of the droplet is decided by the magnitude of the critical Marangoni stress, corresponding to which the droplet remains stationary. In order to analyze practical microfluidic setup, we do numerical simulations where we consider wall effects as well as the effect of thermal convection and finite shape deformation on the cross-stream migration of the droplet.

physics.flu-dyn↗

arXiv2017

Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow

The motion of a viscous deformable droplet suspended in an unbounded Poiseuille flow in the presence of bulk-insoluble surfactants is studied analytically. Assuming the convective transport of fluid and heat to be negligible, we perform a small-deformation perturbation analysis to obtain the droplet migration velocity. The droplet dynamics strongly depends on the distribution of surfactants along the droplet interface, which is governed by the relative strength of convective transport of surfactants as compared with the diffusive transport of surfactants. The present study is focused on the following two limits: (i) when the surfactant transport is dominated by surface diffusion, and (ii) when the surfactant transport is dominated by surface convection. In the first limiting case, it is seen that the axial velocity of the droplet decreases with increase in the advection of the surfactants along the surface. The variation of cross-stream migration velocity, on the other hand, is analyzed over three different regimes based on the ratio of the viscosity of the droplet phase to that of the carrier phase. In the first regime the migration velocity decreases with increase in surface advection of the surfactants although there is no change in direction of droplet migration. For the second regime, the direction of the cross-stream migration of the droplet changes depending on different parameters. In the third regime, the migration velocity is merely affected by any change in the surfactant distribution. For the other limit of higher surface advection in comparison to surface diffusion of the surfactants, the axial velocity of the droplet is found to be independent of the surfactant distribution. However, the cross-stream velocity is found to decrease with increase in non-uniformity in surfactant distribution.

physics.flu-dyn↗

arXiv2017

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. 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.

physics.flu-dyn↗

arXiv2017

Thermocapillary effect on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The present study is focused on two limiting situations of surfactant transport: (i) small surface Peclet number, and (ii) high surface Peclet number. Thermocapillary-induced Marangoni stress, strength of which relative to viscous stress is represented by thermal Marangoni number, has strong influence on the distribution of surfactant on the droplet surface. Temperature field not only affects the axial velocity of the droplet but also has significant effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of Poiseuille flow, the droplet migrates towards the flow centerline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centerline or away from it. Present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centerline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow for which droplet always moves towards the flow centerline.

physics.flu-dyn↗

arXiv2016

Migration of a surfactant-laden droplet in non-isothermal Poiseuille flow

The motion of a surfactant-laden viscous droplet in the presence of background non-isothermal Poiseuille flow is studied analytically and numerically. Specifically, the effect of interfacial Marangoni stress due to non-uniform distribution of surfactants and temperature at the droplet interface on the velocity and direction of motion of the droplet along the centerline of imposed Poiseuille flow is investigated in the presence of linearly varying temperature field. In the absence of thermal convection, fluid inertia and shape deformation, the interfacial transport of bulk-insoluble surfactants is governed by the surface Peclet number which represents the relative strength of the advective transport of surfactant over the diffusive transport. We obtain analytical solution for small and large values of the surface Peclet number. Numerical solution is obtained for arbitrary surface Peclet number, which compares well with the analytical solution. Depending on the direction of temperature gradient with respect to the imposed Poiseuille flow, the surfactant-induced Marangoni stress affects the droplet velocity differently. When the imposed temperature increases in the direction of imposed Poiseuille flow, surfactants retard the droplet motion as compared with a surfactant-free droplet. However, when the imposed temperature decreases in the direction of imposed Poiseuille flow, presence of surfactants may increase or decrease the magnitude of droplet velocity depending on the relevant governing parameters. Further, for particular values of governing parameters, we observe change in direction of droplet motion due to presence of surfactants, which may bear significant consequences in the design of droplet based microfluidic systems.

physics.flu-dyn↗

arXiv2015

Droplet migration characteristics in confined oscillatory microflows

We analyze the migration characteristics of a droplet in an oscillatory flow field in a parallel plate micro-confinement. Using phase filed 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 in 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 by 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.

physics.flu-dyn↗