We numerically investigate the hydrodynamics of a compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core-shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. We also find that the migration of the compound drop affects the eccentricity of the core significantly. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in stable state pushes the compound drop towards the walls, and the revolving core in limit-cycle state makes the compound drop to oscillate at its equilibrium position. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and increase in any parameter sufficiently causes a transition from limit-cycle state to stable state.
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…
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…
Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are seldom explored. Herein, we report our study on understanding the influ…
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 fo…
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 o…
In the present study, we investigate the cross-stream migration of a deformable droplet suspended in a non-isothermal Poiseuille flow in the presence of bulk-insoluble surfactants. Owing to the non-linearity present in the system of governing equations, an asymptotic approach is adopted, in an effort to capture the intricate and non-trivial coupling between the various influencing parameters. With the assumption of negligible inertia in fluid flow and convective transport of thermal energy, we obtain the droplet migration velocity through small-deformation perturbation analysis for two differe…
Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop is modelled by a cloud of many non-touching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the {\sc hydromultipole} numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynam…
The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer de…
The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. In contrast to other shear flows, PPF has a number of different coherent states that are relevant for the transition. We here discuss the different states, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux, the ones for constant pressure dr…
We investigate the motion of a spherical drop in a general quadratic flow acted upon by an arbitrarily oriented externally applied uniform electric field. The drop and media are considered to be leaky dielectrics. The flow field affects the distribution of charges on the drop surface, which leads to alteration in the electric field, thereby affecting the velocity field through the Maxwell stress on the fluid-fluid interface. The two-way coupled electrohydrodynamics is central towards dictating the motion of the drop in the flow field. We analytically address the electric potential distribution…
The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface Péclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface Péclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surfa…
Inertial lift forces are exploited within inertial microfluidic devices to position, segregate, and sort particles or droplets. However the forces and their focusing positions can currently only be predicted by numerical simulations, making rational device design very difficult. Here we develop theory for the forces on particles in microchannel geometries. We use numerical experiments to dissect the dominant balances within the Navier-Stokes equations and derive an asymptotic model to predict the lateral force on the particle as a function of particle size. Our asymptotic model is valid for a …
Vesicle dynamics in unbounded Poiseuille flow is analyzed using a small-deformation theory. Our analytical results quantitatively describe vesicle migration and provide new physical insights. At low ratio between the inner and outer viscosity $λ$ (i.e. in the tank-treading regime), the vesicle always migrates towards the flow centerline, unlike other soft particles such as drops. Above a critical $λ$, vesicle tumbles and cross-stream migration vanishes. A novel feature is predicted, namely the coexistence of two types of nonequilibrium configurations at the centreline, a bullet-like and a para…
Most of the works on the dispersion of droplets and their COVID-19 (Coronavirus disease) implications address droplets' dynamics in quiescent environments. As most droplets in a common situation are immersed in external flows (such as ambient flows), we consider the effect of canonical flow profiles namely, shear flow, Poiseuille flow, and unsteady shear flow on the transport of spherical droplets of radius ranging from 5$μ$m to 100 $μ$m, which are characteristic lengths in human talking, coughing or sneezing processes. The dynamics we employ satisfies the Maxey-Riley (M-R) equation. An order-…
We simulate solid particles moving in the two-dimensional channel with the Poiseuille flow. We found that the collective chain excitation emerges with the increasing number of particles in the chain. We measured the spectrum of the chain oscillations varying the width of the channel and found the spectrum intensity became sharper for the more significant confinement ratio. The simulations were done using the Immersed boundary and Lattice Boltzmann methods. We compare our results with the experiments of the drop movement in the quasi-two-dimensional channel and with the simulations of other gro…
Surfactant solutions exhibit multilamellar surfactant vesicles (MLVs) under flow conditions and in concentration ranges which are found in a large number of industrial applications. MLVs are typically formed from a lamellar phase and play an important role in determining the rheological properties of surfactant solutions. Despite the wide literature on the collective dynamics of flowing MLVs, investigations on the flow behavior of single MLVs are scarce. In this work, we investigate a concentrated aqueous solution of linear alkylbenzene sulfonic acid (HLAS), characterized by MLVs dispersed in …
In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts that the direction of migration is always towards the flow centerline.
Compound droplets can be used in substance encapsulation and material compartmentalization to achieve a precise control over the relevant processes in many applications, such as bioanalysis, pharmaceutical manufacturing, and material synthesis. The flow fields in compound droplets directly affect the performance of these applications, but it is challenging to measure them experimentally. In this study, the flow in compound droplets in axisymmetric microchannels is simulated using the Finite Volume Method, and the interface is captured using the Level Set Method with surface tension accounted f…
Droplets on fibers have been extensively studied in the recent years. Although the equilibrium shapes of simple droplets on fibers are well established, the situation becomes more complex for compound fluidic systems. Through experimental and numerical investigations, we show herein that compound droplets can be formed on fibers and that they adopt specific geometries. We focus on the various contact lines formed at the meeting of the different phases and we study their equilibrium state. It appears that, depending on the surface tensions, the triple contact lines can remain separate or merge …
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 wit…
Deformation and breakup of a ferrofluid compound droplet migrating in a microchannel under a magnetic field: A phase-field-based multiple-relaxation time lattice Boltzmann study
Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g., nucleated cells, hydrogels, microcapsules etc. In this work, we analyze the flow in and around a concentric compound particle and investigate the deformation and reorientation dynamics of the confining drop and its stability against breakup in imposed linear flows. We obtain analytical expressions for the flow fields upto O(Ca) (capillary number) and the deformed shape of the conf…
This work investigates electroviscous effects in presence of charge-dependent slip in steady pressure-driven laminar flow of a symmetric (1:1) electrolyte liquid through a uniformly charged slit contraction - expansion (4:1:4) microfluidic device. The mathematical model comprising Poisson's, Nernst-Planck, Navier-Stokes, and current continuity equations are solved numerically using finite element method (FEM). The flow fields (electrical potential, charge, induced electric field strength, pressure drop, and electroviscous correction factor) have been obtained and presented for a wide range of …
In this paper, a wetting boundary scheme used to describe the interactions among ternary fluids and solid is proposed in the framework of the lattice Boltzmann method. This scheme for three-phase fluids can preserve the reduction consistency property with the diphasic situation such that it could give physically relevant results. Combining this wetting boundary scheme and the lattice Boltzmann (LB) ternary fluid model based on the multicomponent phase-field theory, we simulated several ternary fluid flow problems involving solid substrate, including the spreading of binary drops on the substra…
Simulating mobile liquid-gas interfaces with the free-surface lattice Boltzmann method (FSLBM) requires frequent re-initialization of fluid flow information in computational cells that convert from gas to liquid. The corresponding algorithm, here referred to as the refilling scheme, is crucial for the successful application of the FSLBM in terms of accuracy and numerical stability. This study compares five refilling schemes that extract information from the surrounding liquid and interface cells by averaging, extrapolating, or assuming one of the three different equilibrium states. Six numeric…
The multiphase flow of droplets is widespread, both at the industrial and the microscale, for both biological and non-biological applications alike. But the ensemble interactions of such systems are inherently nonlinear and complex, compounded by interfacial effects, making it a difficult many-body problem for theory. In comparison, the self-assembly dynamics of solid particles in flow have long been described and successfully exploited in the field of inertial microfluidics, where particle crystals can be realized from inertial forces and hydrodynamic interactions. Here, we report novel self-…
