The mechanical deformability of single cells is an important indicator for various diseases such as cancer, blood diseases and inflammation. Lab-on-a-chip devices allow to separate such cells from healthy cells using hydrodynamic forces. We perform hydrodynamic simulations based on the lattice-Boltzmann method and study the behavior of an elastic capsule in a microfluidic channel flow in the inertial regime. While inertial lift forces drive the capsule away from the channel center, its deformability favors migration in the opposite direction. Balancing both migration mechanisms, a deformable capsule assembles at a specific equilibrium distance depending on its size and deformability. We find that this equilibrium distance is nearly independent of the channel Reynolds number and falls on a single master curve when plotted versus the Laplace number. We identify a similar master curve for varying particle radius. In contrast, the actual deformation of a capsule strongly depends on the Reynolds number. The lift-force profiles behave in a similar manner as those for rigid particles. Using the Saffman effect, the capsule's equilibrium position can be controlled by an external force along the channel axis. While rigid particles move to the center when slowed down, very soft capsules show the opposite behavior. Interestingly, for a specific control force particles are focused on the same equilibrium position independent of their deformability.
Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulation captures the effect of the type of imposed pressure oscillations on the migration pattern of the capsule. An oscillatory channel flow enables the focusing of extremely small biological particles by eliminating the need to design impractically long channels. The presented results show that the eq…
A computational study of capsule ejection from a narrow channel into a reservoir is undertaken for a combination of varying deformable capsule sizes and channel dimensions. A mass spring membrane model is coupled to an Immersed Boundary Lattice Boltzmann model solver. The aim of the present work is the description of the capsules motion, deformation and the response of the fluid due to the complex particle dynamics. The interactions between the capsules affect the local velocity field significantly and are responsible for the dynamics observed. Capsule membrane deformability is also seen to af…
This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded shear flow. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by capillary number Ca, which represents the ratio of viscous stresses to elastic restoring stresses. For a capsule with small bending stiffness, at a given Ca, the orientation converges over time towards a unique stable orbit independent of the initial orientation. With increasing Ca, four dynamical…
Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants. The aim of this study is twofold. Firstly, a combined Lattice Boltzmann-Immersed Boundary (LBM-IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM Dynamic IB. Secondly, this strate…
This work investigates the motion of neutrally-buoyant, slightly deformable straight and curved prolate capsules in unbounded simple shear flow at zero Reynolds number using direct simulations. The curved capsules serve as a model for the typical crescent-shaped sickle red blood cells in sickle cell disease (SCD). The effects of deformability and curvature on the dynamics are revealed. We show that with low deformability, straight prolate spheroidal capsules tumble in the shear plane as their unique asymptotically stable orbit, which contrasts with that for rigid spheroids where infinitely man…
In this paper, the dynamic of inertial capsules into microfluidic bifurcations is studied. The fluid evolution is based on the solution of the BGK -- lattice Boltzmann scheme including a forcing term accounting for immersed geometries. The dynamic-Immersed Boundary forcing strategy is adopted for imposing no-slip boundary conditions on moving deformable or rigid structures, while, on fixed immersed geometries the Bouzidi-Firdaouss-Lallemand second-order bounce back technique is implemented. The proposed computational framework is employed to detail dynamics and deformation of rigid and deforma…
The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neo-Hookean model is used as the constitutive law of the capsule membrane. The maximum wall-normal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of high-frequency oscillation. The migration ve…
In this work, a dynamic-Immersed--Boundary method combined with a BGK-Lattice--Boltzmann technique is developed and critically discussed. The fluid evolution is obtained on a three-dimensional lattice with 19 reticular velocities (D3Q19 computational molecule) while the immersed body surface is modeled as a collection of Lagrangian points responding to an elastic potential and a bending resistance. A moving least squares reconstruction is used to accurately interpolate flow quantities and the forcing field needed to enforce the boundary condition on immersed bodies. The proposed model is widel…
We perform fully Eulerian numerical simulations of an initially spherical hyperelastic particle suspended in a Newtonian pressure-driven flow in a cylindrical straight pipe. We study the full particle migration and deformation for different Reynolds numbers and for various levels of particle elasticity, to disentangle the interplay of inertia and elasticity on the particle focusing. We observe that the particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline. We note that the migration dynamics and the final equi…
Inertial migration of deformable particles has become appealing in recent years due to its numerous applications in microfluidics and biomedicine. The physics underlying the motion of such particles is contingent upon the presence of lift forces in microchannels. This importance initiated several works to analyze and quantify such forces acting on particles. However, since most of such attempts have focused on solid and non-deformable particles, we extend the lift force analysis for the case of deformable droplets and study the effects of Capillary numbers on their dynamics in this paper. Furt…
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…
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…
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…
The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing and only a limited number of experimental and theoretical studies is available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that…
We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account…
We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional simulations based on the lattice Boltzmann method to compute the flow of the suspending fluid, and on the immersed boundary method to achieve the two-way fluid-structure interaction. The mechanics of the capsule membrane elasticity is computed with the finite element method. We obtain two main states: continuous passage of the particles, and their blockage that …
We study the coupled hydrodynamics between a motile slender microswimmer and a deformable interface that separates two Newtonian fluid regions. From the disturbance field generated by the swimming motion, we quantitatively characterize the interface deformation and the manner in which the coupling modifies the microswimmer translation itself. We treat the role of the swimmer type (pushers and pullers), size and model an interface that can deform due to both surface tension and bending elasticity. Our analysis reveals a strong dependence of the hydrodynamics on the swimmer orientation and posit…
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 equati…
When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical meth…
In studies on Marangoni type motion of particles the surface tension is often approximated as a linear function of temperature. For deformable particles in a linear external temperature gradient far from the reference point this approximation yields a negative surface tension which is physically unrealistic. It is shown that H.Zhou and R.H.Davis J. Colloid Interface Sci., n.181,60,1996 presented calculation where the leading deformable drop moved into a region of negative surface tension. With respect numerical studies the restriction of the migration of two deformable drops is given in terms …
The effects of cell size and deformability on the lateral migration and deformation of living cells flowing through a rectangular microchannel has been numerically investigated and compared with the inertial-microfluidics data on detection and separation of cells. The results of this work indicate that the cells move closer to the centerline if they are bigger and/or more deformable and that their equilibrium position is largely determined by the solvent (cytosol) viscosity, which is much less than the polymer (cytoskeleton) viscosity measured in most rheological systems. Simulations also sugg…
We consider suspensions of deformable particles in a Newtonian fluid by means of fully Eulerian numerical simulations with a one-continuum formulation. We study the rheology of the visco-elastic suspension in plane Couette flow in the limit of vanishing inertia and examine the dependency of the effective viscosity $μ$ on the solid volume-fraction $Φ$, the capillary number $\mbox{Ca}$, and the solid to fluid viscosity ratio $\mbox{K}$. The suspension viscosity decreases with deformation and applied shear (shear-thinning) while still increasing with volume fraction. We show that $μ$ collapses to…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid and fluid domains. An immersed boundary algorithm is exploited known as the immersed finite element method (IFEM) which accurately determines the internal forces in the solid domain. The scheme utilized has the advantages of requiring no costly re-meshing, handling finite Reynold's number, as well as incorporating non-linear viscoelasticity in the fluid domain…
We present a numerical analysis of the lateral movement and equilibrium radial positions of red blood cells (RBCs) with major diameter of 8 $μ$m under a Newtonian fluid in a circular channel with 50-$μ$m diameter. Each RBC, modelled as a biconcave capsule whose membrane satisfies strain-hardening characteristics, is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$, the latter of which indicate the ratio of the fluid viscous force to the membrane elastic force. The effects of initial orientation angles and positions on the equilibrium radial position of an RBC centroid a…
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry, and geometry, and govern important biological processes such as cellular traffic, division, migration, or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics an…
Thermocapillary migration of a planar non-deformable droplet in flow fields with two uniform temperature gradients at moderate and large Marangoni numbers is studied numerically by using the front-tracking method. It is observed that the thermocapillary motion of planar droplets in the uniform temperature gradients is steady at moderate Marangoni numbers, but unsteady at large Marangoni numbers. The instantaneous migration velocity at a fixed migration distance decreases with increasing Marangoni numbers. The simulation results of the thermocapillary droplet migration at large Marangoni number…
Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering applications. Computer simulations of this kind of fluid-structure (membrane) interaction in low-Reynolds-number flows raise significant challenges faced by an intricate interplay between flow stresses, complex particles' interfacial mechanical properties, and fluidic confinement. Here, we present an isogeometric computational framework by combining the finite-element …
We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles…
