Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance $c$ between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxén mirror image technique for $a/(a+c)\ll 1$ (here $a$ is the bubble radius), when the clearance parameter $\varepsilon(= c/a)$ is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing $\varepsilon$. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble-wall gap. The numerical and lubrication analyses consistently demonstrate that when $\varepsilon\leq 1$, the lubrication effect makes the migration velocity asymptotically $μV_{B1}^2/(25\varepsilon γ)$ (here, $V_{B1}$, $μ$, and $γ$ denote the rising velocity, the dynamic viscosity of liquid, and the surface tension, respectively).
Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a small clearance $c$ between the bubble interface and the wall. Motivated by the fact that experimentally measured migration velocity (Takemura et al. (2002, J. Fluid Mech. {\bf 461}, 277)) is higher than the velocity estimated by the available analytical solution (Magnaudet et al. (2003, J. Fluid Mech. {\bf 476}, 115)) using the Faxén mirror image technique for $κ(=a/(a+c))\ll 1$ (her…
We investigate the motion of a sedimenting spherical drop in the presence of an applied uniform electric field in an otherwise arbitrary direction in the limit of low surface charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the drop velocity through perturbations in powers of the electric Reynolds number which signifies the importance of the charge relaxation time scale as compared to the convective time scale. We show that in the presence of electric field either in the …
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…
A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration and equilibrium of the particle are similar to the Segré-Silberberg effect in our numerical simulations. Surprisingly, two lateral equilibrium positions are observed corresponding to the releasing positions of the biconcave particle. The upper equilibrium positions significantly decrease with the growth of the Reynolds number, whereas the lower ones are almost insensitive to the Reynolds number. …
Dynamics of a droplet in oscillatory and pulsating flows of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, surface tension, and channel flow rate have been explored by simulating the drop within a microchannel. These types of flows introduce new equilibrium positions for the drop compared to steady flows with similar conditions. The simulation results are very sensitive to the grid resolution due to the unsteady behavior of the base flow. Therefore, a set of fine grids have been used in this study to capture the physics of this problem m…
We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. In addition, the lateral trajectories of spheres and oblates collapse into an…
In the present study, the role of surfactants on the cross-stream migration of droplets is investigated both experimentally and theoretically. For experimental analysis, sunflower oil is used as the carrier phase and DI water as the dispersed phase which is intermixed with Triton X-100 that acts as the surfactant. A T-junction is used in the microchannel for the purpose of droplet generation. Presence of an imposed pressure driven flow induces droplet deformation and disturbs the equilibrium that results in subsequent surfactant-redistribution along the interface. This further induces a gradie…
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…
Dynamics of non-Brownian flexible fibers in Poiseuille flow between two parallel planar solid walls is evaluated from the Stokes equations, solved numerically by an accurate multipole code HYDROMULTIPOLE. Fibers migrate towards a critical distance from the wall zc, which depends significantly on the fiber length N and bending stiffness A. Therefore, the calculated values of zc can be used to sort fibers. Three modes of the dynamics are found, depending on a shear-to-bending parameter Gamma. In the first mode, stiff fibers deform only a little and accumulate close to the wall, as the result of …
This work investigates the migration of spherical particles of different sizes in a centrifuge-driven deterministic lateral displacement (c-DLD) device. Specifically, we use a scaled-up model to study the motion of suspended particles through a square array of cylindrical posts under the action of centrifugation. Experiments show that separation of particles by size is possible depending on the orientation of the driving acceleration with respect to the array of posts (forcing angle). We focus on the fractionation of binary suspensions and measure the separation resolution at the outlet of the…
The buoyancy-driven motion of two identical gas bubbles released in line in a liquid at rest is examined with the help of highly resolved simulations, focusing on moderately inertial regimes in which the path of an isolated bubble is vertical. Assuming first an axisymmetric evolution, equilibrium configurations of the bubble pair are determined as a function of the buoyancy-to-viscous and buoyancy-to-capillary force ratios which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. The three-dimensional solutions reveal that this axisymmetric equilibrium is actually ne…
A microfluidic band-pass filter for flexible fiber separation
École Supérieure de Physique et de Chimie Industrielles de la ville de Paris（巴黎市高等物理化工学院）；Université Paris Sciences et Lettres（巴黎文理研究大学）；Sorbonne Université（索邦大学）；Université Paris Cité（巴黎西岱大学）；CNRS（法国国家科学研究中心）；LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris（巴黎理工学院高等流体力学实验室，法国国家科学研究中心，巴黎理工学院）；Institut universitaire de France (IUF)（法兰西学术院）
Laboratory experiments were conducted to study particle migration and flow properties of non- Brownian, non-colloidal suspensions ranging from 10% to 40% particle volume fraction in a pressure-driven flow over and through a porous structure at low Reynolds number. Particle concentration maps, velocity maps and corresponding profiles were acquired using a magnetic resonance imaging (MRI) technique. The model porous medium consists of square arrays of circular rods oriented across the flow in a rectangular microchannel. It was observed that the square arrays of the circular rods modify the veloc…
The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always drifts out of the wake of the leading one. Then, depending on the ratios of the buoyancy, viscous and capillary forces which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, five distinct regimes specific to such conditions are identified, in which the two bubbles may rise independently or continue to interact and possibly collide in the end. …
Carbon dioxide (CO2) capture and subsurface storage is one method for reducing anthropogenic CO2 emissions to mitigate climate change. It is well known that large-scale fluid injection into the subsurface leads to a buildup in pressure that gradually spreads and dissipates through lateral and vertical migration of water. This dissipation can have an important feedback on the shape of the CO2 plume during injection, and the impact of vertical pressure dissipation, in particular, remains poorly understood. Here, we investigate the impact of lateral and vertical pressure dissipation on the inject…
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…
Understand and predict the dynamics of dispersed micro-objects in microfluidics is crucial in numerous natural, industrial and technological situations. In this paper, we experimentally characterized the equilibrium velocity $V$ and lateral position $\varepsilon$ of various dispersed micro-objects such as beads, bubbles and drops, in a cylindrical microchannel over an unprecedent wide range of parameters. By systematically varying the dimensionless object size ($d \in [0.1; 1]$), the viscosity ratio ($λ\in [10^{-2}; \infty[$), the density ratio ($φ\in [10^{-3}; 2]$), the Reynolds number ($\Re …
Interface-resolved direct numerical simulations are performed to examine the combined effects of soluble surfactant and viscoelasticity on the structure of a bubbly turbulent channel flow. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is achieved through a non-linear equation of state which relates the surface tension to the surfactant concentration at the interface. The two-fluid Navier-Stokes equations are solved using a front-tracking method, augmen…
