Inertial focusing of a neutrally buoyant particle in stratified flows
TL;DR: In this paper, a numerical method based on the combined Immersed Boundary-Lattice Boltzmann Method is used to study inertial focusing of neutrally buoyant particles in stratified Couette flows and pressure driven flows.
Abstract: Particles in microfluidic channels experience two dominant lift forces in the direction transverse to the flow—the shear gradient lift force and the wall lift force. These forces contribute to the lift experienced by the particle and cause their cross stream migration until they attain an equilibrium position where the net lift force in the transverse direction is zero. Stratified coflow of two liquids with different viscosities is a stable flow-regime observed under some operating conditions. The presence of the second fluid alters the shear gradient induced lift force and the wall force acting on the particle at each point, changing the final equilibrium position. These positions can be tuned and controlled by altering the viscosity or the flow rates of the two fluids so that the particles focus in one fluid. A numerical method based on the combined Immersed Boundary-Lattice Boltzmann Method is used to study inertial focusing of neutrally buoyant particles in stratified Couette flows and pressure driven flows. We analyze how different factors such as the Reynolds number, flow rate ratio, viscosity ratio of the fluids, and particle size affect the particle migration in two-dimensional (2D) and three-dimensional (3D) geometries. Our study shows that in Couette flows, the particle focuses in the low viscosity fluid when the interface is at the center. We also found that a critical viscosity ratio exists beyond which particle focusing in low viscous fluid is guaranteed, for a given flow rate ratio in pressure driven flows.
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TL;DR: In this article , the authors numerically studied the self-ordering and organization of an in-line particle chain flowing through a square microchannel, and the effects of particle Reynolds number (Rep), length fraction (Lf), and particle size are focused.
Abstract: Precise determination of microfluidic behaviors is theoretically significant and has shown remarkable application prospects. This work numerically studies the self-ordering and organization of an in-line particle chain flowing through a square microchannel. The immersed boundary-lattice Boltzmann method is employed, and effects of particle Reynolds number (Rep), length fraction (⟨Lf⟩, characterizes particle concentration), and particle size are focused. Results imply a relatively complex migration of small-particle chains. Three typical states are observed, that is, the equilibrium position finally in a stabilized, fluctuated, or chaotic condition. The corresponding dynamic processes are presented. Interestingly, how interparticle spacing evolves with time shows similar regularity with the three states, corresponding to a particle chain either being evenly distributed, moving like a bouncing spring, or continuously in disordered motions. The flow field and force conditions are analyzed to clarify the mechanisms, suggesting the subtle interaction among vortex-induced repulsive force, wall-induced lift force, and shear gradient lift force is the reason behind. Based on different states, migratory patterns are categorized as Stable Pattern, Spring Pattern, and Chaotic Pattern, and an overall classification is also obtained. Moreover, effects of Rep and ⟨Lf⟩ are identified, where a rising Rep leads to an equilibrium position toward the wall and larger volatility of interparticle spacings. The dynamic characteristics are characterized by lagging, translational, and angular velocities of particles in the chain. Finally, a contrastive study of large particles is performed. The present investigation is expected to provide insight into regularities of in-line particle chains and possible applications.
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TL;DR: In this paper, the formation and stability of a pair of identical soft capsules in channel flow under mild inertia was investigated, and it was shown that particle softness increases the likelihood of a stable pair forming, while the pair stability is determined by the lateral position of the particles.
Abstract: 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. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.
8 citations
TL;DR: In this paper , the formation and stability of a pair of identical soft capsules in channel flow under mild inertia was investigated, and it was shown that particle softness increases the likelihood of a stable pair forming, while the pair stability is determined by the lateral position of the particles.
Abstract: 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. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.
8 citations
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TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.
Abstract: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.
4,164 citations
TL;DR: In this paper, a review of applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions is presented, together with some of the important applications of these methods.
Abstract: This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.
1,117 citations
TL;DR: In this paper, Segre and Silberberg showed that a rigid sphere transported along in Poiseuille flow through a tube is subject to radial forces which tend to carry it to a certain equilibrium position at about 0.6 tube radii from the axis, irrespective of the radial position at which the sphere first entered the tube.
Abstract: It is shown that a rigid sphere transported along in Poiseuille flow through a tube is subject to radial forces which tend to carry it to a certain equilibrium position at about 0.6 tube radii from the axis, irrespective of the radial position at which the sphere first entered the tube. It is further shown that the trajectories of the particles are portions of one master trajectory and that the origin of the forces causing the radial displacements is in the inertia of the moving fluid. An analysis of the parameters determining the behaviour is presented and a phenomenological description valid at low Reynolds numbers is arrived at in terms of appropriate reduced variables. These phenomena have already been described in a preliminary note (Segre & Silberberg 1961). The present more complete analysis confirms the conclusions, but it appears that the dependence of the effects on the particle radius go with the third and not the fourth power as was then reported.It is also shown that the description of the phenomena becomes more complicated at tube Reynolds numbers above about 30.
813 citations
TL;DR: In this paper, a new computational method, the immersed boundary-lattice Boltzmann method, is presented, which combines the most desirable features of the lattice Boltzman and immersed boundary methods and uses a regular Eulerian grid for the flow domain and a Lagrangian grid to follow particles contained in the flow field.
804 citations
TL;DR: Nonlinearity in finite-Reynolds-number flow results in particle migration transverse to fluid streamlines, producing the well-known "tubular pinch effect" in cylindrical pipes.
Abstract: Nonlinearity in finite-Reynolds-number flow results in particle migration transverse to fluid streamlines, producing the well-known "tubular pinch effect" in cylindrical pipes. Here we investigate these nonlinear effects in highly confined systems where the particle size approaches the channel dimensions. Experimental and numerical results reveal distinctive dynamics, including complex scaling of lift forces with channel and particle geometry. The unique behavior described in this Letter has broad implications for confined particulate flows.
501 citations