Cheong Bong Chang

Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method

An improved penalty immersed boundary method (pIBM) has been proposed for simulation of flow-induced deformation of three-dimensional (3D) elastic capsules. The motion of the capsule membrane is described in the Lagrangian coordinates. The membrane deformation takes account of the bending and twisting effects as well as the stretching and shearing effects. The method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C^1 continuous. The membrane motion is then solved by the subdivision-surface based finite element method on the triangular unstructured mesh. On the other hand, the fluid motion is defined on the Eulerian domain, and is advanced by the fractional step method on a staggered Cartesian grid. Coupling of the fluid motion and the membrane motion is realized in the framework of the pIBM. Using the proposed method, deformation of 3D elastic capsules in a linear shear flow is studied in detail, and validations are examined by comparing with previous studies. Both the neo-Hookean membrane and the Skalak membrane are tested. For an initially spherical capsule the tank-treading motion is formed under various dimensionless shear rates and reduced bending moduli. It is found that buckling occurs near the equator of the capsule for small shear rates but near the tips for large shear rates, which is suppressed by including the bending rigidity of the membrane. Effects of the Reynolds number and the membrane density are investigated for an initially spherical capsule. For a non-spherical capsule, with the initial shape of the oblate spheroid or the biconcave circular disk as a model of the red blood cell, the swinging motion is observed due to the shape memory effect. By decreasing the dimensionless shear rate or increasing the reduced bending modulus, the swinging motion is transited into the tumbling motion.

An improved penalty immersed boundary method for fluid-flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid-flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid-flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.

Optical levitation of a non-spherical particle in a loosely focused Gaussian beam

The optical force on a non-spherical particle subjected to a loosely focused laser beam was calculated using the dynamic ray tracing method. Ellipsoidal particles with different aspect ratios, inclination angles, and positions were modeled, and the effects of these parameters on the optical force were examined. The vertical component of the optical force parallel to the laser beam axis decreased as the aspect ratio decreased, whereas the ellipsoid with a small aspect ratio and a large inclination angle experienced a large vertical optical force. The ellipsoids were pulled toward or repelled away from the laser beam axis, depending on the inclination angle, and they experienced a torque near the focal point. The behavior of the ellipsoids in a viscous fluid was examined by analyzing a dynamic simulation based on the penalty immersed boundary method. As the ellipsoids levitated along the direction of the laser beam propagation, they moved horizontally with rotation. Except for the ellipsoid with a small aspect ratio and a zero inclination angle near the focal point, the ellipsoids rotated until the major axis aligned with the laser beam axis.

Optical mobility of blood cells for label-free cell separation applications

This paper describes the optical mobilities of blood cell components. Blood cells are heterogeneous, and their optical behaviors depend on size, morphology, and other optical properties. In a step toward the label-free separation of blood cells, the optical mobility resulting from the optical scattering and cell properties was derived and evaluated for each cell component. The optical mobilities of red blood cells, lymphocytes, granulocytes, and monocytes were measured under various flow conditions of a cross-type optical particle separator.

Optical separation of ellipsoidal particles in a uniform flow

The behavior of an ellipsoidal particle subjected to a vertical optical force by a loosely focused laser beam in a uniform flow was studied numerically. The fluid flow and the particle motion were separately solved and coupled using the penalty immersed boundary method, and the optical force was calculated using the dynamic ray tracing method. The optical force and optically induced torque on the ellipsoidal particle varied according to the aspect ratio and initial inclination angle. The ellipsoidal particle, whose major axis was initially aligned with the laser beam axis, was more migrated as the aspect ratio increased. The migration distance also depended on the initial inclination angle, even for a given ellipsoidal particle shape. As the laser beam power increased and the flow velocity decreased, the effect of the initial inclination angle increased. The ellipsoidal particles with different aspect ratios could be effectively separated if the rotation along the spanwise direction was suppressed. Moreov...

Cross-type optical separation of elastic oblate capsules in a uniform flow

The dynamic behavior of an elastic capsule with an initially oblate spheroidal shape during cross-type optical separation was numerically investigated. The penalty immersed boundary method was adopted for the fluid-membrane interaction, and the optical force calculation was conducted by using the ray optics method including the ray-surface intersection algorithm. The oblate elastic capsule of b/a = 0.5 with different surface Youngs moduli and different initial inclination angles was considered. The oblate capsule with higher surface Youngs moduli was less deformed, and was more migrated for each initial inclination angle. Unlike the oblate rigid particle, the initially inclined capsules with moderate inclination angles were similarly migrated since the oblate elastic capsule was deformed during rotation near the laser beam axis. The oblate capsules can be separated according to the surface Youngs modulus, except for nearly non-inclined capsules. As the fluid velocity decreased, the migration distance i...

Lateral migration of a microdroplet under optical forces in a uniform flow

The behavior of a microdroplet in a uniform flow and subjected to a vertical optical force applied by a loosely focused Gaussian laser beam was studied numerically. The lattice Boltzmann method was applied to obtain the two-phase flow field, and the dynamic ray tracing method was adopted to calculate the optical force. The optical forces acting on the spherical droplets agreed well with the analytical values. The numerically predicted droplet migration distances agreed well with the experimentally obtained values. Simulations of the various flow and optical parameters showed that the droplet migration distance nondimensionalized by the droplet radius is proportional to the S number (zd/rp = 0.377S), which is the ratio of the optical force to the viscous drag. The effect of the surface tension was also examined. These results indicated that the surface tension influenced the droplet migration distance to a lesser degree than the flow and optical parameters. The results of the present work hold for the refr...

Simulation of Valveless Pump Using Pumping Chamber Connected to Elastic Tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet through a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient, bending coefficient, and aspect ratio of the elastic tube. Photographs of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump to gain a better understanding of the mechanism underlying the valveless pump. The relationship between the gap in the elastic tube and the average flow rate of the pump was analyzed.

Flow‐Induced Deformation of 3D Elastic Capsules

We present an improved penalty immersed boundary (pIB) method for simulation of flow‐induced deformation of 3D elastic capsules. The membrane deformation takes full account of the bending and twisting effects as well as the stretching and shearing effects. Hence, the method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C1 continuous. Using the proposed pIB method, the deformation of 3D elastic capsules in simple shear flow is studied in detail. For an initially spherical capsule the steady tank‐treading motion is formed, in which the capsule maintains constant shape and orientation but rotates around the interior fluid. Time histories of the deformation parameter at various dimentionless shear rates and reduced bending moduli are presented and compared with data from previous studies.

An Improved Penalty Immersed Boundary Method for Fluid-Flexible Body Interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid-flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, three-dimensional simulations of fluid-flexible body interaction are carried out, including deformation of a spherical capsule in a linear shear flow. A comparison between the numerical results and the theoretical solutions is presented.© 2011 ASME