Motion of a sphere and the suspending low-Reynolds-number fluid confined in a cubic cavity

Dynamics of a spherical particle and the suspending low-Reynolds-number fluid confined by a cubic cavity were studied numerically.We calculated the particle’s hydrodynamic mobilities along x-,y-,and zdirections at various locations in the cavity.The mobility is largest in the cavity center and decays as the particle becomes closer to no-slip walls.It was found that mobilities in the entire cubic cavity can be determined by a minimal set in a unit tetrahedron therein.Fluid vortices in the cavity induced by the particle motion were observed and analyzed.We also found that the particle can exhibit a drift motion perpendicular to the external force.Magnitude of the drift velocity normalized by the velocity along the direction of the external force depends on particle location and particle-to-cavity sizes ratio.This work forms the basis to understand more complex dynamics in microfluidic applications such as intracellular transport and encapsulation technologies.

Propulsive matrix of a helical flagellum

We study the propulsion matrix of bacterial flagella numerically using slender body theory and the regularized Stokeslet method in a biologically relevant parameter regime. All three independent elements of the matrix are measured by computing propulsive force and torque generated by a rotating flagellum, and the drag force on a translating flagellum. Nu- merical results are compared with the predictions of resistive force theory, which is often used to interpret micro-organism propulsion. Neglecting hydrodynamic interactions between different parts of a flagellum in resistive force theory leads to both qualitative and quantitative discrepancies between the theoretical prediction of resistive force theory and the numerical results. We improve the original theory by empirically incorporating the effects of hydrodynamic interactions and propose new expressions for propulsive matrix elements that are accurate over the parameter regime explored.

Extension of Near-Wall Domain Decomposition to Modeling Flows with Laminar-Turbulent Transition

The near-wall domain decomposition method(NDD)has proved to be very efficient for modeling near-wall fully turbulent flows.In this paper the NDD is extended to non-equilibrium regimeswith laminar-turbulent transition(LTT)for the first time.The LTT is identified with the use of the e^(N)-method which is applied to both incompressible and compressible flows.TheNDD ismodified to take into account LTT in an efficientway.In addition,implementation of the intermittency expands the capabilities of NDD to model non-equilibrium turbulent flows with transition.Performance of the modified NDD approach is demonstrated on various test problems of subsonic and supersonic flows past a flat plate,a supersonic flow over a compression corner and a planar shock wave impinging on a turbulent boundary layer.The results of modeling with and without decomposition are compared in terms of wall friction and show good agreement with each other while NDD significantly reducing computational resources needed.It turns out that the NDD can reduce the computational time as much as three times while retaining practically the same accuracy of prediction.