Direct simulations of flexible cylindrical fiber suspensions in finite Reynolds number flows

Abstract

Direct simulations of flexible cylindrical fiber suspensions in a finite Reynolds number flow are reported. The simulation method is based on a lattice Boltzmann equation and a flexible fiber model. A slender solid body is discretized into a chain of cylindrical segments contacting each other at the their ends through ball and socket joints that allow adjacent segments to rotate around the joints in three dimensional space. A constraint force is imposed at each joint. In general, motion and rotational matrices of each segment are functions of constraint forces. It is necessary to linearize the rotational matrices in forces and torques so that constraint forces could be solved using joint contacting conditions. Therefore, quaternion parameters as well as rotational matrix could be expanded in a power series of the length of time step up to a second order. A half leapfrog algorithm D. Fincham, [CCP5 Quarterly, 2, 6 (1981)] is modified to ensure the ball and socket joint conditions to be satisfied at each time step. The validation of the present flexible fiber method is tested by using a rigid particle method. It is shown that the computational results are consistent with the existing experimental and theoretical results at finite Reynolds number flows. With the present method, nonlinear inertial interactions between fluid and flexible filaments can be naturally studied. A few applications are included.