Friction and mobility of many spheres in Stokes flow

Abstract

An efficient scheme is presented for the numerical calculation of hydrodynamic interactions of many spheres in Stokes flow. The spheres may have various sizes, and are freely moving or arranged in rigid arrays. Both the friction and mobility matrix are found from the solution of a set of coupled equations. The Stokesian dynamics of many spheres and the friction and mobility tensors of polymers and proteins may be calculated accurately at a modest expense of computer memory and time. The transport coefficients of suspensions can be evaluated by use of periodic boundary conditions.

Hydrodynamic orienting of asymmetric microobjects under gravity

“…The accuracy is controlled by a varied order of the multipole truncation L (see Ref. [19] for the definition of L and Refs. [19,27] for discussion of the accuracy estimates).…”

“…The algorithm from Ref. [19] and its accurate numerical FOR-TRAN implementation HYDROMULTIPOLE [20] are applied. The accuracy is controlled by a varied order of the multipole truncation L (see Ref.…”

“…In Sec. II, the accurate spherical multipole method [18,19] of solving the Stokes equations is introduced, with the lubrication correction for the relative motion of close surfaces [20], and the HYDROMULTIPOLE numerical code [20]. In Sec.…”

Numerical Determination of Truncation Orders in the Correction Method for Stokes Equations

“…Unfortunately, we do not have a nice explicit expression for DN such as (4 A large amount of research has been studied to develop numerical tools to approximate the friction operator, such as [5], [6], [8], [9], [13]. Recently, in [15], the authors developed a method which is called the correction method for computing very accurate numerical solutions.…”

“…The advantage of decomposing the solution resides in the possibility of using di erent methods for solving problems (5) and (6). The singular parts are solution of the Stokes equations (5) around only two solid particles.…”