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Stokesian Dynamic Simulation of Sedimenting Spheres in a Newtonian Fluid

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
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Stokesian Dynamics, a method developed by Brady and Bossis in the 80s, simulate the 3D motion of hydrodynamically interacting spheres at low Reynolds numbers. This program was originally written Professor Ron Phillips during his PhD thesis at MIT in 1989. The code was adapted from Fortran 77 to a Mathematica notebook by Housam Binous. Permission was obtained from Professor Phillips to post this work. Using Euler's integration scheme was one simplification of the original code that was performed by Housam Binous. The code call a .m file called NEWTON2.m, which needs three files TEMPM.m, FTMOB.m and SSI.m as well as a data file called data.m. Several simulations are presented in the notebook Main_Stokesian_Dynamics.nb. Two sphere's falling at low Reynolds numbers can have lateral motion during their fall. Two spheres can also rotate, as they sediment, for certain initial configurations. Four vertically aligned spheres, initially at equal distance from each others, will tend to drift apart. Four and six spheres sedimenting will show periodic arrangements that are very peculiar. This Stokesian Dynamics method was extended to non-Newtonian fluids by Binous and Phillips in 1999 by using FENE dumbbell suspensions.

*Engineering > Chemical Engineering
*Engineering > Mechanical and Structural Engineering

Stokesian Dynamics, low Reynolds numbers, sedimentation, hydrodynamics, mobility and resistance matrices, far-field and lubrication matrices

StokesianDynamics.zip (157 KB) - ZIP archive