Resistance-drag matrix

This equation shows that the resistance-drag force for a certain particle depends on the relative velocities of all the particles of the macromolecule and also on the relative distance between the particles. This expression determines an approximate matrix of hydrodynamic resistance... 

In the case of a high-intensity wet magnetic separation process, the principal force acting to resist particles from being captured in the matrix is the fluid drag force, FD, which is given by the expression ... 

An effective medium approach, which uses hydraulic permeabilities to define the resistance of the fiber network to diffusion, has been used to estimate reduced diffusion coefficients in gels [77]. For a particle diffusing within a fiber matrix, the rate of particle diffusion is influenced by steric effects (due to the volume excluded by the fibers in the gel, which is inaccessible to the diffusing particle) and hydrodynamic effects (due to increased hydrodynamic drag on the diffusing particle caused by the presence of fibers). Recently, it was proposed that these two effects are multiplicative [78], so that the diffusion coefficient observed for particles in a fiber mesh can be predicted from ... 

At this point we are able to compare the drag forces for the different simulation methods. First, we would like to show the difference between the two methods for a small particle ensemble, namely two doublets and a 7-particle star. Results are given in Tables 1 and 2 for both uniform and shear flow, respectively. For two particles the resistance matrix is known exactly and the solution as calculated by SD... 

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