Continuum dynamics of suspensions at low Reynolds number

The dynamics of suspensions particles has been an active area research since Einstein first calculated the leading-order correction to viscosity a suspension spherical (Einstein, Proc. R. Soc. , vol. A102, 1906, pp. 161–179). Since then, researchers have strived develop accurate description behaviours that goes beyond just leading order in particle volume fraction. Here, we consider low-Reynolds-number behaviour particles. Working from Green's functions for flow due single particle, derive continuum-level suspensions. Our analysis corrects error derivation these equations work Jackson ( Chem. Engng Sci. 52, 1997, 2457–2469) and leads stable motion fluid. In addition, our resulting naturally give sedimentation speed suspended correct separate calculation by Batchelor J. Fluid Mech. 1972, 245–268). Using pair-correlation function hard spheres, are able compute out seventh fraction, which agrees with experimental data up 30 %–35 %, also get higher-order corrections viscosity, agree experiments $\sim$ 15 %. Then, using pair distribution spheres shear flow, find alterations both second normal stresses.