On the theory of stability of a cylindrical hydrodynamic suspension

Modeling the effect of centering of a spherical hydrodynamic suspension

“…The stability on the mobile equilibrium curve of a weakly loaded spherical suspension at low oscillatory Reynolds numbers was studied earlier [1]. Cylindrical hydrodynamic suspension is quickly centered with increasing oscillatory Reynolds number [2]. Experimental data [1] confirm this effect for spherical hydrodynamic suspension.…”

“…We assume that the sensitivity axis coincides with the Oz axis of the Oxyz coordinate system, the origin of which is in the center of mass of the inner sphere, and all the decentering forces lie in the Oxy plane. In disregard of some terms of the order of the square of the small relative thickness of the spherical layer (which is justified in [2]) and the small compressibility of the liquid, the equations of equilibrium of the suspension in dimensionless variables follow from [15] and take the form 2 3 11 20 00 0 4 0 2 8 2 1 2 2 2 2 1/2 00 3 v p vv v hx hx hx v p vv vv hx hx hx…”