Couple on a rotary oscillating sphere in a dusty gas

Rotary oscillations of a sphere about its vertical diameter in an infinite expanse of viscous, incompressible fluid with imbedded identical spherical particles are studied. The problem is solved by the method of separation of variables and explicit expressions for the velocity of fluid particles and the couple experienced by the sphere due to fluid stresses are obtained. The couple is expressed in terms of two parameters and graphs have been drawn to represent the variation in these parameters and some interesting conclusions are made.Nomenclature u⁵ velocity of fluid particles - v⁶ velocity of dust particles - P⁵ pressure - ⁶ fluid density - t⁹ time - m mass of a dust particle - N number density of dust particles - k⁵ Stokes resistance coefficient - ³ viscosity - ⁶ kinematic viscosity - ⁷ particle relaxation time - ⁴ frequency of oscillation of the sphere - f⁹ mass concentration of the dust particles