Solution of the Problem of the Motion of a Disperse Inclusion in a Fluid with Account for the "Hereditary" Basset Force

The problem of the motion of a spherical disperse inclusion (particle, bubble, etc.) in a viscous incompressible fluid in gravity field is considered with account for nonstationary forces including the "hereditary" force of the Basset type. An exact solution of the problem determining the variation of the disperse inclusion in a fluid with time is derived using the methods of mathematical physics. By way of illustration of the application of the solution obtained the coordinates and velocities of a bubble moving in a fluid are calculated and it is shown that taking account for the "hereditary" Basset force leads to a considerable increase in the characteristic time and distance, when and where a stationary bubble velocity is attained.