Stokes Flow in Cylindrical Containers With Rotating Ends

Abstract

The Stokes flow in cylindrical containers with rotating ends was studied. Based on the characteristics of the flow, the problem was reduced to the eigenvalue and eigensolution problem of Hamiltonian dual equations with the axial coordinate simulated as the time scale. By means of the completeness of the symplectic eigensolution space and the adjoint symplectic orthogonality relationship between the eigensolutions, the expansion of the solution to the problem was obtained, and the numerical method for calculating the expansion coefficients was given. In the cases of one-end rotating, two-end rotating at the same or opposite angular velocity, the velocity and stress distributions of the flow in the cylindrical containers with different aspect ratios (of the length to the radius), were investigated. The velocity and stress distributions, and the characteristics of the flows under different boundary conditions were revealed.