Spherical Particle In Viscous Fluid Research Articles

Axisymmetric Slow Motion of a Porous Spherical Particle in a Viscous Fluid Using Time Fractional Navier–Stokes Equation

In this paper, we present the unsteady translational motion of a porous spherical particle in an incompressible viscous fluid. In this case, the modified Navier–Stokes equation with fractional order time derivative is used for conservation of momentum external to the particle whereas modified Brinkman equation with fractional order time derivative is used internal to the particle to govern the fluid flow. Stress jump condition for the tangential stress along with continuity of normal stress and continuity of velocity vectors is used at the porous–liquid interface. The integral Laplace transform technique is employed to solve the governing equations in fluid and porous regions. Numerical inversion code in MATLAB is used to obtain the solution of the problem in the physical domain. Drag force experienced by the particle is obtained. The numerical results have been discussed with the aid of graphs for some specific flows, namely damping oscillation, sine oscillation and sudden motion. Our result shows a significant contribution of the jump coefficient and the fractional order parameter to the drag force.

Analysis of general creeping motion of a sphere inside a cylinder

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

Unsteady solution of viscous fluid flow in an infinite cylinder with a variable body force

In this Brief Communication, the unsteady viscous flow with a variable body force in an infinite cylinder is solved exactly. The solution describes the transient velocity profiles and pressure gradients, which can be used in the application of sedimentation of spherical particles in viscous fluid. The current solution is compared with the previously solved problem between two infinite parallel plates. It is found that, for a similar body force, the central-line velocity of the cylinder will be greater than that of the two-infinite-plate case. But the slip velocity at the wall of cylinder will be smaller than that of the flow between two infinite plates. The transient pressure gradients are also different, resulting in a smaller value for the cylindrical case with a similar body force.

Generalized diffusion theory of non-rotational, rigid spherical particle sedimentation in viscous fluid

This paper is devoted to application of Generalized Diffusion Theory for solving a sedimentation problem of rigid spherical particles in viscous fluid. The governing equations have been obtained. It is shown that, in this case the governing equation system is a hyperbolic one, and the equations in the characteristic form have been derived. The mathematical properties of the obtained equation system and the solution for stationary sedimentation where investigated numerically.