E. A. Ashmawy

Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

The method of associated matrices is used to obtain Galerkin type representations. Fundamental solutions are then obtained for the cases of a point body couple and a point microstretch force. A formula for calculating the total couple acting on a rigid body rotating axi-symmetrically in a microstretch fluid is deduced. A generalized reciprocal theorem is deduced. An application for a rigid sphere rotating in a microstretch fluid is discussed. The results of the application are represented graphically.

Axi-symmetric translational motion of an arbitrary solid prolate body in a micropolar fluid

The translational motion of an arbitrary body of revolution in a micropolar fluid is investigated by a combined analytical–numerical method. The governing equations are obtained under the assumption of Stokesian flow. A singularity method based on a continuous distribution of a set of micropolar Sampsonlet singularities along the axis of symmetry within a prolate body is used to find the general solution for the fluid velocity and microrotation components. Employing a constant/linear approximation for the density function and applying the collocation technique to satisfy the boundary conditions on the surface of the body, a system of linear algebraic equations is obtained and solved numerically. The drag force exerted on a prolate spheroid is evaluated for various values of the aspect ratio and for different values of the micropolarity parameters. Numerical results show that convergence to at least four decimal places is achieved. It is found that the drag force on the prolate spheroid increases monotonically with an increase of the aspect ratio of the spheroid and also with an increase of the micropolarity parameters. In order to demonstrate the generality of the present method, the technique is also applied to the prolate Cassini ovals and shows good convergence.

Slow motion of a sphere moving normal to two infinite parallel plane walls in a micropolar fluid

In the present work, we consider the slow steady motion of a rigid sphere moving normal to two parallel plane walls in a micropolar fluid. Non-dimensional variables are introduced. A combined analytical-numerical technique based on the superposition principle and a numerical method, namely the collocation method, is used. The drag force and the wall correction factor are evaluated. Numerical results are obtained and represented graphically.

Unsteady Rotational Motion of a Slip Spherical Particle in a Viscous Fluid

The unsteady rotational motion of a slip spherical particle with a nonuniform angular velocity in an incompressible viscous fluid flow is discussed. The technique of Laplace transform is used. The slip boundary condition is applied at the surface of the sphere. A general formula for the resultant torque acting on the surface of the sphere is deduced. Special fluid flows are considered and their results are represented graphically.

Stokes flow of a micropolar fluid past an assemblage of spheroidal particle-in-cell models with slip

In a cell model it is assumed that the three-dimensional assemblage may be considered to consist of a number of identical unit cells, each of which contains a particle surrounded by a fluid envelope with a fictitious surface (free surface) containing a volume of fluid sufficient to make the fractional void volume in the cell identical to that in the entire assemblage. The quasi-steady axisymmetric translational motion of a spherical or spheroidal cell of an incompressible micropolar fluid is investigated utilizing the cell model method. The inner particle of the cell is assumed to be solid and the outer to be fictitious. Linear velocity and microrotation slip boundary conditions on the surface of the solid particle are proposed. Normalized mobility is obtained for both spherical and spheroidal particles in the cell model and is represented graphically. Expressions for the superficial fluid velocity through an assemblage of spherical and spheroidal particles are obtained.

Interaction of two spherical particles rotating in a micropolar fluid

Abstract The steady-state axisymmetric flow of an incompressible micropolar fluid past two spherical particles is considered. The spherical particles are in general of different sizes and are rotating with different angular velocities about the line connecting their centers. Under the Stokes flow approximation, a general solution is constructed using superposition of the basic solutions in two moving spherical coordinate systems based on the centers of the particles. A collocation technique is used to satisfy the boundary conditions on the surfaces of the particles. Numerical results for the normalized couples acting on each particle are obtained with rapid convergence for various values of the employed parameters.

Unsteady unidirectional micropolar fluid flow

This paper considers the unsteady unidirectional flow of a micropolar fluid, produced by the sudden application of an arbitrary time dependent pressure gradient, between two parallel plates. The no-slip and the no-spin boundary conditions are used. Exact solutions for the velocity and microrotation distributions are obtained based on the use of the complex inversion formula of Laplace transform. The solution of the problem is also considered if the upper boundary of the flow is a free surface. The particular cases of a constant and a harmonically oscillating pressure gradient are then examined and some numerical results are illustrated graphically.