M. S. Faltas

Bio: M. S. Faltas is an academic researcher from Alexandria University. The author has contributed to research in topics: Slip (materials science) & Drag. The author has an hindex of 13, co-authored 51 publications receiving 459 citations.

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

Abstract: The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid.

Axisymmetric motion of two spherical particles in a Brinkman medium with slip surfaces

Abstract: An effective-medium approach, based on the Brinkman equation is used to study the axisymmetric quasi-steady motion of two spherical particles embedded in a porous medium. The particles are in general of different sizes and translating with different velocities along the line connecting their centers, and allowing for the hydrodynamic slip at their surfaces. 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 drag force acting on each particle are obtained with rapid convergence for various values of slip coefficients, size ratio, separation parameter, velocity ratio of the particles, and permeability parameter. The normalized drag force on each particle reach the single particle limit as the distance between centers grows large enough and each particle then may be translated independent of each other. The accuracy of the numerical technique has been tested against known solutions for two spheres with no-slip surfaces and when the porous medium becomes a clear fluid.

Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models

Abstract: The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of slip eccentric spherical particle-in-cell models with Happel and Kuwabara boundary conditions is investigated. A linear slip, Basset type, boundary condition on the surface of the spherical particle is used. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on the particle and fictitious spherical envelope. The boundary conditions on the particle's surface and fictitious spherical envelope are satisfied by a collocation technique. Numerical results for the normalized drag force acting on the particle are obtained with good convergence for various values of the volume fraction, the relative distance between the centers of the particle and fictitious envelope and the slip coefficient of the particle. In the limits of the motions of the spherical particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

Abstract: 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.

The Kinetic Theory of Gases

Abstract: THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

Prospects of Membrane Science Development

Abstract: Membranes are widely used in modern technology. The demand for different types of membranes and membrane processes is increasing every year. This review summarizes the current state of the art and prospects of membrane science developments including membrane materials for gas separation, pervaporation, and pressure-driven membrane processes; ion-exchange, hybrid, and track-etched membranes; membranes for electrochemical sensors; and mathematical modeling of membrane separation processes and ion and water transport in membrane systems. Studies aimed at improving the selectivity and performance of membranes and their stability are surveyed. New approaches to the synthesis and modification of membranes as well as their advanced applications are discussed.