D. Palaniappan

Bio: D. Palaniappan is an academic researcher from Texas A&M University. The author has contributed to research in topics: Stokes flow & Drag. The author has an hindex of 11, co-authored 29 publications receiving 310 citations. Previous affiliations of D. Palaniappan include University of the West Indies & Indian Institute of Science.

Lamb's solution of stokes's equations: a sphere theorem

Abstract: The velocity and pressure in Stokes flow are written in terms of two functions A and B, where A is biharmonic and B is harmonic. Lamb's (1) general solution of Stokes's equations and Oseen's (2) solution due to a Stokeslet in the presence of a no-slip spherical boundary have the same structure as our representation. Ranger's (3) representation follows as a special case of our result. A sphere theorem for non-axisymmetric flow outside or inside a sphere is stated and proved. Collins's theorem (4) for axisymmetric flow follows as a special case of our theorem. A few illustrative examples are given and in each case the drag and torque on the sphere are calculated.

Creeping flow about a slightly deformed sphere

Abstract: The problem of slow streaming flow of a viscous incompressible fluid past a spheroid which departs but little in shape from a sphere with mixed slip-stick boundary conditions, is investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterising the deformation. The case of an oblate spheroid is considered as a particular example and the force on this non-spherical body is evaluated. It is found that the parameter λ1, which arises in connection with the boundary condition, has significant effect upon the hydrodynamic force. In fact, it is shown that, the force is a quadratic function of this parameter up to the first order of deformation. Also, it is observed that the drag in the present case is less than that of the Stokes resistance for a slightly oblate spheroid. Some other special cases are also deduced from the present result. A brief discussion of the results to other body shapes is presented.

Longitudinal and transverse polarizability of the conducting double sphere

Abstract: Exact expressions are derived for the longitudinal and transverse polarizability of two overlapping conducting spheres of arbitrary radii and with arbitrary angle of intersection. The transverse polarizability is expressed as a single integral, which can be performed if the angle of intersection is a rational fraction of π, i.e., the angle of intersection can be expressed as mπ/n, with m and n integers. The longitudinal polarizability can be expressed as a single integral if the two spheres are equal. For unequal spheres it involves two integrals, as well as the capacity, which itself was expressed as a single integral earlier. For equal spheres the second integral vanishes by symmetry, and the capacity is not needed. Both integrals can be performed if the angle of intersection is a rational fraction of π. In earlier work by the authors the longitudinal and transverse polarizability were found only for discrete angles of intersection π/n with n integer. Our result for the longitudinal polarizability of two equal overlapping conducting spheres shows that an earlier result of Radchik et al. [J. Appl. Phys. 76, 4827 (1994)] for overlapping dielectric spheres is incorrect.

Electrostatics of the conducting double sphere

Abstract: General solutions to the electrostatic problem of a pair of intersecting, conducting spheres of arbitrary radii (a double sphere) placed in an arbitrary potential field are derived. The method is based on Kelvin’s transformation combined with reflection and translation properties for harmonic functions. The basic idea is described in detail for orthogonally intersecting spheres. A theorem is offered for finding the image system for the two-sphere assembly placed in a given electrostatic potential. From the general formula, the image systems for various applied potentials are obtained in a straightforward fashion. The earlier special solutions for equal-sized spheres are recovered from our results. The fundamental quantities of interest in electrostatics such as capacity and polarization (dipole moment) are computed. The polarizability tensor is found to be diagonal with different components for the directions parallel and perpendicular to the line of centers. The general solutions to the problem of a pair...

Motion through a non-homogeneous porous medium: Hydrodynamic permeability of a membrane composed of cylindrical particles

Abstract: The present problem is concerned with the flow of a viscous steady incompressible fluid through a non-homogeneous porous medium. Here, the non-homogeneous porous medium is a membrane built up by cylindrical particles. The flow outside the membrane is governed by the Stokes equation and the flow through the non-homogeneous porous membrane composed by cylindrical particles is governed by Darcy’s law. In this work, we discussed the effect of various fluid parameters like permeability parameter $ k_{0}$ , discontinuity coefficient at fluid-non homogeneous porous interface, viscosity ratio of viscous incompressible fluid region and non-homogeneous porous region, etc. on hydrodynamic permeability of a membrane, stress and on velocity profile. The comparative study for hydrodynamic permeability of membrane built up by non-homogeneous porous cylindrical particles and porous cylindrical shell enclosing a cylindrical cavity has been studied. The effects of various fluid parameters on the streamlines flow patterns are also discussed.

Dielectric polarization and particle shape effects

Abstract: This article reviews polarizability properties of particles and clusters. Especially the effect of surface geometry is given attention. The important parameter of normalized dipolarizability is studied as function of the permittivity and the shape of the surface of the particle. For nonsymmetric particles, the quantity under interest is the average of the three polarizability dyadic eigenvalues. The normalized polarizability, although different for different shapes, has certain universal characteristics independent of the inclusion form. The canonical shapes (sphere, spheroids, ellipsoids, regular polyhedra, circular cylinder, semisphere, double sphere) are studied as well as the correlation of surface parameters with salient polarizability properties. These geometrical and surface parameters are essential in the material modeling problems in the nanoscale.

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Abstract: The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.