T. Miloh

Imperfect soft and stiff interfaces in two-dimensional elasticity

Abstract A thin curved isotropic layer of constant thickness between two elastic isotropic media in a two-dimensional plane strain setting is considered. The properties of the curved layer are allowed to vary in the tangential direction. We aim at modeling this layer by an interface between the two media across which certain conditions on the tractions and displacements will prevail. It is shown that depending on the softness or stiffness of the layer with respect to the neighboring media, there exist seven distinct regimes of interface conditions. Two of these conditions describe the case of a layer which is soft with respect to the neighboring media; they will be referred to as “soft interface” conditions. One condition describes ideal contact. The remaining four, called “stiff interfaces”, concern the case of a stiff interphase. The stiff interface conditions which bear a close resemblance to membrane and classical shell theories are new and constitute the main contribution of this work. The derivation is based on the use of an asymptotic expansion for the elastic field in the layer.

On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces

The effective conductivity of composite media with ellipsoidal inhomogeneities and highly conducting interfaces is studied. At such interfaces the temperature field is continuous, but the normal component of the heat flux undergoes a discontinuity which is proportional to the local surface Laplacian of the temperature field. The dilute approximation for the case of ellipsoidal inhomogeneities in such circumstances is derived. The derivation involves the solution of an auxiliary problem of a single particle embedded in an infinite medium and employs ellipsoidal harmonics. This solution is also used to derive a mean–field approximation for non–dilute concentrations.

A generalized self‐consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies

This paper is concerned with the determination of the effective thermal conductivity of particulate composites with ellipsoidal‐type inclusions at nondilute concentrations with special emphasis given to the case of cracked bodies with elliptical cracks. The inclusions or cracks are randomly oriented so that the solid is effectively isotropic. The adopted micromechanics model is the ‘‘generalized self‐consistent’’ scheme which is based on the concept that a particle surrounded by some matrix material ‘‘sees’’ an effective medium. The method, whose reliability has already been proved in the literature, is applied for the first time in the present paper to composites containing inclusions of ellipsoidal shape. The generality of the presented analysis allows the treatment of cracked bodies with randomly oriented elliptical cracks. New results are given for particulate composites and cracked bodies.

ON THE EFFECTIVE THERMAL CONDUCTIVITY OF COATED SHORT-FIBER COMPOSITES

Effective‐medium theories are formulated which predict the effective thermal conductivity of coated short‐fiber composites. Composite aggregates that contain coated inclusions which may be aligned or randomly oriented are considered. A basic result which simplifies considerably the analysis of such systems in heat conduction problems is first established: It is shown that under certain situations a coated ellipsoidal inclusion can be replaced by an equivalent homogeneous but anisotropic one. For the composite with aligned short fibers, a microgeometry is constructed which possesses an exact solution for the effective conductivity. Self‐consistent and differential schemes are formulated for the composite with randomly oriented coated short fibers.

Symmetry breaking in induced-charge electro-osmosis over polarizable spheroids

We study the induced-charge electro-osmotic flow around a stationary polarizable dielectric spheroid in the presence of a uniform arbitrarily oriented external electric field. A Robin-type condition connecting the respective electric potentials within the dielectric solid and the bulk electro-neutral solution is highlighted in formulating the macroscale description for the limit of thin electric double layers and low potentials. The results illustrate symmetry breaking phenomena in the ensuing flow and demonstrate qualitative differences associated with variations of the dielectric constant. We briefly discuss the potential impact of these differences on the rotation of freely suspended spheroids.

The Ultimate Image Singularities for External Ellipsoidal Harmonics

The image system of singularities of an arbitrary exterior potential field within a triaxial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field within a sphere and spheroid. A proof of Havelock’s spheroid theorem, which apparently is not available in the literature, is also given.The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem.The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation.

On electro-osmotic flows through microchannel junctions

We study the electro-osmotic flow through a T-junction of microchannels whose dielectric walls are weakly polarizable. The present global analysis thus extends earlier studies in the literature concerning the local flow of an unbounded electrolyte solution around nearly insulated wedges. The velocity field is obtained via superposition of an irrotational part associated with the equilibrium zeta potential and the induced-charge electro-osmotic flow originating from the interaction of the externally applied electric field and the charge cloud it induces owing to field leakage through the polarizable dielectric channel walls. Along the channel walls the latter component gives rise to fluid velocities converging toward the corner which dominate the flow in its immediate vicinity. Recent experimental observations in the literature regarding the appearance and subsequent expansion of flow reversal and vortices downstream (initially) and upstream (subsequently) of the junction, are both rationalized in terms of...

Neutral inhomogeneities in conduction phenomena

Abstract A neutral inhomogeneity in heat conduction is defined as a foreign body which can be introduced in a host solid without disturbing the temperature field in it. The existence of neutral inhomogeneities in conduction phenomena is studied in the present paper. Both the inhomogeneity and the host body are assumed to be isotropic, with the inhomogeneity being either less or more conducting than the surrounding body. The property of neutrality is defined in this work with respect to an applied constant temperature gradient in the host solid. It is achieved by introducing a non-ideal interface between the two media across which the continuity requirement of either the temperature field or the normal component of the heat flux is relaxed. These interfaces are called non-ideal interfaces and represent a thin interphase of low or high conductivity; they are characterized in terms of some scalar interface parameters which usually vary along the interface in order to ensure neutrality. The conditions to be satisfied by the field variables at a non-ideal interface with a variable interface parameter are first derived, and closed form solutions are presented for the interface parameters at neutral inhomogeneities of various shapes. In two-dimensional problems, duality relations are established for composite media with non-ideal interfaces and variable interface parameters. These are implemented in establishing general criteria for neutrality. The terminology of heat conduction is used throughout in the paper but all the results can be directly transferred to the domains of electrical conduction, dielectric behavior or magnetic permeability.

ON THE INITIAL-STAGE SLAMMING OF A RIGID SPHERE IN A VERTICAL WATER ENTRY

Analytic expressions are obtained for the small-time slamming coefficient and wetting factor of a rigid spherical shape in a vertical water entry. The theoretical model neglects gravity, compressibility and viscous effects with respect to inertia, which is usually the dominant effect during the early stages of water impact. Replacing the free-surface by a flat equipotential surface enables us to solve the incompressible inviscid flow problem about a double spherical bowl for the Stokes stream function expressed in terms of toroidal coordinates 12 . A semi-Wagner approach is then used to compute the wetting factor and the Lagrange equations are employed in order to determine the slamming force from the kinetic energy of the fluid. Good argeement between theoretical model and available experimental measurements has been obtained, both for the early-stage impact force and the free-surface rise at the vicinity of the three-phase contact line (wetting correction factor).

Unsteady Lagally theorem for multipoles and deformable bodies

The Lagally theorem for unsteady flow expresses the forces and moments acting on a rigid body moving in an inviscid and incompressible fluid in terms of the singularities of the analytically continued flow within the body. Previous generalizations of the Lagally theorem, originally given by Lagally (1922) for steady flows, are due to Cummins (1957) and Landweber & Yih (1956), who consider the effect of flow unsteadiness on the forces and moments. In these, the system of image singularities within the body was assumed to consist of isolated or continuous (surface or volume) distributions of sources and doublets. A further extension of Lagallys theorem ie due to Landweber (1967), who derived expressions for the steady forces and moments acting on a rigid body generated by isolated or a continuous distribution of multipoles. The purpose of the present paper is to generalize the Lagally theorem so as to include the effects of multipoles in unsteady flow, and deformability of the body, as well as to present a briefer derivation of the resulting formulae. Two examples, illustrating the application of the force and moment formulae, will be presented.