Conductivity and permittivity of dispersed systems with penetrable particle-host interphase

A model for the study of the effective quasistatic conductivity and permittivity of dispersed systems with particle-host interphase, within which many-particle polarization and correlation contributions are effectively incorporated, is presented. The structure of the system's components, including the interphase, is taken into account through modelling their low-frequency complex permittivity profiles. The model describes, among other things, a percolation-type behavior of the effective conductivity, accompanied by a considerable increase in the real part of the effective complex permittivity. The percolation threshold location is determined mainly by the thickness of the interphase. The "double" percolation effect is predicted. The results are contrasted with experiment.Comment: 10 pages, 10 figure

Water entry of an expanding wedge/plate with flow detachment

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to π. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions

Liquid impact on a permeable solid body

All rights reserved.The free surface flow and the hydrodynamic loads generated by impact between a liquid wedge and a permeable solid body are investigated. The study is carried out within the framework of self-similar solution, which is realistic for this kind of configuration and over the short period of impact. We study the effect of liquid penetration through the porous/perforated solid surface on the pressure distribution and flow pattern. An integral hodograph method is employed to convert the differential equation in the fluid domain into integral equations along the axes of a parameter plane, from which the problem corresponding to the impermeable solid surface is a special case. The system of integral equations are solved numerically using the method of successive approximations. Results are presented for streamline patterns and pressure distribution along the solid surface of permeable wedges

Free-surface gravity flow due to a submerged body in uniform current

The hydrodynamic problem of a body submerged beneath a free surface in a current is considered. The mathematical model used is based on the velocity potential theory with fully nonlinear boundary conditions. The integral hodograph method used previously in a simply connected domain is extended for the present problem to a doubly connected domain. Analytical expressions for the complex velocity and for the complex potential are derived in a rectangular region in a parameter plane, involving the theta functions. The boundary-value problem is transformed into a system of two integral equations for the velocity modulus on the free surface and for the slope of the submerged body surface in the parameter plane, which are solved through the successive approximation method. Case studies are undertaken both for a smooth body and for a hydrofoil with a sharp edge. Results for the free surface shape, pressure distribution as well as resistance and lift are presented for a wide range of Froude numbers and depths of submergence. It further confirms that at each submergence below a critical value there is a range of Froude numbers within which steady solution may not exist. This range increases as the submergence decreases. This applies to both a smooth body and a hydrofoil. At the same time it is found that at any Froude number beyond a critical value the wave amplitude and the resistance decrease as the body approaches the free surface. In these cases nonlinear effects become more pronounced

Splash jet generated by collision of two liquid wedges

A complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined