Papers by Author: Tov Elperin

Abstract: We consider non-stationary convective mass transfer in a binary system comprising a stationary dielectric two-dimensional fluid drop embedded into an immiscible dielectric liquid under the influence of a constant uniform electric field. The partial differential equation of diffusion is solved by means of a similarity transformation, and the solution is obtained in a closed analytical form. Dependence of Sherwood number vs. the strength of the applied electric field is analyzed. It is shown that an electric field can be used for enhancement of the rate of mass transfer in terrestrial and reduced gravity environments.

Abstract: In 1974 an unusual phenomenon called Usherenko effect was observed in impact experiments [1,2]. Surprisingly large were impact produced craters whose depth varied between 100 and 10000 times the impactor’s size. For materials whose static strength is small or zero, e.g., sand or water, the depth of penetration is no larger than 100 times the size. When a macro-size body impacts on a barrier, it produces a crater whose depth is normally in a ratio of no larger than 6-10 to the body’s size regardless impact parameters. The papers [1,3] give overviews of models which were developed to explain the phenomenon. They all try to answer why material resistance to the penetration of micro-size impactors suddenly decreases. We suggest a model that uses the concept of particle entrainment by a shock produced by the impact of a bunch of particles on a barrier. The approach was proposed by V.A. Simonenko [4]. It is based on calculations by the finite-difference technique TWS [5,6]. Such an approach shows prospects for further development with account for new experimental results obtained after 1991. The goal of this paper is to demonstrate feasibility of applying this approach for justification of impactor’s acceleration in solid.

Abstract: Numerous experimental investigations on the reflection of plane shock waves over straight wedges indicated that there is a domain, frequently referred to as the weak shock wave domain, inside which the resulted wave configurations resemble the wave configuration of a Mach reflection although the classical three-shock theory does not provide an analytical solution. This paradox is known in the literature as the von Neumann paradox. While numerically investigating this paradox Colella & Henderson [1] suggested that the observed reflections were not Mach reflections but another reflection, in which the reflected wave at the triple point was not a shock wave but a compression wave. They termed them it von Neumann reflection. Consequently, based on their study there was no paradox since the three-shock theory never aimed at predicting this wave configuration. Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later concluded that the wave configuration, inside the questionable domain, includes in addition to the three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave configuration, which was first predicted by Guderley [3], was recently observed experimentally by Skews & Ashworth [4] who named it Guderley reflection. The entire phenomenon was re-investigated by us analytically. It has been found that there are in fact three different reflection configurations inside the weak reflection domain: • A von Neumann reflection – vNR, • A yet not named reflection – R, • A Guderley reflection – GR. The transition boundaries between MR, vNR, R and GR and their domains have been determined analytically. The reported study presents for the first time a full solution of the weak shock wave domain, which has been puzzling the scientific community for a few decades. Although the present study has been conducted in a perfect gas, it is believed that the reported various wave configurations, namely, vNR, R and GR, exist also in the reflection of shock waves in condensed matter.