Ethical Ideas of the New Period

This article deals with the philosophical and ethical views of scientists of the new epoch, who expressed their ideas on morality and contributed to the development of the science of ethics. The task of the work is to identify, reveal and show important aspects of the ethical views of the new period of world history

Evolution of the interface in a stratified anisotropic porous material

It is shown that the boundary-value problem describing the evolution of the interface during impregnation of a stratified inhomogeneous anisotropic porous material with a viscous fluid can be reduced to a similar problem for a stratified inhomogeneous isotropic material by nonorthogonal transformation of the coordinates. As a result, the well-known estimates of the problem parameters determining the interface configuration for impregnation of an isotropic material can be extended to the anisotropic case. © 2010 Springer Science+Business Media, Inc

Exact solution of the Muskat–Leibenzon problem for a growing elliptic bubble

© 2016, Pleiades Publishing, Ltd.The exact solution of the two-phase time-dependent Hele–Shaw problem (in other words, the plane Muskat–Leibenzon problem) in which a fluid occupied an unbounded channel is displaced by another fluid incoming through a slitted cut in the channel. In this case the interface between the phases, namely, fluids of different viscosity, evolves as an ellipse whose area and eccentricity vary continuously

Construction of exact solutions to the Muskat problem

A modification of Howison's method is proposed to construct exact nonstationary solutions of the unsteady two-phase Hele-Shaw problem (Muskat problem). The effectiveness of the modified method is demonstrated by reproducing D. Crowdy's exact solution for the evolution of an elliptic bubble of a viscous fluid surrounded by another fluid in an unbounded Hele-Shaw cell. This solution is found to be directly related to the explicit solution of the single-phase Hele-Shaw problem. A comparison of these solutions shows that allowance for the second phase leads to a weak regularizing effect: the single-phase solution exists over a finite time, while the two-phase solution exists over an infinite time under the same initial conditions. © 2011 Pleiades Publishing, Ltd

Unsteady motion of a bubble in a Hele-Shaw cell

© 2016, Pleiades Publishing, Ltd.New exact solutions of an idealized unsteady single-phase Hele-Shaw problem of air-bubble motion in a slot-type channel are constructed under the assumption of bubble symmetry relative to the central axis of the channel. Qualitative features of the interface evolution, which distinguish this case from the earlier considered cases of Hele-Shaw flow with different geometry, are detected

Piercing the water surface with a blade: Singularities of the contact line

© 2016 AIP Publishing LLC. An external meniscus on a narrow blade with a slit-like cross section is studied using the hodograph formulation of the Laplace nonlinear equation of capillarity. On narrow blades, the menisci are mostly shaped by the wetting and capillary forces; gravity plays a secondary role. To describe a meniscus in this asymptotic case, the model of Alimov and Kornev ["Meniscus on a shaped fibre: Singularities and hodograph formulation," Proc. R. Soc. A 470, 20140113 (2014)] has been employed. It is shown that at the sharp edges of the blade, the contact line makes a jump. In the wetting case, the contact line sitting at each side of the blade is lifted above the points where the meniscus first meets the blade edges. In the non-wetting case, the contact line is lowered below these points. The contours of the constant height emanating from the blade edges generate unusual singularities with infinite curvatures at some points at the blade edges. The meniscus forms a unique surface made of two mirror-symmetric sheets fused together. Each sheet is supported by the contact line sitting at each side of the blade

An external meniscus on a thin ovoidal fiber (the case of full wetting)

© 2017, Pleiades Publishing, Ltd. A complex shape of an external meniscus formed due to the capillary rise of a liquid along a fiber having the ovoidal profile is considered. Within the framework of the asymptotic approach and under the assumption on the complete wetting of the fiber material by the liquid, an analytical solution of the problem is derived. The particular examples of the meniscus configuration are presented in the cases in which the fiber profile has the shape of an ovoid or an ellipse

Impregnation of liquids into a laminated porous material with a high permeability contrast

This paper sets the physical basis for an efficient method designed to fill low permeable porous materials with liquids. Fast filling of these materials is achieved if one sandwiches a slightly permeable sample between highly permeable layers. We derived a useful engineering formula for the front speed as a function of the layer permeability and thickness. An asymptotic analysis of the two-dimensional liquid flow with moving front is performed assuming that the covering layers are much thinner than the sample thickness. It is shown that the front forms sawteeth with the tooth apexes moving along the highly permeable layers. If the surface layers are made of the same material, two sawteeth are mirror symmetric with respect to the sample midplane. The angle which they form drastically depends on the ratio of layer-to-sample permeabilities and on the ratio of skin-to-core thicknesses. The theory presented in this paper can be used to optimize the processes of impregnation of nanostructured materials. © 2007 American Institute of Physics