Экспериментально и теоретически изучено развитие конвективной неустойчивости в двухслойной системе смешивающихся жидкостей, помещённых в узкий вертикальный зазор. Верхний и нижний слои образованы, соответственно, водными растворами кислоты и основания. При приведении жидкостей в контакт в системе начинается фронтальная реакция нейтрализации. В процессе проведения экспериментальных исследований выявлен новый тип конвективной неустойчивости, характерной особенностью которой является пространственная локализация и периодичность возникающих конвективных структур, что в системах смешивающихся жидкостей наблюдается впервые. Предложена математическая модель явления, включающая систему уравнений реакции-диффузии-конвекции, записанных в приближении Хеле-Шоу. Показано, что воспроизведение в численном эксперименте обнаруженной неустойчивости возможно только при учёте зависимости коэффициентов диффузии как реагирующих компонентов, так и продукта реакции от их концентрации. Представлены результаты численных расчётов основного состояния, нейтральных кривых и нелинейных режимов конвекции. Данные лабораторного и численного моделирования демонстрируют хорошее согласование. We study theoretically and experimentally the development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid-base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction-diffusion-convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction-diffusion-convection equations written within a Hele-Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration-dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and non-linear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-c...

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The problem about the indentation of the rigid spherical stamp into the cylindrical specimen was considered. The material of the specimen was assumed to be weakly compressible. The formulation of the problem was performed for the case of finite deformations. The method of construction of the constitutive relations in terms of logarithmic strain tensor for elastic media and the variant of the algorithm to take into account the variation of the contact zone were proposed. The expansion of Hencky tensor and its time derivative into the series in powers of Cauchy strain tensor were used to calculate correctly the components of these tensors. Within the indentation problem, we used the model of nonlinear elastic material which provides the best agreement between numerical solution and experimental data among other used types of constitutive relations including various elastic and hypoelastic models.

This work is devoted to the new variant of relations between the energetically conjugated Hencky strain tensor and corotational Kirchhoff stress tensor. The elastic energy is represented as a third-order polynomial of the Hencky tensor containing five material constants. Unlike the Almansi tensor in the Murnaghan model, the Hencky tensor allows assigning a clear physical meaning to material constants. Linear part of the constitutive relation represents the Hencky model and contains the bulk modulus and the shear modulus. The two extra constants express nonlinear effects at a purely volumetric strain and a purely isochoric strain, whereas the third constant takes into account the possible deviation from the similarity of the deviators of the Hencky stress and strain tensors. The resulting relations are naturally generalized for incompressible materials. In this case, the overall number of constants decreases from five to two. The designed test unit was used for a compression test of prismatic specimens made of incompressible material. The proposed version of the relations is in good agreement with the experimental data on the compression of rubber samples.

The possibility to apply a physically and geometrically non-linear model of a hyperelastic isotropic material to the description of strains of non-rocky soils is considered. The study examines the stability of the model, restrictions on the model constants, and the definition of the range of deformations within which the model is Drucker stable.