Dual-frequency generator with strong subharmonic

The self-excited oscillations of a generator whose nonlinear amplifier has a nonlinear input (output) capacitance are analyzed theoretically. The excitation of dual-frequency oscillations with a strong subharmonic component is examined. Experimental results are presented that confirm the possibility of the simultaneous generation of fundamental and subharmonic components with comparable amplitudes.Scientific-Industrial Organization, Almaz. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 1, pp. 97–104, January, 1993.     

Thermocapillary convection in a liquid layer with local heating

The motion induced in a liquid by a heat pulse is mathematically described. The velocity and temperature distributions on the surface and in the body of the liquid are determined numerically. The theoretical results obtained are compared with the experimental data of [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–156, September–October, 1987.The authors are very grateful to V. A. Al'vares-Suares for discussing their results.     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.     

Influence of transport processes on steady regimes of a chemical flow reactor with reaction of the type a → b,a+b→2c

An approximate analytic solution is obtained to the problem of the concentration distribution in a one-dimensional chemical flow reactor for a reaction of the type A B, A + B 2C in the approximation of a weak reaction. The method of small perturbations up to terms of third order is used. A study is made of the influence of the intensity of longitudinal mixing on the degree of transformation, the selectivity, and the yield. It is found that the optimal level of longitudinal mixing in the weak reaction approxmation is determined by a dimensionless parameter that is a combination of the dimensionless rates of the chemical reactions. The dependence of the optimal Péclet number on this parameter is found. Characteristic regions are determined on the plane of the determining parameters in which the interaction of the physical and chemical processes in the reactor leads to different results, which must be taken into account when choosing the type and the parameters of a chemical reactor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–113, November–December, 1982.     

Uniqueness and stability of steady states of continuous chemical reactors

We examine the uniqueness and stability of the solutions to the problem of steady-state operation of a continuous chemical reactor in which longitudinal diffusion and heat conduction are taken into account. We investigate an adiabatic reactor in which the concentration and temperature distributions are similar (the thermal diffusivity and diffusion coeffecient are equal) and an isothermic reactor. These two cases are considered together because the mathematical formulations of the problem are equivalent.The question of the existence and number of steady states was analyzed in [1, 2], where references were made to earlier investigations. The results obtained in [1, 2] are now extended. The stability of the steady states is investigated by the small-perturbation method.     

Chemoconcentration capillary effect associated with the motion of a drop in a liquid

The effect of a surface chemical reaction involving a weak soluble surface active substance on the motion of a drop in a liquid is investigated. It is shown that as a result of the Marangoni effect the non-uniformity in the distribution of the substance along the surface associated with the proper motion of the drop and the chemical reaction has an important influence on the nature of the motion of the drop and on the force exerted by the surrounding Liquid. Under certain conditions this Leads to the development of a thrust proportional to the velocity of the drop (chemoconcentration capillary effect). The condition of occurrence of the thrust is obtained, together with its dependence on various physical parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 147–154, January–February, 1988.     

On the theory of stationary velocity of propagation of an exothermic reaction front in a condensed medium

It has been demonstrated experimentally that in the combustion of many explosives and powders in the condensed phase (k-phase) an exothermic chemical reaction occurs. Although the heat release in the k-phase is usually small in comparison with the calorific value, it may play an important role in the multistage reaction in the combustion zone.Analysis of the heat balance of the k-phase reveals that in a number of cases heating of the substance before gasification is primarily due to self-heating. According to the thermocouple measurements made by A. A. Zenin, the heat release in the k-phase during combustion of nitroglycerine N powder is more than 80% of the total quantity of heat in the heated layer of the k-phase (pressure 50 atm). This makes it possible to speak of the propagation of the exothermic reaction front in a condensed medium as the first stage in the combustion of condensed systems. Cases are also known where the propagation of the reaction front is maintained only by self-heating (flameless combustion [1]), and there are cases when such propagation is not accompanied by gasification (combustion of thermites, sometimes the polymerization process). Theoretical investigations of stationary propagation of a reaction front in a condensed medium were made in [2–6]. We note that this problem is also of interest in relation to the study of various nonstationary phenomena associated with the combustion of powders [7–9]. One of the principal theoretical problems is the derivation of a formula for the velocity of propagation of the reaction front in the k-phase. The Zel'dovich-Frank-Kamenetskii method [10] was used in [2–5] in the solution of this problem.This paper is an investigation of the applicability of the Zel'dovich-Frank-Kamenetskii method to the case of propagation of a zero-order reaction front in the k phase. A method is proposed for deriving a formula for the propagation velocity of the front leading in the case of a zero-order reaction to a formula identical to that obtained using the Zel'dovich-Frank-Kamenetskii method, and this method is then used to derive a formula for the propagation velocity of a first-order reaction front in the k-phase. The upper and lower limits of the velocity given by this formula are investigated.     

Diffusion flux to a distorted gas bubble at large Reynolds numbers

The diffusion flux to a distorted gas bubble situated in a uniform viscous incompressible fluid flow is determined for large Reynolds and Péclet numbers and finite Weber numbers. The bubble has the shape of an ellipsoid of revolution, oblate in the flow direction, making it possible to use the flow field derived by Moore [1] in the form of a two-term expansion with respect to the flow parameter =R^–1/2 (R is the Reynolds number; the zeroth term of the expansion corresponds to potential flow). The dependence of the diffusion flux onto the bubble surface on the Weber and Reynolds numbers is determined. The results of Winnikow [2] and Sy and Lightfoot [3] are thus generalized to the case of finite Weber numbers and a broader range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–76, July–August, 1976.