Some general invariance relations in problems of convective heat and mass transfer at large péclet numbers

Some general invariance relations are obtained for the integral diffusion fluxes of the reactant on the surface of one or several reacting particles of arbitrary shape in Stokes flow of a viscous incompressible fluid around the particles at large Péclet numbers. The case of irrotational flow is also considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 92–97, October–December, 1981.     

Steady states of a continuous-flow adiabatic chemical reactor

Flow reactors are widely used in the chemical industry for purposes of catalytic reactions [1,2]. Calculation of reactors of this type, even in one-dimemional approximation, is complicated and possible only with the use of numerical methods [1, 3]. Such calculations make it possible to find the steady-state distribution of temperature and concentration in the chemical reactor if one exists; in general, however, there may be other steady-state regimes which may be preferable from the standpoint of obtaining a different degree of conversion of the starting product, operating stability, etc.In this connection special interest attaches to the question of the existence and number of steady-state solutions of the system of equations describing the reactor process.This problem was previously considered in [4–7]. Thus, in [4, 5] it was pointed out that in certain special cases more than one steady-state regime may exist. In [6, 7] the question of sufficient conditions of uniqueness was investigated. In [7] it was shown that the steady-state regime is unique in the ease of short reactors or a dilute mixture of reactants. In [8] the problem of the existence and uniqueness of the steady-state regime was examined for a chain reaction model with direct application of the general theorems of functional analysis.The present paper includes an analysis of a very simple mathematical model of an adiabatic chemical reactor in which an exothermic or endothermie reaction takes place. It is established that in the case of an endothermic process a unique steady-state regime always exists. In the exothermic case the problem of the steady-state regime also always has a solution which, however, may be nonunique; the possibility of the existence of several steady-state regimes, associated with the form of the temperature dependence of the heat release rate, is substantiated.The authors thank G. I. Barenblatt, A. I. Leonov, L. M. Pis'men, and Yu. I. Kharkats for discussing and commenting on the work.     

Heat flow in a channel with discontinuity of the temperature on the wall

We study the temperature field in the flow of a viscous fluid in a circular tube when there is an abrupt change in the boundary condition for the temperature on the walls at a section of the channel. Following the classical studies [1, 2], this problem has often been considered (for example, in [3, 4, 5]) under different assumptions about the type of flow, the form of the boundary conditions, and the values of the Péclet number. The solutions hitherto obtained are frequently cumbersome and do not exhaust all situations of physical interest. In the present paper, we find the solution to the problem for the case of Poiseuille flow, boundary conditions of the first kind for the temperature, and arbitrary values of the Péclet number. We establish an expression that determines the Nusselt number at different sections of the channel. The results of calculations based on the obtained formulas are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 5, pp. 194–198, September–October, 1979.     

An Approximate Method for Solving an Inverse Coefficient Problem for the Heat Equation

Journal of Applied and Industrial Mathematics - We construct a numerical method for recovering a variable coefficient in the Cauchy problem and also in the initial boundary value problem for the...     

Color Tuning in rhodopsins: the origin of the spectral shift between the chloride-bound and anion-free forms of halorhodopsin

Detailed knowledge of the molecular mechanisms that control the spectral properties in the rhodopsin protein family is important for understanding the functions of these photoreceptors and for the rational design of artificial photosensitive proteins. Here we used a high-level ab initio QM/MM method to investigate the mechanism of spectral tuning in the chloride-bound and anion-free forms of halorhodopsin from Natronobacterium pharaonis (phR) and the interprotein spectral shift between them. We demonstrate that the chloride ion tunes the spectral properties of phR via two distinct mechanisms: (i) electrostatic interaction with the chromophore, which results in a 95 nm difference between the absorption maxima of the two forms, and (ii) induction of a structural reorganization in the protein, which changes the positions of charged and polar residues and reduces this difference to 29 nm. The present study expands our knowledge concerning the role of the reorganization of the internal H-bond network for color tuning in general and provides a detailed investigation of the tuning mechanism in phR in particular.     

Nonstationary motion of drops under the action of capillary and mass forces

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 28–35, July–August, 1991.