Asok K. Sen

Steady thermocapillary flows in two-dimensional slots

Liquid in a slot flows owing to a temperature gradient applied along its free surface. The thermal variation of surface tension induces a steady viscous flow directed on the surface from hot to cold, and recirculating below. For small aspect ratios A, giving flow in thin, two-dimensional slots, an asymptotic theory valid for A yields to 0 is used to obtain the fluid and thermal fields as well as the interfacial shapes. Solutions are obtained for both fixed lines and fixed angles at the contact between the interface and the solid side walls.

An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction

Abstract An approximate analytical solution for the transient phase of the Michaelis-Menten reaction is derived using the Adomian decomposition method. The analytical solution, which is given in the form of a power series, is found to be highly accurate in predicting the behavior of the reaction in the very early stages. To accelerate the convergence of the power series solution and extend its region of applicability throughout the entire transient phase, we have used (a) the method of Pade approximants and (b) the iterated Shanks transformation. Both the Pade approximant and the Shanks transformation are shown to converge rapidly throughout and beyond the transient period and yield very accurate results. A comparison of the various analytical approximations and a direct numerical solution of the nonlinear initial value problem is also presented.

Thermocapillary convection in a rectangular cavity with a deformable interface

Steady thermocapillary convection is examined in a differentially heated rectangular cavity of small aspect ratio A. It is shown that when the capillary number is C=O(A3), the interface undergoes an O(1) deformation from its flat position and the flow inside the cavity becomes nonparallel everywhere. The velocity and temperature profiles and the shape of the deformed interface are derived using the method of matched asymptotic expansions.

Natural convection in a shallow porous cavity—the Brinkman model

Abstract The natural convection in a shallow porous rectangular cavity with differentially heated sidewalls is examined using the Brinkman model. The heat transfer rate through the cavity is determined in terms of a Nusselt number, in the limit of vanishingly small aspect ratio. Two types of boundary conditions are considered. Case I deals with a cavity with all rigid boundaries so that the no-slip boundary conditions can be imposed. In case II, the cavity has a free upper surface. The present analysis shows that the Brinkman model and Darcys law give virtually the same result for the heat transfer rate when the Darcy number, based on the depth of the cavity, is less than the order of 10 −4 . We also find that the presence of a free surface can significantly increase the heat transfer rate through the cavity, especially when the permeability of the medium is high.

Topological analysis of metabolic control

A topological approach is presented for the analysis of control and regulation in metabolic pathways. In this approach, the control structure of a metabolic pathway is represented by a weighted directed graph. From an inspection of the topology of the graph, the control coefficients of the enzymes are evaluated in a heuristic manner in terms of the enzyme elasticities. The major advantage of the topological approach is that it provides a visual framework for (1) calculating the control coefficients of the enzymes, (2) analyzing the cause-effect relationships of the individual enzymes, (3) assessing the relative importance of the enzymes in metabolic regulation, and (4) simplifying the structure of a given pathway, from a regulatory viewpoint. Results are obtained for (a) an unbranched pathway in the absence of feedback the feedforward regulation and (b) an unbranched pathway with feedback inhibition. Our formulation is based on the metabolic control theory of Kacser and Burns (1973) and Heinrich and Rapoport (1974).

The Near-Stoichiometric Behavior of Combustible Mixtures Part II: Dissociation of the Products

Abstract The burning rate of a combustible mixture is experimentally found to be maximum when the unburnt mixture is slightly fuel-rich. In Part I the authors explained this neat-stoichiometric behavior purely on the basis of diffusion of the reactants. The usual explanation is based on dissociation of the products, according to which dissociation causes the maximum flame temperature and therefore the maximum burning rate to occur slightly on the fuel-rich side of stoichiometry. However, as indicated in Part I, several aspects of this explanation are unsatisfactory. The purpose of the present paper is to show that while dissociation explains the shift of the maximum temperature onto the fuel-rich side, it has only a subsidiary effect on the maximum burning rate.

A graph-theoretic analysis of metabolic regulation in linear pathways with multiple feedback loops and branched pathways

With the aid of signal flow graphs, we have analyzed the flux-control distribution in linear metabolic pathways with multiple feedback loops and branched pathways. It is shown that the flux control coefficients of the enzymes in a linear pathway with multiple feedback loops can be evaluated by modifying the signal flow graph of the unregulated pathway in a step-by-step fashion. On the basis of the results obtained with the signal flow graphs, a principle of superposition is suggested for calculating the flux control coefficients of a linear pathway with a general pattern of feedback inhibition. Using this superposition principle, it is possible to determine the flux control coefficients directly from an examination of the topology of the feedback loops in the metabolic pathway, without drawing a signal flow graph. In a branched pathway the control coefficients of the enzymes depend on the fluxes through the various branches in addition to the enzyme elasticities. We show how these fluxes can be incorporated into a signal flow graph from which the flux control coefficients are found. We also describe a systematic procedure for converting a signal flow graph to a simpler form which may significantly reduce the effort necessary for calculating the flux control coefficients. Modifications of a signal flow graph for assessing the relative importance of the enzymes in flux control are also discussed. Based on our findings from the signal flow graphs, we have presented a heuristic method for determining the flux control coefficients directly from the reaction sequence of the pathway, without drawing a signal flow graph. The present analysis applies to metabolic pathways in a steady state.

Enhancement factors for gas absorption with chemical reaction: approximate analytical solutions

Abstract In this paper we examine the problem of absorption of two gases in an inert liquid with simultaneous chemical reaction. In the slow reaction regime, a regular perturbation solution is derived for the enhancement factors of the solute gases. Using the methods of Pade approximants and Shanks transformations, the regular perturbation solution (which is strictly valid in the slow reaction regime) is extended so that the results are applicable in the intermediate reaction regime and, in many cases, in the fast reaction regime. The results obtained by Pade approximants and Shanks transformations are found to be in excellent agreement with the direct numerical solutions of the enhancement factors. By virtue of their analytical nature and high accuracy, the present results may be used as a valuable tool in setting forth design criteria for many mass transfer operations in gas-liquid systems.

Mass transfer with chemical reaction—I. A second-order irreversible reaction

Abstract The process of simultaneous absorption of two gases which react between themselves in an inert liquid is examined in the realistic limit of fast reaction. In this limit the nonlinear mass balance equations based on film theory are solved analytically using the method of matched asymptotic expansions. Explicit analytical expressions for the enhancement factors and concentration profiles of the gaseous solutes are derived. Results are given for the case where the two gases undergo an irreversible chemical reaction and the reaction rate is first order with respect to each of the solute concentrations. The nonlinear mass-transfer equations are also solved numerically using a shooting technique. When the dimensionless reaction rate constant is large, the analytical solution for the enhancement factor is found to be in excellent agreement with the numerical solution, with an error of less than 0.2% (better than any previously achieved).

Effects of Mass Diffusion on the Burning Rate of Non-Dilute Mixtures,

Diffusion effects on the burning rate of a combustible mixture have been examined on the basis of multicomponent diffusion laws. Explicit dependencies of the burning rates on the Lewis numbers, corresponding to the various binary diffusion coefficients, are established in terms of “effective” Lewis numbers. For all practical purposes the nearstoichiometric behavior of a non-dilute mixture is found to be the same as that of a mixture whose reactants are dilute in an inert (provided that, in the absence of any inert, the product is used in calculating Lewis numbers). Motivation comes from the experimental finding that the burning rate invariably has its maximum slightly on the fuel-rich side of stoichiometry, both in the presence and absence of dissociation (cool flames). The authors have previously explained the phenomenon purely on the basis of diffusion (in contrast to the current reliance on dissociation, which excludes cool flames), but used a dilute-mixture theory. That defect is here removed.