Theoretical investigation of gas dissolution in a vortex chamber without taking account of bubble coagulation

The problem is examined of motion of a single spherical bubble with mass transfer in a swirling liquid flow. It is assumed that the bubble rotates without tangential slip while the dissolution process occurs without chemical reaction and heat release. A numerical solution is performed of the system of motion and dissolution equations by the method of prediction and correction. The floating velocity and the change in bubble mass as it moves toward the vortex axis are computed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 1, pp. 48–51, July, 1990.     

Numerical modelling of fluids mixing,heat transfer and non‐equilibrium redox chemical reactions in fluid‐saturated porous rocks

Non‐equilibrium redox chemical reactions of high orders are ubiquitous in fluid‐saturated porous rocks within the crust of the Earth. The numerical modelling of such high‐order chemical reactions becomes a challenging problem because these chemical reactions are not only produced strong non‐linear source/sink terms for reactive transport equations, but also often coupled with the fluids mixing, heat transfer and reactive mass transport processes. In order to solve this problem effectively and efficiently, it is desirable to reduce the total number of reactive transport equations with strong non‐linear source/sink terms to a minimum in a computational model. For this purpose, the concept of the chemical reaction rate invariant is used to develop a numerical procedure for dealing with fluids mixing, heat transfer and non‐equilibrium redox chemical reactions in fluid‐saturated porous rocks. Using the proposed concept and numerical procedure, only one reactive transport equation, which is used to describe the distribution of the chemical product and has a strong non‐linear source/sink term, needs to be solved for each of the non‐equilibrium redox chemical reactions. The original reactive transport equations of the chemical reactants with strong non‐linear source/sink terms are turned into the conventional mass transport equations of the chemical reaction rate invariants without any non‐linear source/sink terms. A testing example, for some aspects of which the analytical solutions are available, is used to validate the proposed numerical procedure. The related numerical solutions have demonstrated that (1) the proposed numerical procedure is useful and applicable for dealing with the coupled problem between fluids mixing, heat transfer and non‐equilibrium redox chemical reactions of high orders in fluid‐saturated porous rocks; (2) the interaction between the solute diffusion, solute advection and chemical kinetics is an important mechanism to control distribution patterns of chemical products in an ore‐forming process; and (3) if the pore‐fluid pressure gradient is lithostatic, it is difficult for the chemical equilibrium to be attained within permeable cracks and geological faults within the crust of the Earth. Copyright © 2005 John Wiley & Sons, Ltd.     

Mass transfer from a particle in a shear flow with surface reactions

Summary The steady mass transfer from a spherical particle (drop, bubble or solid particle) in a shear flow with chemical surface reactions is considered. For the complete range of Peclet numbers the numerical solution for the problem is obtained. The approximate formulae for the average rate of mass transfer are suggested. The comparison between the numerical results for the rate of transfer and those which are given by the approximate formulae is discussed.     

Mass transfer accompanied by a chemical reaction taking place rapidly inside a moving spherical drop

The article deals with the problem of convective mass exchange between a liquid drop and a continuous medium, accompanied by an irreversible chemical reaction of second order at high Pe and K values. A numerical solution of the transfer equations is given. The limits of applicability of the resulting solutions are defined.     

Evaluating the Dissolution Behavior of Zinc-Complexed Protein Suspensions by Computer Modeling and Simulation

ABSTRACT

In vitro dissolution of zinc insulin suspensions can be promoted by the complexation of zinc with an ionic species for which the zinc ion has a greater affinity. Studies conducted by our group have previously shown that the rate-limiting steps that govern the dissolution of zinc-complexed insulin suspension may be chemical complexation (surface reaction) and subsequent drug mass transport (diffusion and solubility). The purpose of this work was to use a computer simulation model to predict the dissolution behavior of zinc-complexed insulin suspensions and determine the influence of the above rate-limiting steps on the overall process of dissolution. A quasi-steady-state model was chosen which included the effects of a shrinking particle radius, the drug's solubility, and a convective mass transfer term. Based on this model, the computer simulation program evaluated dissolution behaviors of various model drugs, including zinc insulin suspensions. The experimental data obtained from actual dissolution experiments were superimposed on computer-generated profiles that incorporated quantitative values to key terms, namely the α (diffusion resistance) and β (surface reaction resistance) values. Results demonstrated that the computer simulations could be used to predict the dissolution behavior of zinc-complexed protein suspensions by manipulating the α and β values. Overall, the computer simulations indicated the involvement of both the surface reaction and the diffusion rate-limiting steps in zinc insulin dissolution, which was consistent with the results obtained from actual experimental studies.     

“Averaging” method in problems of convective mass and heat transfer

An approximate method is proposed for the solution of nonlinear boundary problems of convective heat and mass transfer; the method is based on the procedure of averaging equations or boundary conditions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 2, pp. 205–215, August, 1984.     

Evaluating the dissolution behavior of zinc-complexed protein suspensions by computer modeling and simulation

In vitro dissolution of zinc insulin suspensions can be promoted by the complexation of zinc with an ionic species for which the zinc ion has a greater affinity. Studies conducted by our group have previously shown that the rate-limiting steps that govern the dissolution of zinc-complexed insulin suspension may be (1) chemical complexation (surface reaction) and (2) subsequent drug mass transport (diffusion and solubility). The purpose of this work was to use a computer simulation model to predict the dissolution behavior of zinc-complexed insulin suspensions and determine the influence of the above rate-limiting steps on the overall process of dissolution. A quasi-steady-state model was chosen which included the effects of a shrinking particle radius, the drug's solubility, and a convective mass transfer term. Based on this model, the computer simulation program evaluated dissolution behaviors of various model drugs, including zinc insulin suspensions. The experimental data obtained from actual dissolution experiments were superimposed on computer-generated profiles that incorporated quantitative values to key terms, namely the alpha (diffusion resistance) and beta (surface reaction resistance) values. Results demonstrated that the computer simulations could be used to predict the dissolution behavior of zinc-complexed protein suspensions by manipulating the alpha and beta values. Overall, the computer simulations indicated the involvement of both the surface reaction and the diffusion rate-limiting steps in zinc insulin dissolution, which was consistent with the results obtained from actual experimental studies.     

Mass transfer from a moving bubble during a slow chemical reaction

A previously proposed method for solving inhomogeneous problems in the theory of heat and mass transfer is refined. As an illustration, the stationary mass transfer from a moving bubble during a slow chemical reaction of first or second order is examined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 4, pp. 595–599, April, 1982.     

Solving the equation of mass transfer in a stationary bed of granular material

A general procedure is proposed for the exact integration of a system of quasilinear differential equations often encountered in problems concerning the convective mass transfer in a bed of granular material with reaction at the surface and in the volume of particles.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 2, pp. 308–315, August, 1972.     

A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate

The influence of thermal radiation and chemical reaction on the steady MHD heat and mass transfer by a mixed convective flow of a viscous, incompressible, electrically conducting Newtonian fluid (an optically thin gray gas) past a vertical permeable plate was investigated with account for the induced magnetic field. The similarity solutions of the transformed nondimensional governing equations are obtained by the series solution technique. The influence of numerous parameters on the process characteristics is studied.     

Modeling heterogeneous chemical reactions under the action of a turbulent jet

The chemical reaction of a solution with a metallic surface is modeled by the physical process of mass transfer. The general form of solution of the equation of convective diffusion is found and the possibility of calculating parameter values for which the process will occur efficiently is examined. The results of analysis are confirmed by experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 3, pp. 429–434, March, 1977.     

Coupled simultaneous heat and mass transfer in multicomponent two-phase mixtures

A method is proposed for calculating the parameters of simultaneous heat and mass transfer in a multicomponent two-phase gas-liquid system, this method being based on solving the system of differential equations of convective heat transfer and convective diffusion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 421–428, September, 1985.     

Coupled thermo/hydro/chemical/mechanical model for unsaturated soils—Numerical algorithm

This paper presents the implementation of a numerical algorithm for a new coupled thermal–hydraulic–chemical–mechanical model for unsaturated soil. A brief treatment of the theoretical development of the coupled model is presented first, with specific attention to the multi‐component chemical transport theory and its cross couplings with other primary variables. The system of coupled equations is based on a mechanistic approach with conservation of mass or energy equations defining the flow behaviour and a stress–strain equilibrium equation defining the mechanical behaviour. The geochemical interactions are incorporated by linking a geochemical model with the system of coupled flow and deformation equations. Two coupling strategies, namely, sequential non‐iterative and sequential iterative approaches are incorporated to link the multi‐component chemical transport equation with geochemical interactions. The model's ability is then demonstrated via a series of 1D examples, which consider complex coupling scenarios involving all the primary variables. Specifically, the effects of multi‐component precipitation/dissolution and ion exchange reactions in a variable thermal–hydraulic–mechanical field are considered. The numerical efficiency of the model is also analysed based on these examples. It is concluded that the model not only provides a stable solution but is able to produce results that are qualitatively consistent with observed behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Mass transfer correlation of NH3–H2O bubble absorption

The objectives of this paper are to study the effect of key parameters on absorption performance and to develop an experimental correlation of mass transfer coefficient for ammonia–water bubble absorption. The orifice diameter, liquid concentration and vapor velocity are considered as the key parameters. This study successfully visualized the bubble behavior and measured the volumetric diameter of bubbles during the bubble absorption process. The bubble absorption is grouped into two processes, bubble growth (process I) and bubble disappearance (process II), respectively. The following conclusions were drawn from the present study. A new experimental correlation for the volumetric bubble diameter was proposed with ±15% error band, which could be applied to calculate the mass transfer coefficient. The mass transfer coefficient increased with a decrease of the liquid concentration. In process II, the mass transfer coefficient increased with an increase of the Galileo number. Finally, experimental correlations of mass transfer coefficient were developed for processes I and II with ±18% error bands.     

Mathematical modeling of convective heat and mass transfer in the drying of solid particles in a bed

A closed system of equations is proposed for calculating convective heat and mass transfer in the drying of solid particles by a gaseous heat transfer agent in a moving bed. As an example, the operation of a belt-type dryer with crossed interaction of a drying agent and a bed of fruit cut into circular slices is considered. Results of a numerical solution of the problem are presented in figures.Institute of Engineering Thermophysics, Academy of Sciences of Ukraine, Kiev. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 1–2, pp. 48–53, July–August, 1994.     

Unsteady three-dimensional combined heat and mass free convective flow over a stretching surface with time-dependent chemical reaction

Summary This paper investigates the combined effects of the free convective heat and mass transfer on the unsteady three-dimensional laminar boundary layer flow over a stretching surface. The stretching rates of the surface are assumed to vary as a reciprocal of a linear function of time. Generation or consumption of the diffusing species due to a homogeneous chemical reaction is considered. The chemical reaction rate is assumed to vary with time according to a power law. With appropriate similarity transformation, the boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying a fifth-order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Prandtl number Pr, Schmidt number Sc, the unsteadiness parameter λ, the chemical reaction parameter γ₀ and the reaction order n are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various values of the parameters. A comparison is made between the present work and previous results.     

Growth of a bubble of noncondensing gas injected into a liquid

The solution of the problem of growth of a gas-vapor bubble injected into a liquid is obtained. The growth of the bubble depends on mass transfer in the gas phase and heat transfer in the liquid phase. Experimental and theoretical data are compared.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 6, pp. 978–989, June, 1977.     

Multicomponent heat and mass transfer during the turbulent flow of liquid films

A method is proposed for calculating the parameters of simultaneous heat and mass transfer in turbulent multicomponent liquid films which is based on solving the system of differential equations for convective heat conduction and multicomponent convective diffusion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 1, pp. 16–22, July, 1989.     

Slip at a uniformly porous boundary: effect on fluid flow and mass transfer

An approximate solution to the 2-D Navier-Stokes equations for steady, isothermal, incompressible, laminar flow in a channel bounded by one porous wall subject to uniform suction is derived. The solution is valid for small values of the Reynolds number based on the suction velocity and channel height. Solute transport is considered numerically by decoupling the equations representing momentum and mass transfer. The effect of fluid slip at the porous boundary on the axial and transverse components of fluid velocity, axial pressure drop and mass transfer is investigated.     

Non-equilibrium thermodynamics and variational principles for fully coupled thermal–mechanical–chemical processes

In this paper, the chemical Gibbs function variational principle, the Helmholtz function variational principle and the internal energy variational principle based on irreversible thermodynamics are proposed for the thermal–chemical–mechanical fully coupling problems. The complete fully coupling governing equations, including the heat conduction, mass diffusion and chemical reactions, are derived from the variational principles. The convective effect can also be derived in the diffusion and energy equations from the variational principles naturally. Moreover, the concentrations and entropy jump conditions on the moving interface between the products due to chemical reactions and the matrix can be derived from the variational principles naturally. This work provides the basis for the analyses and computations of thermochemomechanical coupling problems.