Showing papers on "Transport phenomena published in 1971"

The Electrochemical Method in Transport Phenomena

Abstract: Publisher Summary This chapter discusses the method of the diffusion-controlling electrochemical reaction and its applications in the study of transport phenomena. The applications discussed are to mass transfer measurements, to shear stress measurements, and to fluid velocity measurements. In electrode reactions, there exist concentration polarization and chemical polarization in series—that is, the ions move from the bulk of the solution to the surface of the electrode, where the chemical and physical changes occur. In measuring the rates of mass transfer by the use of electrochemical reactions, it is better and more usual to make the chemical polarization negligible because the mass transfer coefficients are most easily obtained from the limiting current when the concentration at the liquid-solid interface can be assumed to be zero. The ions are transferred from the bulk of the solution to the surface of the electrode principally by: (a) migration due to the potential field, (b) diffusion due to the concentration gradient, and (c) convection by the flow.

A Hydrodynamic Model for Electroosmosis

Abstract: A hydrodynamic model fur electroosmosis in ion-exchange membranes has been developed, based on the unidirectional flow of macroscopic spheres in a homogeneous bounded medium. Corrections have been incorporated to account for the influence of the matrix, viscosity changes due to ion-solvent interaction, and the molecular size of the ionic sphere. Measurements of membrane properties have been made on both cation- and anion-exchange membranes in a variety of ionic states. Calculated electroosmotic coefficients (solvent transference numbers) were found to agree with most experimentally measured values within &5%. The results indicate that membrane pore structure is well approximated by a model employing parallelplate pores and that ions are partially stripped of their hydration sheath while within the membrane. of the many phenomena which take place across ion-. exchange membranes, electroosmosis is one that has evoked particular interest for many years. In spite of the many experimental and theoretical studies on electroosmosis (the movement of solvent from an ionic solution across an electrically conducting barrier in response to an electric current), one finds wide variance between predictions based on mechanistic models and experiment. The reasons for these discrepancies are reasonably well understood, at least qualitatively. On the other hand, various models based on irreversible thermodynamics (Katchalsky and Kedem, 1962; Kedem and Katchalsky, 1963; Spiegler, 1958), while providing a basis for the description of transport phenomena across membranes, provide little or no insight into the mechanism by which such transport occurs. The classical mechanistic theory of electroosmosis, due to Helmholtz (1879), Lamb (1888), Perrin (1904), and Smoluchowski (1914), assumes the existence of an electrical double layer adjacent to the cylindrical pore walls, whose dimensions are small compared to the pore diameter. The fluid in the core of the pore is assumed to be essentially bulk fluid. This model, while qualitatively verified for such wide pore systems as clay plugs, was shown to exhibit systematic deviations when applied to membrane systems by Manegold and Solf (1931) in studies on collodion diaphragms of graded pore size. Schmid (1950, 1951, 1952, 1965) and Schmid and Schmarz (1951, 1952) were able to explain some of these deviations by ignoring the double layer and postulating an even distribution of ions in the pore, with certain of the ions immobilized. In particular, the Schmid theory, was able to explain the previously unexplained facts observed by Manegold and Solf that the electroosmotic permeability was proportional to the pore size and to the hydraulic permeability, while the electroosmotic pressure was independent of pore size. However, Despic and Hills (1956), working with copolymers of methacrylic acid and ethylene glycol dimethacrylate, showed that the Schmid theory was inapplicable to highly cross-linked, highly charged ion-exchange membrane systems. Other workers who came to similar conclusions include Graydon and Stewart (1955, 1957), Oda and Yaivataya (1955, 1956,1957), R'inger, Ferguson, and Kunin (1956), Mackie and Meares (1959), and many others. So far, a model for the process which does explain observations made with highly charged ion-exchange membrane systems has not been found. In this contribution, a new model for electroosmosis is developed from a hydrodynamic point of view. This model, specifically applicable to highly cross-linked, highly charged ion-exchange membrane systems, assumes that ions may be represented as spherical particles moving in a continuous medium, with the membrane matrix forming the boundary of the medium. Appropriate equations are derived which relate the forces acting on the ion, the solvent medium, and the matrix, taking account of ion-solvent interactions. After certain approximations are made, the equations are used to predict pore sizes and electroosmotic transport for a variety of membrane ionic states, and these predictions are then compared to experiment. Electroosmotic Model

The influence of isotropic turbulence on the critical ignition energy

Abstract: Theoretical considerations are presented which indicate that the increase of spark-ignition energy under turbulent-flow conditions is mainly due to an increase in transport phenomena resulting from turbulent heat diffusivity. In order to account for the relatively small diffusion times involved in ignition phenomena, turbulent diffusivity should be considered as time dependent. For diffusion times (t) much smaller than the characteristic lifetimes of the turbulent eddies (defined as time scale/turbulence intensity), the turbulent mass diffusivity Dt becomes equal to u12t/2. This turbulent diffusivity acts on the ignition energy in two ways: o 1. By increasing the flame-front thickness according to the proportionality et/e= (u12t/2Dm+1) it causes a relatively important increase in the minimum critical volume of flammable mixture that must be heated up by the ignition energy; 2. It increases the fraction ξ of the spark energy that is available for ignition, the complementary fraction (1-ξ) of the spark energy being wasted beyond the critical volume. This secondary effect of turbulent diffusivity is rather small, but depends on the spark duration θ and on the energy release function. Calculations of the fraction ξ as a function of θ are presented under both laminar and turbulent conditions. Experimental evidence of the effect of the spark-duration time and the turbulent diffusivity on ignition energy is obtained from work carried out with flammable methane/air and propane/air mixtures for different turbulent-flow conditions.

Transport Phenomena in Electrochemical Kinetics

Abstract: In the kinetic study of heterogeneous reactions, which comprises, among others, electrode reactions, it is necessary to take into account the rates of the reacting species in reaching the reaction interface. In this sense, particularly for electrochemical reactions, much work has been done with the double purpose of establishing the phenomenological laws linked to the transport phenomena, and of elucidating the inner mechanism of this type of process.

Energy spectrum and transport phenomena in organic semiconductors

Abstract: Kinetic phenomena in anisotropic organic crystals of the anthracene and naphthalene type are considered. Expressions are obtained from the kinetic equation for the kinetic coefficients. Instead of the conventional isotropic relaxation time, a relaxation time matrix is introduced. The values obtained by means of this matrix for anisotropy in mobility are in considerably better agreement with the experimental values than are those reported in the literature.

An investigation of gas dynamic and transport phenomena in the two dimensional jet interaction flow field

Abstract: Pressure, temperature, gas sampling, and optical measurements in two dimensional jet interaction flow field