Mass transfer coefficients introduction

The reported study on gas-liquid interphase mass transfer for upward cocurrent gas-liquid flow is fairly extensive. Mashelkar and Sharma19 examined the gas-liquid mass-transfer coefficient (both gas side and liquid side) and effective interfacial area for cocurrent upflow through 6.6-, 10-, and 20-cm columns packed with a variety of packings. The absorption of carbon dioxide in a variety of electrolytic and ronelectrolytic solutions was measured. The results showed that the introduction of gas at high nozzle velocities (>20,000 cm s ) resulted in a substantial increase in the overall mass-transfer coefficient. Packed bubble-columns gave some improvement in the mass-transfer characteristics over those in an unpacked bubble-column, particularly at lower superficial gas velocities. The value of the effective interfacial area decreased very significantly when there was a substantial decrease in the superficial gas velocity as the gas traversed the column. The volumetric gas-liquid mass-transfer coefficient increased with the superficial gas velocity. 

The current-potential curves discussed so far can be used to measure concentrations, mass-transfer coefficients, and standard potentials. Under conditions where the electron-transfer rate at the interface is rate-determining, they can be employed to measure heterogeneous kinetic parameters as well (see Chapters 3 and 9). Often, however, one is interested in using electrochemical methods to find equilibrium constants and rate constants of homogeneous reactions that are coupled to the electron-transfer step. This section provides a brief introduction to these applications. 

Again the absence of information on both and y leads to the introduction of mass transfer coefficients for the gas and liquid phase, feg and k, respectively. 

Over-all Transfer Units. As explained in Chap. 5, the practical difficulties entering into the use of true equilibrium interfacial concentrations xe% and xrx have led to the introduction of over-all mass-transfer coefficients Ke and Kr which express the rate of diffusion in terms of over-all concentration gradients xr — x r) and x% — Xe) [Eqs. (5.57) and (5.59)]. Their use requires that the distribution coefficient. 

Introduction. For many years mass-transfer coefficients, which were based primarily on empirical correlations, have been used in the design of process equipment. A better understanding of the mechanisms of turbulence is needed before we can give a theoretical explanation of convective-mass-transfer coefficients. Some theories of convective mass transfer, such as the eddy diffusivity theory, have been presented in this chapter. In the following sections we present briefly some of these theories and also discuss how they can be used to extend empirical correlations. 

Introduction. Film or single-phase mass-transfer coefficients k y and k or and are often difficult to measure experimentally, except in certain experiments designed so that the concentration difference across one phase is small and can be neglected. As a result, overall mass-transfer coefficients K y and K are measured based on the gas phase or liquid phase. This method is used in heat transfer, where overall heat-transfer coefficients are measured based on inside or outside areas instead of film coefficients. 

For mass transfer from a fluid phase to a solid surface, the characteristic length of diffusion is the film thickness S, and by introduction of the mass transfer coefficient B we obtain ... 

When the experimental values for different static bed heights in these figures are compared with the results obtained from the experiments with no solid particles (bubble column) which are also given on the ordinate, it may be concluded that introduction of solid particles improved the volumetric mass transfer coefficients as well as interfacial area by a factor of at least 2. k and k seem to be negatively affected by use of solid particles in the bed. These results then show that interfacial area increases very appreciably with addition of solid particles and this increase in interfacial area causes the increase in volumetric mass transfer coefficients resulting in higher mass transfer capacities for three-phase fluidization in comparison with bubble columns. 

In Equation 6.59, the concentration gradient at the fluid-solid interface is obtained from the solution of the fluid equation of motion and mass species transport equation. Determination of convection mass transfer from a solid surface through the solution of flow field and mass species transport equation could be quite complex and time-consuming depending on the flow and surface geometry under consideration. This procedure is often simplified with the introduction of the convection mass transfer coefficient similar to the convection heat transfer coefficient. 

Molecular diffusion is an inherent and ubiquitous mass transport process by which chemical species move within and between environment phases. All environmental mass transfer coefficients, in one way or another, reflect the molecular diffusivity of the chemical species in the environmental solvents (i.e., air, water, organic matter, nonaqueous liquids, solids, etc.). It is therefore the fundamental transport parameter for molecular mass transport. It is important to keep in mind that diffusion is generally only used to describe molecular motion in the absence of mechanical mixing or advection. The material in this chapter provides a brief, theoretical introduction to diffusivities and follows this with estimation techniques, developed using empirical data, for chemicals in the significant environmental media compartments. The chapter concludes with example calculations. 

The proportionality constant k is called a mass transfer coefficient. Its introduction signals one of the two basic models of diffusion. Alternatively, we can recognize... 

The chapter itself is organized as follows. In Section 11.1, we discuss experiments in which data can be organized using mass transfer coefficients. Section 11.2 describes blood oxygenators and artificial kidneys, mass transfer devices whose geometry is exactly known. Section 11.3 discusses the role of mass transfer in pharmacokinetics, where the system s geometry is unknown, lumped into other parameters which may include the mass transfer coefficient. Thus the chapter provides an introduction for life scientists to important engineering ideas. 

Upon introduction of equations (11.74), (11.75), and (11.76), the equation of continuity and the Navier-Stokes equations can be solved numerically. As shown by Cochran, the variables F, G, and H can be written as two sets of series expansions for small and large values of respectively. The series solutions for small values of are especially relevant to the mass-transfer problem. In particular, the derivatives at = 0 are essential in order to determine the first coefficient of the series expansions. The other coefficients are deduced from the first one by using the equation of continuity eind the Navier-Stokes equations. 

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