Statistical rate theory of interfacial transport. II. Rate of isothermal bubble evolution in a liquid–gas solution

Abstract

The statistical rate theory approach is used to derive the expression for the rate of gas absorption by a liquid. This process involves two sequential rates−the rate of transport from the gas to the surface and the rate of transport from the surface to the bulk liquid. According to the statistical rate theory, the rate limiting step is the rate of transport from the surface. After deriving the rate expression for the rate limiting step, it is incorporated in an integral equation approach for predicting the rate of evolution of a bubble evolving isothermally in a liquid–gas solution. This approach accounts for the movement of the bubble boundary in the diffusion problem. Statistical rate theory leads to a complete expression for the rate of gas absorption; thus by comparing the predicted rate of bubble evolution with a set of measurements, one can investigate the validity of the statistical rate theory. This comparison is carried out and the predictions are found to be in close agreement with the experiments throughout the experimental period.

Theoretical description of the kinetics of solute adsorption at heterogeneous solid/solution interfaces

“…Soon it was applied to describe successfully the rates of interfacial transports of various kinds, i.e. the rate of exchange at the liquid/gas interface [17][18][19], hydrogen adsorption by metals [20], electron exchange between ionic isotopes in solution [21], permeation of ionic channels in biological membranes [22], and rate of liquid evaporation [23][24][25]. Ward and co-workers were the first to show how the SRT approach can be applied to describe the kinetics of isothermal adsorption at the gas/solid interfaces [26][27][28][29], and the kinetics of thermodesorption [30].…”

Methodology of non-equilibrium thermodynamics for kinetics research of CO2 capture by ionic liquids

“…In the CO 2 dissolution kinetics investigations in brines by Ji et al [111], the concentration of CO 2 (aq) at the vapor-liquid interface was considered as the instantaneous equilibrium concentration. However, the investigations of Ward et al showed that the usual assumption of the instantaneous equilibrium at the liquid-gas interface may lead to the illogical consequence [112], and they developed the statistical rate theory (SRT) to describe the molecular transport rate at the vapor-liquid and solid-liquid interfaces based on a first-order perturbation analysis of the Schrödinger equation and the Boltzmann definition of entropy [113][114][115]. In this paper, SRT is used to describe the molecular transport rate at the vapor-liquid interface, and the rate expression is composed of the following three parts [114] as shown in eq.…”

A Statistical Rate Theory of Interface Concentration during Solution ZeoliteCrystal Growth

“…In the statistical rate theory, the equilibrium exchange rate K e is typically defined as the production of the collision frequency of the solute molecules with the solid surface, and the cross-sectional areas of the available sites for solute transfer from one phase to the other under equilibrium condition [19,20]. However, in the case of zeolite crystal growth, the collision frequency of the TO 4 units with the solid surface is significantly influenced by the flow condition resulting from the motion of growing crystals.…”

“…Substituting Equation (20) into Equation (2), we can rewrite the equilibrium exchange rate of solute molecules across the interface as,…”