A statistical rate theory study of interface concentration during crystal growth or dissolution

Abstract

The concentration at the interface of a growing or dissolving crystal has been previously found experimentally to be different from the equilibrium value; however, a method for predicting this concentration has not been available. We report an investigation that uses statistical rate theory to obtain the expression for the rate of molecular transport across the interface of a growing or dissolving crystal. This expression is in terms of the concentration at the interface, and serves as the boundary condition for the convective diffusion equation. The solution of this system of equations contains two constants that appear in the expression for the equilibrium exchange rate. To evaluate the validity of the system of equations obtained, KAlum dissolution in a rotating disk apparatus was examined using data that had been previously reported. In the series of experiments, saturated, aqueous solutions of KAlum were prepared, and the temperature changed to form undersaturated solutions. KAlum{111} crystals were then dissolved isothermally at a series of different temperatures and rotation rates, and their steady state rates of dissolution measured. Using the measured dissolution rates at one temperature, the values of the two constants were determined, and the system of equations was then used to predict the rate of dissolution at the other four temperatures. The predictions were found to be in agreement with the measured dissolution rates at the other temperatures. The predicted interfacial concentration was less than the equilibrium value at all dissolution rates and the difference increased with increasing dissolution rates.

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.…”

Modelling of mass transfer coupling with crystallization kinetics in microscale

“…Ac is obtained as an average area value. k d is determined with the modified statistical rate theory (SRT) (Dejmek and Ward, 1998;Ji et al, 2001) from the dissolution kinetics data that are measured in this work, which will be described in detail in the later part of this paper. The modified SRT (Dejmek and Ward, 1998;Ji et al, 2001) can be used to describe the instantaneous rate of molecular transport across the interface between the solid and liquid phases.…”

“…k d is determined with the modified statistical rate theory (SRT) (Dejmek and Ward, 1998;Ji et al, 2001) from the dissolution kinetics data that are measured in this work, which will be described in detail in the later part of this paper. The modified SRT (Dejmek and Ward, 1998;Ji et al, 2001) can be used to describe the instantaneous rate of molecular transport across the interface between the solid and liquid phases. The rate expression is in terms of (a) the chemical potential of the molecules in the solid; (b) the chemical potential of the molecules in the liquid solution at the interface with the solid phase and (c) the equilibrium exchange rate between the phases that would exist if the isolated system is allowed to evolve into equilibrium and both phases are present.…”

Splitting methods for relaxation two-phase flow models

“…The probability of each event is calculated using a first-order perturbation analysis of the Schrödinger equation, together with the Boltzmann definition of entropy. Since its introduction by Ward et al (1982), SRT has been used to model a number of different transport processes, including crystal growth (Dejmek & Ward, 1998), solution/solid adsorption (Azizian et al, 2008;Rudzinski & Plazinski, 2006), gas/solid adsorption (Elliott & Ward, 1997a;, temperature programmed desorption (Elliott & Ward, 1997b), ion permeation across lipid membranes (Bordi et al, 2000), chemical reactions (Harding et al, 2000), and evaporation and condensation (Ward & Fang, 1999;Kapoor & Elliott, 2008;Ward & Stanga, 2001). Lund and Aursand (2012) developed an explicit expression for the phase transfer source term Γ in Eqs.…”