New curved boundary scheme in lattice Boltzmann framework for simulation of dissolution through nonlinear heterogeneous reactions in general form

Abstract

Nonlinear heterogeneous reactions are important for simulating dissolution as they involve reactant adsorption, reaction, and product desorption, leading to nonlinear behavior. This study proposes a new curved reaction boundary condition in general form in the lattice Boltzmann framework. This method calculates the unknown distribution functions and the interface concentration using extrapolated distribution functions on actual interface position. Various analytical benchmarks were used to compare this method's accuracy with two available schemes, including Kashani et al. and Huber et al. methods. According to the results, in the simulation of reactant transport on straight and curved surfaces with and without dissolution, errors obtained by the proposed method did not exceed 1.7% in different conditions, while errors of the two other methods were up to 50%. The convergence rate of different methods was determined, and based on the results, the convergence rate of the proposed method was second-order, while the corresponding values for the two other methods were only first-order. The results of different root-finding methods in the proposed method including Bisection, Newton-Raphson, and linear approximation were compared to determine the interface concentration. The results showed that Bisection errors did not exceed 1%. At the same time, using Newton-Raphson and linear approximation led to errors of 12.9% and 25.3%, respectively. The effect of reaction orders on an obstacle dissolved under reactive flows in a channel was investigated. According to the results, in each Damköhler number, increasing the reaction order decreased the dissolution rate; however, increasing the Damköhler number significantly restricted the effect of orders.