Numerical Analysis of Liquid-Solid Adsorption Model

Abstract

In this paper, the numerical algorithms for solution of pore volume and surface diffusion model of adsorption systems are constructed and investigated. The approximation of PDEs is done by using the finite volume method for space derivatives and ODE15s solvers for numerical integration in time. The analysis of adaptive in time integration algorithms is presented. The main aim of this work is to analyze the sensitivity of the solution with respect to the main parameters of the mathematical model. Such a control analysis is done for a linearized and normalized mathematical model. The obtained results are compared with simulations done for a full nonlinear mathematical model.

Novel Machine Learning-Based Method for Estimation of the Surface Area of Porous Silica Particles

“…Since a slurry containing silica particles is added to the dye solution, the volume of the solution varies with time. The overall process may be described by following mass balances: 23,24 V t q d d =…”

“…Since a slurry containing silica particles is added to the dye solution, the volume of the solution varies with time. The overall process may be described by following mass balances: , normald V normald t = q normald ( V α normals ) normald t = q α sF normald ( V C normalD ) normald t = − V k SL S̅ ( C normalD − C Ds ) where V is the volume of solution, t is the time, q is the flow rate of slurry, α s is the volume fraction of solids, C D is the concentration of dye, k SL is the solid–liquid mass transfer coefficient, and S̅ is the surface area per volume. α sF is the volume fraction of solids in fed slurry and C Ds is the equilibrium concentration of dye on solid surface.…”