Control‐oriented modeling of colloid transport by solute gradients in dead‐end channels

Abstract

AbstractWhen colloids are placed in the nonuniform solute concentration, they transfer toward or away from the higher solute concentration side. This phenomenon is called diffusiophoresis, which is widely founded in many solute–particle interaction processes. In this paper, we consider the colloid transport by solute gradients in dead‐end channels with a boundary solute concentration being manipulated, which is a step‐like concentration input. We model this process by a coupled solute–particle system, which involves the solute diffusion model and the colloid transport model, and establish a control‐oriented model, which is important for controller strategy synthesis in practice. We use the method of separation of variables to obtain the analytical solution of the solute diffusion model and proposed an effective computational scheme for solving the colloid transport model. Thus, we give the simulation results of colloid transfer by considering different boundary solute concentration inputs and show the effectiveness and feasibility for more flexible external control. Finally, because the control‐oriented modeling is a switching system governed by partial differential equations essentially, we reformulate the colloid transfer control problem and discuss this problem in detailed from the viewpoint of the computational optimal control. Copyright © 2017 Curtin University of Technology and John Wiley & Sons, Ltd.