Optimal Open-Loop Control for 2-D Colloid Transport in the Dead-End Microchannel

When rigid colloids are placed in the nonuniform solute concentration, the colloid is driven toward or away from the higher solute concentration side by solute gradients. This phenomenon, called diffusiophoresis, has been exploited in many microfluidic applications. In this brief, the colloid transport process driven by the solute gradients in a dead-end microchannel is modeled by a 2-D solute diffusion model and a 2-D colloid transport model. Then, an optimal control problem for the colloid transport process with a boundary solute concentration being manipulated is formulated. To solve this optimal control problem, the control parameterization method first is applied to discretize the boundary control actuation. Then, the adjoint approach based on the Lagrange multiplier functions is employed to derive the gradient formulas of the objective functional with respect to the parameterized control variables. An effective computational method with the FEniCS Project (a finite-element-method-based computational physics package) is proposed, and an existing gradient-based optimization technique is used for minimizing the objective functional. Finally, we give the simulation results to demonstrate that the objective functional based on the proposed method is less nearly three orders of magnitude than that of a constant value control strategy, which well illustrates the effectiveness of the proposed method.