Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

Background: Models based on the Helmholtz ‘slip’ approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis.

Methods: We show that the direct formulation of the ‘slip’ model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled ‘slip’ model, which is shown to be well-posed, and therefore automatically adjoint-consistent.

Results: Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems.

Conclusions: An adjoint-consistent formulation for Helmholtz ‘slip’ models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.

Uncontrolled Keywords

Adjoint techniques; Electroosmosis; Microfluidics; Slip boundary conditions