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.