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

SUMMARY The objective of the paper is to construct adjoint consistent formulations of the Helmholtz 'slip' model for the simulation of electroosmotic flows. The motivation is to apply adjoint-based methods for the development of adaptive finite element tools and parameter sensitivity analyses to microfluidic problems. Issues in the current formulation of the 'slip' model lie in the fact that it induces an ill-posed adjoint problem and may yield suboptimal convergence rates. A modified formulation of the coupled 'slip' model is thus proposed that results in well-posed primal and adjoint problems. Numerical examples are presented that show that the resulting adjoint solution exhibits the correct behavior on various two-dimensional test problems.