An integral analysis in tensorial notation for streaming-potential phenomena

In microfluidic applications, induced-charge electroosmosis can be used to drive fluids. Moreover, the same electrohydrodynamic effects play an essential role in the behavior of particles and bio surfaces at the microscale. Nonlinear electrohydrodynamic effects induce strong gradients in the thin geometry of the Debye layer. Thus, an integral description of the layer that illustrates those effects in a simplified form is valuable for their understanding and computation. 

Therefore, we present jump conditions for integral parameters, such as stress, mass flux, and ion fluxes. Our approach relies on previous asymptotic solutions to streaming-potential phenomena within Debye layers. We expand this model to curved surfaces by solving the contravariant form of the set of differential equations for the flow, electric potential, and charge distributions. These integral jump conditions suggest multiple definitions for the Debye layer thickness, all considering the zeta-potential, and conservation of various properties can be derived.

References:

[1] Marthaler & Class (2021) PAMM 20. 

[2] Yariv et al. (2011) J. Fluid Mech. 685.

[3] Class et al. (2003) J. Fluid Mech. 491.