Consider a microchannel with slit-like geometry. The height of the channel is 2d. The fluid in the channel is water ( = 80; p = 1 mPa-s) with a symmetric, monovalent electrolyte. The thin-EDL and Debye-Huckel approximations are valid and can be invoked for this analysis. A pressure gradient, dp/dx is applied to the channel and it induces a flow-induced convective charge transfer for a measurable streaming current for the fluid moving at velocity u. The charge density is pe and the depth at any location in the channel can be denoted by h and the current per unit depth is given by l'. Address the following questions: - What is a general expression for l' in terms of d, u, pe? The coordinate direction along the channel depth is y. Note, your expression will be an integral. You do not need to evaluate the integral. If the problem asks to evaluate for a steady-state potential gradient across the channel, we would need two additional parameters to solve. Qualitatively, explain your thought process and identify the two additional parameters needed to compute the stead-state potential gradient, given by dE/dx, where E is the potential and x is the streamwise coordinate. Consider a microchannel with slit-like geometry. The height of the channel is 2d. The fluid in the channel is water ( = 80; p = 1 mPa-s) with a symmetric, monovalent electrolyte. The thin-EDL and Debye-Huckel approximations are valid and can be invoked for this analysis. A pressure gradient, dp/dx is applied to the channel and it induces a flow-induced convective charge transfer for a measurable streaming current for the fluid moving at velocity u. The charge density is pe and the depth at any location in the channel can be denoted by h and the current per unit depth is given by l'. Address the following questions: - What is a general expression for l' in terms of d, u, pe? The coordinate direction along the channel depth is y. Note, your expression will be an integral. You do not need to evaluate the integral. If the problem asks to evaluate for a steady-state potential gradient across the channel, we would need two additional parameters to solve. Qualitatively, explain your thought process and identify the two additional parameters needed to compute the stead-state potential gradient, given by dE/dx, where E is the potential and x is the streamwise coordinate