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Analysis of microfluidic flow driven by electrokinetic and pressure forces

This work presents an analysis of microfluidic flow introduced by mixed electrokinetic force and pressure gradient. Analytical solutions are presented for the case of constant surface heat flux, taking the Joule heating effect into account. The present problem is governed by two scale ratios and the dimensionless source term. The two important ratios are the length scale ratio ε (the ratio of Debye length to the tube radius R) and the velocity scale ratio Γ (the ratio of the pressuredriven velocity scale for Poiseuille flow to Helmholtz-Smoluchowski velocity for electroosmotic flow). For mixed electroosmotic and pressure-driven flow, the resulting velocity profile is the superimposed effect of both electroosmotic and Poiseuille flow phenomena. It is found that the velocity profile decreases as ε increases and the normalized temperature profiles across the tube increases monotonously form the core to the wall. The maximum dimensionless temperature is observed at the wall and the wall temperature increases with increasing Joule heating. Also, the temperature is increased with increasing the value of ε . The fully developed Nusselt number takes the maximum value at the limiting case of ε → 0 , and then decreases with increasing ε . Moreover, the Nusselt number decreases with Γ and then goes asymptotically to the limit of Poiseuille flow as Γ → ∞ , where the flow is dominated by the pressure force.