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Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels. (English) Zbl 1162.76007
Summary: We investigate transient electro-osmotic flow of viscoelastic fluids in rectangular micro-channels. The general twofold series solution for velocity distribution of electro-osmotic flow of viscoelastic fluids with generalized fractional Oldroyd-B constitutive model is obtained by using finite Fourier and Laplace transforms. Under three limiting cases, the generalized Oldroyd-B model simplifies to Newtonian model, fractional Maxwell model and generalized second-grade model, where all the explicit exact solutions for velocity distribution are found through the discrete Laplace transform of sequential fractional derivatives. These exact solutions may predict the flow behavior of viscoelastic biological fluids in bioMEMS and lab-on-a-chip devices, and thus could benefit the design of these devices.

MSC:
76A10 Viscoelastic fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
Software:
Algorithm 368
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