Nonlinear Smoluchowski velocity for electroosmosis of Power‐law fluids over a surface with arbitrary zeta potentials

Abstract

Electroosmotic flow of Power-law fluids over a surface with arbitrary zeta potentials is analyzed. The governing equations including the nonlinear Poisson-Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek exact solutions for the electroosmotic velocity, shear stress, and dynamic viscosity distributions inside the electric double layer. Specifically, an expression for the general Smoluchowski velocity is obtained for electroosmosis of Power-law fluids in a fashion similar to the classic Smoluchowski velocity for Newtonian fluids. The existing Smoluchowski slip velocities under two special cases, (i) for Newtonian fluids with arbitrary zeta potentials and (ii) for Power-law fluids with small zeta potentials, can be recovered from our derived formula. It is interesting to note that the general Smoluchowski velocity for non-Newtonian Power-law fluids is a nonlinear function of the electric field strength and surface zeta potentials; this is due to the coupling electrostatics and non-Newtonian fluid behavior, which is different from its counterpart for Newtonian fluids. This general Smoluchowski velocity is of practical significance in determining the flow rates in microfluidic devices involving non-Newtonian Power-law fluids.

Electro-osmotic mobility of non-Newtonian fluids

“…II B for the electro-osmotic flow of non-Newtonian fluids can also characterize the electrophoresis of a particle with thin EDL in an unbounded non-Newtonian fluid domain. 22 For the latter case, we can change the reference system and imagine that the fluid velocity asymptotically approaches zero far from the charged surface. Then we can obtain a velocity −ū s for the charged surface.…”

“…Electro-osmotic flows of non-Newtonian fluids in the microchannels were also addressed theoretically. [16][17][18][19][20][21][22][23] Recently, experimental investigations 24,25 were performed for the electro-osmotic flow of a typical polymer solution in microchannels. In addition, the generalized Helmholtz-Smoluchowski velocity derived in Ref.…”

“…The effects of rheological properties of the fluids on the Helmholtz-Smoluchowski velocity were reported. 20,22 However, the constitutive model for non-Newtonian fluids adopted in these studies is only an extreme case of the more general non-Newtonian Carreau fluid model. In view of no general treatment of electro-osmotic mobility of non-Newtonian fluids, the present study focuses on the electro-osmotic motion near an arbitrarily charged surface with a nonNewtonian fluid whose rheological behavior can be described by the Carreau model.…”

Transient electro-osmotic flow of generalized Maxwell fluids in a straight pipe of circular cross section

“…The first research of nonNewtonian effects to electro-osmotic flow was done by Das and Chakraborty [8,9], in their studies, the biofluids were treated as power-law fluids, and the analytical solution, describing the transport characteristics of a non-Newtonian fluid flow in a rectangular microchannel, was obtained under the sole influence of electrokinetic effects. For the same non-Newtonian fluid model, Zhao and Yang [10] obtained the general Smoluchowski velocity for electroosmosis over a surface with arbitrary zeta potentials. Furthermore, they presented a comprehensive review of electrokinetics pertaining to non-Newtonian fluids [11].…”

Transient electroosmotic flow of general Maxwell fluids through a slit microchannel

“…The EOF of power-law fluids was studied in Refs [18][19][20][21][22]. It was found that the behavior index n of the power-law fluid substantially influences velocity profiles.…”