Time-periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates.

*(English)*Zbl 1282.76053Summary: Analytical solutions are presented using method of separation of variables for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the electrokinetic width \(K\) denoting the characteristic scale of half channel width to Debye length, the periodic EOF electric oscillating Reynolds number \(\mathrm{Re}\) and normalized relaxation time \(\lambda_{1}\omega\) on velocity profiles and volumetric flow rates are presented. Results show that for prescribed electrokinetic width \(K\), lower oscillating Reynolds number \(\mathrm{Re}\) and shorter relaxation time \(\lambda_{1}\omega\) reduces the plug-like EOF velocity profile of Newtonian fluids. For given Reynolds number \(\mathrm{Re}\) and electrokinetic width \(K\), longer relaxation time \(\lambda_{1}\omega\) leads to rapid oscillating EOF velocity profiles with increased amplitude. With the increase of the \(K\), the velocity variations are restricted to a very narrow region close to the EDL for small relaxation time. However, with the increase of the relaxation time, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. As far as volume flow rates are concerned, for given electrodynamic width \(K\), larger oscillating Reynolds number \(\mathrm{Re}\) results in a smaller volume flow rates. For prescribed oscillating Reynolds number \(\mathrm{Re}\), with the changes of relaxation time \(\lambda_{1}\omega\), volume flow rates will produce some peaks no matter how the electrodynamic width \(K\) varies. Moreover, the time periodic evolution of the velocity profiles provides a detail insight of the flow characteristic of this flow configuration.