investigation of mixed electro-osmotic/poiseuille slip flows of viscoelastic fluids in rectangular microchannels with hydrophobic surfaces

In this paper, we conduct a numerical study of mixed electro-osmotic/poiseuille slip flows of viscoelastic fluids in microchannels with rectangular cross sections by means of second order finite difference method. in this regard, the complete form of the ptt-constitutive equation is used to describe the rheological behavior of the fluid. the numerical results being validated by the same simplified theoretical study reveal an excellent accuracy with relative error less than 0.3%. afterward, the extended numerical study is used to investigate the 2d velocity distribution and volumetric flow rate in the presence of wall surface hydrophobicity through rectangular microchannels. in addition, in this investigation, the exact solution of unidirectional electroosmotic flow of ptt-viscoelastic fluids is derived for slit hydrophobic microchannels, and after validating, the solution is used to investigate the rheological behavior of viscoelastic fluids in the range of operating parameters. the results exhibit a uniform effect of hydrophobicity in increasing the profile of 1d velocity distribution in slit microchannels. finally, in order to determine the stability of the grid network, various under relaxation factors are applied to determine the speed of convergence of finite difference method, and then, by using the analytical procedure, the critical weissenberg number is introduced as a function of velocity scale ratio and debye–hückel parameter. the evaluation of the numerical method in the critical area indicates the stability of viscoelastic fluid flow for the values of the weissenberg number less than the corresponding critical value in the theoretical analysis.