Modeling of laminar flows of nanofluids between two coaxial cylinders in microfluidic devices

Abstract

The laminar flow of three immiscible nanofluids between two coaxial cylinders due to a constant pressure drop at the inlet and outlet of the channel is considered. Experimental studies of the flows of different nanofluids through the tubes and channels of microfluidic devices have shown that the measured relationships between the pressure drop and volumetric flow do not correspond to the calculations of the corresponding Poiseuille flows in the same geometry due to tangential momentum transfer during diffuse scattering of nanoparticles on the wall roughness. When the characteristic roughness scale has the same order as the particle size, the scattering becomes significant in both dilute gases and suspensions of nanoparticles. Accordingly, the solution of the problem was obtained with the second order velocity slip boundary conditions  at the rough walls. The presence of wall layers with a constant thickness and different viscosities is associated with the repulsion of the nanoparticles from the walls into the core of the flow. At the interfaces between the layers, the continuity conditions for velocities and tangential stresses were accepted. An analytical solution of the system for pressure and velocities of the fluids is obtained. Expressions for volumetric flow and wall stresses are calculated. It is shown that for some sets of model parameters it is possible to obtain a significant increase in the flow rate and decrease in viscous dissipation due to tangential momentum transfer at the walls. The effect could increase the efficiency of various microfluidic systems. The formula for the capillary viscometer in the case of measuring the viscosity of nanofluids was also obtained. The derived analytical solution can be used for validation of numerical codes for more complex flows (transient, turbulent) in similar geometries.