Transient flow with memory in a nanocapillar

Abstract

A model of transient flow with memory in a nanocapillar is formulated and anallitically solved. Nanofluidics behavior is described by Navier-Stokes Equation when viscosity is a radially modulated parameter and by a border condition corresponding with hysteretic sliding on the nanocapillar wall. Solution is obtained using the Laplace Transform, and Bromwich Integral and the Residue Theorem for the Inverse Laplace Transform; with the final result being expressed as an infinite series of Bessel Functions. The analytic solution for the case with material memory is compared with the analytic solution for the case with no material memory and with constant viscosity. A formula for the development of nanodynamic impedance is deduced. Analytic results are shown to be relevant in the design of nanofluidics devices with applications in general nanotechnologies and pharmaceutical engineering in particular. Future lines of research are also suggested.