Dynamical aspects of transient electro-osmotic flow of Burgers' fluid with zeta potential in cylindrical tube

Abstract In this article, we consider the flow of a Burgers’ fluid of transient electro-osmotic type in a small tube with a circular cross-section. Analytical results are found for the transient velocity and, electric potential profile by solving the Navier–Stokes and the linearized Poisson–Boltzmann equations. Moreover, these equations are solved with the help of the integral transform method. We consider cases in which the velocity of the fluid changes with time and those in which the velocity of the fluid does not change with time. Furthermore, special results for classical fluids such as Newtonian, second grade, Maxwell, and Oldroyd-B fluids are obtained as the particular cases of the outcomes of this work and that these results actually strengthen the results of the solution. This study of the nonlinear problem of Burgers’ fluid in a specified physical model will help us to understand the behavior of blood clotting and the block of any kind of problem in which this type of fluid is used. The solution of the complex velocity profile of Burgers’ fluid will help us in the future to solve the problems in which this transient electro-osmotic type of small tube is involved. At the end, numerical results are shown graphically that can help us to understand the complex behavior of the Burgers’ fluid, and also the analysis of the Burgers’ fluid shows dissimilarity with other fluids that are considered in this work.