Time-periodic pulse electroosmotic flow of Jeffreys fluids through a microannulus

Abstract

Abstract In this article, we investigate the time-periodic pulse electroosmotic flow (EOF) of Jeffreys fluids through a microannulus. By using the Laplace transform method, the velocity expression of the pulse EOF is derived. The effect of some variables on the time it takes for the fluid to go from a static state to a flowing state is analyzed. We find that increasing the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreasing the inner and outer radius ratio α \alpha will result in longer time for the fluid to reach the flowing state, but the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} and the inner and outer zeta potential ratio β \beta have little effect on it. The impact of some related parameters on the pulse EOF velocity for different inner and outer radius ratios ( α \alpha ) is discussed in detail. The results show that for a smaller inner and outer radius ratio α \alpha , the velocity amplitude increases with the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreases with the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} . As the inner and outer radius ratio α \alpha increases, the effect of relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} on velocity amplitude gradually weakens or even becomes insignificant, and the effect of the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} on the velocity amplitude remains unchanged. Moreover, the velocity amplitude will decrease with the increase in the inner and outer radius ratio α \alpha and its change range will expand from the electric double layer near the annular wall to the entire flow region.