Mass flow-rate control through time periodic electro-osmotic flows in circular microchannels

Abstract

The present study is directed towards devising a scientific strategy for obtaining controlled time-periodic mass flow-rate characteristics through the employment of pulsating electric fields in circular microchannels by exploiting certain intrinsic characteristics of periodic electro-osmosis phenomenon. Within the assumption of thin electrical double layers, the governing equations for potential distribution and fluid flow are derived, corresponding to a steady base state and a time-varying perturbed state, by assuming periodic forms of the imposed electrical fields and the resultant velocity fields. For sinusoidal pulsations of the electric field superimposed over its mean, a signature map depicting the amplitudes of the mass flow rate and the electrical field as well as their phase differences is obtained from the theoretical analysis as a function of a nondimensional frequency parameter for different ratios of the characteristic electric double layer thickness relative to the microchannel radius. Distinctive characteristics in the signature profiles are obtained for lower and higher frequencies, primarily attributed to the finite time scale for momentum propagation away from the walls. The signature characteristics, obtained from the solution of the prescribed sinusoidal electric field, are subsequently used to solve the “inverse” problem, where the mass flow rate is prescribed in the form of sinusoidal pulsations and the desired electric fields that would produce the required mass flow-rate variations are obtained. The analysis is subsequently extended for controlled triangular and trapezoidal pulsations in the mass flow rate and the required electric fields are successfully obtained. It is observed that the higher the double layer thickness is in comparison to the channel radius, the more prominent is the deviation of the shape of the required electric field pulsation from the desired transience in the mass flow-rate characteristics. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.