IntroductionThe development of multifunctional, high throughput lab-on-a-chip devices depends heavily on the ability to measure flow rate and perform quantitative analysis of fluids in minute volumes. Traditionally, there have been many MEMS-based (MEMS = microelectromechanical system) flow sensors for gaseous flows.1In recent times, there has been some advancement in measuring micro-flows of liquids. Examples of sensing principles explored in the measurement of microfluidic flow are heat transfer detection,2–4molecular sensing,5atomic emission detection,6streaming potential measurements,7electrical impedance tomography,8ion-selective field-effect transitors9and periodic flapping motion detection.10Flow sensors form the integral part of micrototal analysis systems11with multisensors. Conversely, a measure of electric current is used for pumping a measurable flow rate of fluids in electro-osmotic flow (EOF).12Flow sensors based on sensing the temperature difference between two points in the microchannel2–4can sense very low flows. However, such flow sensors require a complicated design and the integration of the heater, temperature sensors and membrane shielding is difficult to implement. Moreover, the sensitivity and accuracy of the flow sensors depend on the environment associated in the heat transfer. Most other methods are not capable of measuring very low flow rates. We consider flow sensing by directly measuring the electrical admittance of the fluid using two surface electrodes.In electrolytes flowing in a microchannel under laminar flow conditions, a parabolic velocity profile exists and so the ions in the middle of the channels travel faster than those near the walls. This results in the redistribution of ions within the electric double layer (EDL) formed in the channel.13The ac voltage across the channel electrodes (Fig. 3) drives the ions back and forth across the electrodes. The ionic redistribution develops electrokinetic effects and contributes to change in electric admittance. Thus the flow of fluid is very sensitive to the admittance across microelectrodes14,15in the flow channels, and measuring the increase in admittance precisely accounts for the flow rate. Our flow sensor operating with optimized electric parameters can be efficient and accurate for precise values of flows. This method is relatively simple and suitable for most of the chemical and biochemical microfluidic applications since most of the reagents used are electrolytes. In this paper, we present such a flow sensor based on the measurement of electrical admittance.PrincipleIn hydrodynamic conditions, forced convection dominates the transport of ions to the electrodes within the flow channels. When the width of the microfluidic channel is very small compared to the length of the channel, the lateral diffusion of the ions is significant under laminar flow. Under an ac electrical signal applied across the channel, the equivalent circuit16of the microsystem is shown inFig. 1. The electrical double layer17formed across the channel is formed from two capacitances namely diffuse layer capacitance (Cs) and the outer Helmholtz plane capacitance (Ce). The former is due to ion excess or depletion in the channel, and the latter is due to the free electrons at the electrodes and is independent of the electrolyte concentration. The smaller of these capacitances dominates the admittance since these two capacitances are in series. The frequency of the applied ac voltage, flow rate and conductivity of the fluid are the factors affecting the admittance of the fluidic system and our flow sensing principle is based on the optimization of these parameters.The equivalent circuit for the channel and electrodes flow sensor cell. The solution in the channel offers a parallel resistive (Rs) and capacitive (Cs) impedance while the electrodes by themselves offer serial capacitive (Ce) impedance with the solution.For an electrochemical oxidation of a species A to A+in a microchannel, the convective–diffusive equation for mass transport under steady state conditions is given byeqn. (1):1where [A] is the concentration of the species,DAis the diffusion coefficient andvxis the velocity in the direction of flow. The first term is the lateral diffusion in the microchannel and the second term is the transport along the length of the channel. Under steady state flow conditions the boundary condition is given byeqn. (2). The solution of this equation predicts the mass transport limited current (iL)18as a function of flow rate,Qas given byeqn. (3):23wherenis the number of electrons transferred,F, the Faraday constant,xeis the electrode length,h, the cell half-height,d, the width of the cell andw, the electrode width. It is to be noted that the current due to flow of electrolyte is directly proportional to the cube root of volume flow rate of the fluid. The ac voltage signal is considered rather than dc voltage since the application of an ac voltage in the flow sensor does not promote any electrode reaction. Optimization of the electrical parameters like voltage and frequency of the ac signal are considered as an operating condition for measuring low flow rates. This optimizes the distance of movement of ions and their relaxation behavior across the channel electrodes so that the current admittance suffered is maximum.