Viscosity Measurement for Picoliter Liquid Volumes Using Twin Micro-Cantilever Beams

Abstract

In this paper a novel method to measure viscosity of a liquid with a volume of fraction of pico-litre is presented. The measurement of viscosity keeps into account the effect of evaporation which can result in the total evaporation of the liquid in a short time. At the present time there are several standard methods to measure viscosity of a fluid. All methods require larger volume of liquid and it takes rather long time to measure viscosity. No effect of evaporation is considered in these methods given the large volume of fluid that is used. In the proposed method viscosity of a droplet is measured by considering that in ambient condition such small droplet evaporates in less than a second. The principle of measurement includes two parallel micro-cantilever beams for which their individual dynamic response could be measured. Micro-cantilever beams are being used in MEMS mostly as inertial sensors. In this research the small volume of liquid is assumed to be positioned between the two parallel micro-cantilever beams. The two micro-beams are assumed to be respond to the dynamic excitation with a non-linear response which will be proved below that is related to the viscosity of the fluid. The dynamic system was modelled as a discreet three degree of freedom massdamping-spring. The nonlinear differential equations governing the performance of the above mentioned system is further solved and the results are analysed. The initial deflection of micro-cantilever beams due to capillary force yields to the dynamic behaviour of micro-cantilever beams expressed in three differential equations that are nonlinear and stiff. The used algorithm to solve the coupled differential equations is called LSODE and in usually capable to perform the computation solution for the stiff system of nonlinear initial value differential equations. The time response and phase diagram of the deflection of the beams for the massspring-damper system are numerically derived and the results are compared for two circumstances: the liquid would not evaporate and the liquid evaporates. Conclusion with regards to the equipment capable to perform such measurements are drawn.