Modelling of Leakage Flows Through Smallest Gaps in Microvalves
Micropumps and Microvalves are used to control the movement of fluids. For many applications it is necessary that they do not suffer from high leakage rates. The origin of leakage flows are smallest gaps due to imperfect sealing. In this thesis, the leakage rates of microfluidic devices are examined and a microfluidic model is developed, that is able to describe and estimate the leakage flows of liquid flows and gas flows. The behaviour of fluids at the microscale differs fundamentally from macroscopic flows and is determined by the interplay of between many different forces. Especially surface-related forces like surface tension and viscosity become dominant. Gases and fluids have different physical properties and are therefore treated separately. For gases it turns out that the classical Navier-Stokes equations give not an accurate description, since they do not cover the effect of self-diffusion, which can not be neglected at small length scales. Instead, the extended Navier-Stokes equations, which include the diffusive mass transport, are derived and solved analytically. Also, the characteristic pressure is introduces, which can serve as an important parameter for future studies, since it quantifies the relative importance of convection and diffusion. The theory is compared to leakage measurements of the AMS high flow pump. The agreement between the leakage model and the experimental data is quite good. In the second part of this thesis, the water leakage rates of normally open (NO) valves are examined. The size of the leakage channel, that is a result of surface roughness of the steel foil in the valve, is estimated using the theory of contact mechanics developed by Persson. The microfluidic model is based on a Poiseuille flow, that describes the pressure driven laminar flow of an incompressible fluid, with additional slip effects at the solid walls. A model for the slip length is developed, that incorporates the multi-mechanism of confinement effects, surface diffusion, fractional coverage, work of adhesion, temperature and roughness. In a final step, the water leakage model is validated with leakage measurements of metal-based NO valves actuated at 200V and 400V. In the former case, the theory underestimates the experimental data by a factor of 2, whereas in the latter one, it overestimates the data by a factor of 1.5-6. The difference in the measured flow rates at200V and 400V is higher than the predictions of the theory of contact mechanics. The reason could be that the sealing mechanism can not be described by the simple theory presented here, or it is due to the simplifications, that were made in the definition of the fluidic leakage channel. In the analysis it also turn out that the slip length is much smaller than the sealing size and hence, slip effects can be neglected. They are expected to become more dominant, when the flow dimensions are further decreased and hydrophobic materials are used. Overall, the present theory provides good results with the same order of magnitude as the experimental data.
München, Univ., Master Thesis, 2021