Modeling of roughness effects on acoustic properties of micro-slits

An analytical model is developed to predict the effects of surface roughness on the acoustic properties of micro-slits. Periodic (sinusoidal) roughness distributed with relatively small amplitude on slit surface is assumed, enabling small parameter analysis. Within the incompressible creeping flow regime, the dependence of key fluidic and acoustic properties including static flow resistivity, tortuosity, effective density and compressibility on relative roughness and wave number of roughness is quantified. For validation, analytical predictions are compared with numerical simulation results based on the method of finite elements, with good agreement achieved. The presence of surface roughness is shown to increase both static flow resistivity and tortuosity, causing a significant increase in the effective density of the micro-slits, but has little effect on effective compressibility.