Investigation of scalar measurement error in diffusion and mixing processes

Abstract

In variable density, multi-fluid and reacting flows, the degree of molecular mixing is a critical component of turbulent transfer and mixing models. Also, in many microflows and low Reynolds number flows, scalar diffusion length- and time-scales play a significant role in the mixing dynamics. Characterization of such molecular mixing processes requires scalar measurement devices with a small probe volume size. Spatial averaging, which occurs due to finite probe volume size, can lead to errors in resolving the density or scalar gradients between pockets of unmixed fluids. Given a probe volume size and a priori knowledge of the functional profile of the diffusion layer being measured, we obtain an estimate for the measurement error due to spatial averaging and make the corrections accordingly. An analytical model for the measure of scalar mixing is developed as a predictor for the growth of scalar gradients in a variable scalar flow. The model is applied to a buoyancy-driven mixing layer with a Prandtl number of 7. Measurements within the mixing layer have shown that initial entrainment of unmixed fluid causes a decrease in the measured amount of molecular mixing at the centerplane. Following this period of initial entrainment, the fluids within the mixing layer exhibit an increase in the degree of molecular mixing.