Stretching of material lines in pseudo-turbulence induced by small rising bubbles

Abstract

Direct numerical simulations have been conducted for the stretching of material lines in pseudo-turbulence induced by small rising bubbles in order to understand the mixing characteristics of bubbly flows. Contaminated bubbles are considered and are treated as light solid particles. An immersed boundary method has been used for evaluating the coupling force between the bubbles and the surrounding fluid flows. Numerical results show that the total length of material lines increases exponentially in time as a result of stretching and folding due to the rising bubbles. The material lines tend to accumulate in the wake regions of the bubbles, and they are strongly stretched in the vertical direction there. It is also found that the stretching rate of material lines increases with the mean void fraction when it is normalized by the magnitude of the rate-of-strain tensor of liquid flow in pseudo-turbulence. In the case of high void fractions, material lines tend to align with the direction of maximum stretching, and are effectively stretched.