A simple analytical formulation for microbubble drag reduction

Substantial drag reductions are observed when microbubbles are injected at a surface. A simple analytical formulation for this phenomenon is presented in this paper. It is based on an argument developed by Lumley [Physics Fluids 20(10), S64 (l977)]. Following this argument, particles having certain physical properties could affect the turbulence in the buffer layer and thus increase the sublayer thickness With, as a result, a drag reduction. A simple model is derived from this concept and compared to the data obtained by Madavan et al. [J. Fluid Mech. 156, 237 (l985)] right downstream of the injection section. The agreement is good which tends to prove that this approach is physically meaningful.