New imaginary-valued similarity solutions for laminar boundary layers with a spray Academic Article uri icon


  • A new similarity solution for spray distribution in a boundary layer flow, involving an imaginary-valued variable, is presented. The flow field similarity solution has three branches, the two known solutions for accelerating flow and moderately decelerating flow and a new solution, which is the focus here, for high-rate deceleration. This last family of solutions involves the use of imaginary expressions in the course of the similarity procedure. Although the procedure employs imaginary expressions, the solution in the physical plane admits a fine behavior. The mass distribution of spray droplets in the boundary layer for the latter case shows that the highest concentration is either at the wall or at the edge of the boundary layer, depending on the nature of downstream variation of the aerosol concentration at the outer flow and on the particular branch of the flow solution. The new similarity solution presented here opens the possibility to describe a new range of boundary/shear layer problems. We demonstrate that the option for describing droplet/particle distributions in such configurations has ramifications for transport and deposition of droplets/particles in boundary layers developed in industrial facilities and sizing instrumentation, and we suggest its possible application for cases of spray-surface interactions.

publication date

  • January 1, 2009