Complex-valued variable and solutions for laminar boundary layers with droplets/particles

Aerosol concentrations in a boundary layer with downstream velocity variation reveal a bifurcational behavior. The solution of both the flow and concentration fields involves the use of similarity transformations. The similarity solution of the flow field has 3 bifurcating branches: for accelerating flow, for decelerating flow, and a previously unexplored solution for high-rate deceleration which involves complex values of the similarity solution. Although the latter solution involves complex values of the similarity variable, it still leads to an acceptable solution in the physical variables. The bifurcation in the downstream distribution of the aerosol concentration stems from the bifurcation characteristics of the flow, with a further third branch stemming from downstream behavior outside the boundary layer. These results have ramifications to aerosol dynamics (transport, deposition) in boundary layers developed in industrial facilities and sizing instrumentation, over airfoil, as well as in the human respiratory system.