Dense spray evaporation as a mixing process

We explore the processes bywhich a dense set of small liquid droplets (a spray) evaporates in a dry, stirred gas phase. Adense spray of micron-sized liquid (water or ethanol) droplets is formed in air by a pneumatic atomizer in a closed chamber. The spray is conveyed in ambient air as a plume whose extension depends on the relative humidity of the diluting medium. Standard shear instabilities develop at the plume edge, forming the stretched lamellar structures familiar with passive scalars. Unlike passive scalars however, these lamellae vanish in a finite time, because individual droplets evaporate at their border in contact with the dry environment. Experiments demonstrate that the lifetime of an individual droplet embedded in a lamellae is much larger than expected from the usual d(2) law describing the fate of a single drop evaporating in a quiescent environment. By analogy with the way mixing times are understood from the convection-diffusion equation for passive scalars, we show that the lifetime of a spray lamellae stretched at a constant rate. is t(v) = 1/gamma ln(1+phi/phi), where phi is a parameter that incorporates the thermodynamic and diffusional properties of the vapor in the diluting phase. The case of time-dependent stretching rates is examined too. A dense spray behaves almost as a (nonconserved) passive scalar.