Coalescence and bouncing of small aerosol droplets

The trajectories of 20 and 40 pm radius water droplets colliding with a gas-water interface are observed to determine the conditions under which drops will bounce or coalesce on impact and the apparent coefficient of restitution of the drops that bounce. The experiments were performed in a pressure chamber so that the pressure and composition of the gas could be varied to explore the effects of the viscosity and mean-free path of the gas. The impact velocity is varied by producing drops with a velocity larger than their terminal velocity using a piezoelectric drop generator and adjusting the distance between the generator and the liquid interface. The geometry of the collisions is axisymmetric and the Weber number, We = rho(l)U(2)a/sigma, is O(1) or smaller, so as to facilitate comparison with a theory for weakly deformable gas-liquid interfaces. Here, rho(l) is the liquid density, U the impact velocity, a the drop radius and sigma the surface tension. After a low-Weber-number drop coalesces, a smaller, daughter drop is emitted from the interface with a velocity higher than the incident velocity of the mother drop. The daughter drop radius is about 0.55a and the daughter velocity is 0.38(sigma/(rho(l)a))(1/2) for We < 0.01. The experimental results are compared with a theory in which the small deformations of the drop and surface are expanded in Legendre polynomials and Fourier modes, respectively, the non-continuum lubrication stresses are computed in the thin gas film between the drop and interface, and the liquid flow is approximated as an inviscid potential flow. The coefficient of restitution decreases with increasing Weber number and becomes insensitive to the viscosity of the gas at Weber numbers larger than about 1. At smaller Weber numbers, drops in a less viscous gas lose less energy during the collision. Drops are observed to undergo a transition from coalescence to bouncing as the drop velocity (Weber number) is increased. However, the marginal condition for drop bouncing is much more sensitive to gas mean-free path (Knudsen number) and gas viscosity (Ohnesorge number) than to Weber number. The Knudsen and Ohnesorge numbers are defined as Kn = lambda/a and Oh = mu(g)/(rho(l)asigma)(1/2) where is the mean-free path and mu(g) is the gas viscosity. Theory and experiment show similar trends of increasing critical Weber number with decreasing Ohnesorge number and increasing Knudsen number. Theoretical results are also derived for the coalescence-bounce transition and coefficient of restitution for head-on collisions of equal sized drops.