Behavior of a polydisperse cluster of interacting drops evaporating in an inviscid vortex

Abstract

The dynamics and evaporation of polydisperse collections of liquid drops in an axisymmetric, infinite, cylindrical vortex are described using a statistical model. This model describes both the dense regime where inter-particle effects are important and the dilute regime. The initial size distribution is partitioned into size classes and each initial size-class is followed dynamically and thermodynamically using a class-defined, drop-frame coordinate system. Each initial-size-class develops a continuum of sizes as drops centrifuge towards hotter surroundings and evaporate. A separate coordinate system tracks the gas phase. Because larger drops experience larger centrifugal force, they approach the hotter gas faster. However, for appropriate liquid heating times, the large drops might evaporate at a faster rate, and so the size-differentiated centrifugation previously observed and calculated for cold flow situations does not occur. Instead, a radially peaked drop size distribution is developed in the gas vortex. The centrifugal motion forms a drop-free inner vortex core bound by a cylindrical shell containing all the drops. This shell of gas and drops is called the drop cluster. Numerical calculations show that more parameters control dense clusters than dilute clusters; examples of these parametric relations include: (i the gas vortex, whereas drop size distribution controls the outer region; and (ii increases the maximum mass fraction of the evaporated compound and enhances penetration of the evaporated compound into the surroundings. Except for dilute clusters, the assumption of uniform drop number distribution in the cluster is found to be inappropriate. Instead, the drop size distribution always becomes non-uniform even if the initial size distribution is monodisperse and the initial drop number distribution is uniform. This development of non-uniformity is caused by drops at the cluster peripheries preventing heat conduction/convection to drops in the central cluster.