Liquid bridge length scale based nondimensional groups for mapping transitions between regimes in capillary break-up experiments

Criteria to identify transitions between dynamic self-similar linear thinning regimes of liquid bridges are of utmost importance in order to accurately interpret results in capillary break-up rheometry. Currently available criteria encompass many experimental difficulties or rely on numerical approaches. Here, we introduce a different set of nondimensional groups, OhL=ηin/γρL and a=R/L, based on the experimentally relevant axial length scale of a liquid bridge L, for viscous-dominated fluids undergoing capillary break-up in air. This framework is further extended to encompass the effect of outer viscous fluids. As a result, we present a two-dimensional operating map in which the boundaries are set by fluid properties and a single geometrical parameter, related to the experimental configuration. This approach establishes guidelines to correctly interpret experimental data and identify transitions in capillary break-up experiments of liquid bridges surrounded by fluids of different viscosities.