Breakup of a particulate suspension jet

As viscosity is increased, a liquid capillary jet accelerated by gravity stretches over increasingly large distances before eventually breaking up. This Newtonian behavior is profoundly altered for particulate suspensions. Adding solid particles to a liquid, which increases the effective viscosity, can paradoxically shorten the jet considerably [as first reported by Furbank and Morris, Phys. Fluids 16, 1777 (2004)]. This apparent contradiction is rationalized by considering finite-size effects occurring at the scale of a few particles. A model is presented which captures the breakup length of suspension jets observed experimentally for a broad range of liquid viscosities, particle sizes, and extrusion velocities of the jet and recovers the Newtonian case for vanishing particle sizes. These results can be readily extended to any stretched jet configuration and potentially to other fluid media having a granularity. The fragmentation, or atomization, of a liquid involves the formation of transient, stretched, liquid jets, which eventually break up and resolve in drops [1,2]. For homogeneous viscous jets, the rate of pinching is inversely proportional to the liquid viscosity [3] and pinchoff proceeds continuously down to atomic scales [4-6]. Highly viscous jets can therefore reach considerable lengths before breaking up, which explains the seemingly never-breaking threads one can form with honey [7-11] or the notorious difficulty of atomizing extension-thickening polymer solutions [12]. However, if the case of most homogeneous liquids is understood [13,14], that of polyphasic media, such as particulate suspensions, has received much less attention although they are ubiquitous media demanding increasingly smaller processing scales (of, e.g., encapsulation, of printing or molding, and in food, cosmetic, paper, coating, or building industries), for which specific atomization behaviors can be expected. Indeed, as breakup proceeds, their intrinsic granularity is necessarily probed at some point by the vanishing dimension of the jets, and finite-size effects eventually matter. Recent observations on pending drops [15,16] and liquid bridges [17] have reported different facets of adding macroscopic particles to a viscous liquid thread, such as (i) an increase in the thread effective viscosity delaying the breakup and (ii) finite-size effects specific to particulate suspensions hastening the breakup, but the balance between these antagonist effects at the scale of a wh