Viscoelastic
Involutes: when liquid threads spin
Bavand Keshavarz,
MIT, USA
Abstract
Elongational properties affect the
performance of non-Newtonian fluids in many important biological and industrial
fragmentation processes. Common examples are, but not limited too, human coughing and sneezing, spray coating of paints,
and inkjet printing. Rotary atomization/fragmentation of weakly viscoelastic
fluids is one of these widely used industrial examples. Liquid ligaments are
formed around a spinning cup, with a repeatable geometrical spacing, due to the
destabilizing action of the centripetal acceleration (also known as
Rayleigh-Taylor instability). The resulting filaments then follow a geometrical
path-line that is described by the involute of a circle. We provide a simple
theoretical prediction for the average droplet sizes in this fragmentation
process. We also investigate the resulting droplet size distributions and show
that the appearance of satellite droplets in the pinch-off events leads to the
emergence of bimodal size distributions. These double-peaked distributions are precisely
described by the superposition of two separate Gamma distributions. For weakly
viscoelastic test fluids, we show that the liquid viscoelasticity has a
negligible effect on the average droplet size. However, as viscoelastic effects
become increasingly important, nonlinear elastic effects delay the thinning
dynamics in the ligaments and this leads to broader droplet size distributions.
The ratio of the main to the satellite droplet size increases monotonically
with viscosity and viscoelasticity, and this variation can be captured by a
simple physical model for both Newtonian and viscoelastic liquids.
References:
(1) Keshavarz,
B., Houze, E.C., Moore, J.R., Koerner, M.R. and
McKinley, G.H., 2020. Rotary atomization of Newtonian and viscoelastic liquids.
Physical Review Fluids, 5(3), p.033601.
(2) Keshavarz,
B., Geri, M. and McKinley, G.H., 2019. Viscoelastic fishbones. Physical Review
Fluids, 4(10), p.100509
(3) Keshavarz,
B., Houze, E.C., Moore, J.R., Koerner, M.R. and
McKinley, G.H., 2016. Ligament mediated fragmentation of viscoelastic liquids.
Physical review letters, 117(15), p.154502.
(4) Keshavarz,
B. and McKinley, G.H., 2016. Micro-scale extensional rheometry
using hyperbolic converging/diverging channels and jet breakup. Biomicrofluidics, 10(4), p.043502.
(5) Keshavarz,
B., Sharma, V., Houze, E.C., Koerner, M.R., Moore,
J.R., Cotts, P.M., Threlfall-Holmes, P. and McKinley,
G.H., 2015. Studying the effects of elongational properties on atomization of
weakly viscoelastic solutions using Rayleigh Ohnesorge
Jetting Extensional Rheometry (ROJER). Journal of
Non-Newtonian Fluid Mechanics, 222, pp.171-189.
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