Single Drop Impacts of Complex Fluids: A Review - Drops and Bubbles in Contact with Solid Surfaces - page 279

Figure 10. Effect of the fluid elasticity (Trouton ratio) on the retraction velocity and on the bouncing
height of a polymer solution droplet [37].

served in drops containing flexible polymers impacting on solid surfaces is due to
the drop-surface interaction rather than to an increased energy dissipation connected
to the elongational viscosity of the fluid. Furthermore, measurements of the maxi-
mum bouncing height of Leidenfrost drops (indicative of the fraction of the initial
kinetic energy which is not dissipated during impact) suggest that in some cases
polymer additives indeed reduce instead of increasing the overall energy dissipa-
tion [40]. This result is consistent with recent direct numerical simulations showing
a reduction in small-scale convective motions in dilute polymer solutions hence in
bulk viscous dissipation [41]. Therefore, one must conclude that the real cause of
this phenomenon is to be sought in the dynamic wetting behavior of dilute poly-
mer solutions, and not in some bulk property of the fluid such as the elongational
viscosity.
In order to explain the anti-rebound effect in terms of wetting, Bartolo et al. [42]
suggest that it can be related to the normal stresses arising near the contact line
during drop retraction. Using an equation that generalizes the lubrication theory for
thin films, and accounting for capillarity and normal stresses in addition to shear
stresses, they find that for large contact angles the retraction velocity, v r , assumed to
be identical to the average velocity on the drop height, is related to the normal stress
coefficient, , and to the contact angle, θ , according to the following equation:

4 v r
l m

σ( cos θ − cos θ eq ) = , (5)

where θ eq is the equilibrium contact angle, and l m the microscopic cut-off height
of the drop in the neighborhood of the contact line. Equation (5) is found to be
in good agreement with experimental data obtained from polyethylene oxide and
polyacrylamide solutions with concentrations ranging between 200 and 2000 ppm.