Single Drop Impacts of Complex Fluids: A Review - Drops and Bubbles in Contact with Solid Surfaces - page 269

as water, are generally characterized by a Newtonian constitutive equation, where
the stress tensor is a linear function of the velocity gradient, whereas in complex (or
non-Newtonian) fluids the stress tensor is a generic function of the velocity gradient
and of its derivatives [9, 10].
Thus, the study of non-Newtonian drops requires a completely different model-
ing approach, as well as different sets of experimental data, depending on the form
of the constitutive equation of the fluid. In particular, due to the large spatial and
temporal gradients observed during drop impacts, small changes in the constitutive
equation result into large macroscopic effects (for example, most Newtonian drop
impact models become inaccurate for large fluid viscosities [11]).
The present review describes some recent developments about the study of drop
impact of the most common types of non-Newtonian fluids: power-law fluids, yield-
stress (or viscoplastic) fluids, and viscoelastic fluids. In particular Section B is about
power-law fluids, with focus on shear-thinning fluids; Section C presents recent
works about viscoplastic drop impacts. Finally, Section D reviews the literature
about viscoelastic drop impacts onto both homo-thermal and heated surfaces. An
overview of constitutive equations and of the main features of complex liquids is
presented in an extended Appendix. We advise readers who are not familiar with
complex fluids to read the Appendix before the following chapters.

B. Impact of Power-Law Drops

Existing research into shear-thinning fluid drops focuses mainly on detachment dy-
namics from capillary nozzles [12] and the spreading behavior of sessile drops on
solid surfaces [13-15] rather than on impacting drops. One of the difficulties aris-
ing in the study of shear-thinning drop impacts is that during any dynamic process
the fluid viscosity will vary both spatially and temporally as a function of the lo-
cal shear-rate. This additional complexity increases the difficulty in establishing
relationships between the macroscopic drop dynamic behavior and the underlying
viscometric properties of the fluid. Moreover, common parameters used to char-
acterize drop behavior, such as the Reynolds, the Ohnesorge, and the Capillary
numbers, cannot be defined adequately due to the variation of the viscosity term.
Recently, an experimental study about the impact of shear-thinning drops [16,
17] was carried out using a set of model shear-thinning fluids consisting of aque-
ous solutions of Xanthan gum at mass concentrations of polymer ranging from
0.125% to 0.1%, whose experimental flow curves were fitted using the Ostwald-
De Waele equation to determine the values of the consistency coefficient, K ,and
of the power-law index, n (see Appendix). The effect of surface wettability was
taken into account by comparing impacts on a hydrophilic surface (glass) with im-
pacts on a hydrophobic surface (Parafilm, equilibrium contact angle: 105 ◦ ). This

study shows that although the impact morphology is qualitatively similar to that of
Newtonian drops of comparable average viscosity (Fig. 1), it is not immediately ob-
vious how the consistency coefficient K and the power law index n independently

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