Gravitational Regime of Spreading

If gravity prevails, then the gravitational regime of spreading takes place that is, if... 

Now we can consider the shape of the spreading droplet over the duration of the gravitational regime of spreading. Equation 3.31, taking into account Equation 3.32, now takes the following form ... 

FIGURE 3.4 Time evolution of the radius of spreading in log-log coordinate system (3). (1) capillary spreading (2) gravitational regime of spreading. 

In this section, we shall consider a liquid drop being created and then spread over a sohd substrate with a hquid source. We shall look at both cases, complete and partial wetting, and for small and large drops. Then, we expect to observe spreading and forced flow caused by the liquid source in the drop center. Both capillary and gravitational regimes of spreading shall be considered [15]. 

In the case of the gravitational regime of spreading (R(t) > a), experimental data were compared with the theoretical predictions according to Equation 4.96. This equation can be rewritten as ... 

The latter expression allows the determination of the constant thickness of the spreading drop during the gravitational regime of spreading. Combining Equation A2.3 and Equation A2.32 would result in... 

FIGURE 5.23 Axisymmetric (m = 1) gravitational regime of spreading. Spreading exponent a (Eqnation 5.126) vs. n n = 1 — Newtonian fluid. 

Comparison of Equation 5.126 and Equation 5.136 shows that capillary and gravitational regimes of spreading give the same dependence R(t) if n 1. 

However, a number of liquids (polymer liquids and suspensions [18,19]) show a non-Newtonian behavior. The aim of this section is to extend the similarity solution method used in Chapter 3 to the case of spreading of non-Newtonian liquids (Ostwald-de Waele liquids) over solid surfaces and to deduce the corresponding spreading laws for both gravitational and capillary regimes of spreading. 

In Figure 3.4 the time evolution of radius of spreading is schematically presented in log-log coordinates. Capillary and gravitational regimes are shown by line 1 (according to Equation 3.25, with still unknown) and line 2 (according to Equation 3.36), respectively. 

The theoretically predicted spreading laws for gravitational and capillary regimes have been deduced as R(t) and R(t) respectively, where R(t) is the radius of the base of the spreading drop, and t is the time. Comparison of the predicted spreading laws with experimental data in Chapter 3 has shown excellent agreement. 

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