Gravitational Regime, Complete Wetting

In this case, Eqnation 4.94 becomes p = p + pgh, and substitution of the latter eqnation into the equation of spreading (Equation 4.91) results in 

Using the same similarity coordinate and function (A2.1), we conclude that relations (A2.2-A2.4) are still valid. Using the same procedure as the one previously mentioned, we can transform Equation A2.22 to 

Equation A2.23 should depend on the similarity coordinate only that is, it should not include any time dependence. This is possible only if the following relations are satisfied simultaneously  

Let P = ),/D2and divide the first equation in (A2.24) by the second equation. That results in 

Substitution of Equation A2.25 into Equation A2.24 results in the following time evolution of the radius of spreading, R, 

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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]. 

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