Regime of Spreading

Small drops with an initial characteristic size smaller than the capillary length, a, are considered here. That means, after a short inertial period, the capillary regime of spreading begins. In this case the pressure is given by 

let us introduce dimensionless values using the following characteristic scales h , r , and t . From Equation 3.17 we conclude that 

In Section 3.2 we will see that the estimation of the characteristic time scale is unrealistically small. However, for a moment we ignore this because, as we will see in the following text, the spreading problem cannot be solved precisely in this way. Now, Equation 3.17 and Equation 3.12 can be rewritten as 

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If capillary forces prevail, then the capillary 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. 

This means that the capillary regime of spreading takes place only at t > 10 tue-Equation 4.39 is used in the following text to determine the condition for the fulfillment of the second requirement, Ca 1. This equation can be rewritten as Ca = co0. According to our experimental condition ca = 10- 0 = 0.5. This gives the following estimation of the capillary number Ca 10". This means. 

In any experimental observation, only a limited number of experimental values of L(t) dependency are measured. If some of these measurements are taken at the initial regime of spreading, then a higher value results for the fitted exponent than 0.1. 

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]. 

If the gravity dominates, then the gravitational regime of spreading takes place, therefore... 

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... 

Experimental investigation were carried out on the spreading of small drops of aqueous SDS solutions (capillary regime of spreading) over dry nitrocellulose membranes (permeable in both normal and tangential directions) in the case of partial wetting. Nitrocellulose membranes were chosen because of their partial hydrophiUcity. The time evolution was monitored for the radii of both the drop base and the wetted area inside the porous substrate. 

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 the capillary regime of spreading, the capillary forces dominate, that is. 

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

Capillary Regime of Spreading In this case, Equation 5.116 becomes... 

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. 

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