The Second Spreading Stage

In this stage, the flhn profile and the surfactant concentration obey the same system of equations (5.146) and (5.147) with boundary conditions (5.148 to 5.151) 

Equation 5.174 can be integrated using condition (5.151), which gives tp( ) 0, at oo, that is. 

Equation 5.177 describes decaying capillary waves on the film surface. Indeed, if we introduce a new local variable = ( - X)lx with 

The asymptotic behavior of this equation, according to Chapter 3 (Section 3.5), yields 

In the opposite case, when Equation 5.176 is valid, we obtain from Equation 5.173 using Equation 5.176 that 

---

In conclusion, the radius of the dry sport moves with the speed predicted by the theory while the front edge of the moving part of the layer proceeds slower than theoretically predicted during the second spreading stage. The discrepancy may be due to one ore both of the following reasons ... 

This plot shows that (1) aU three experimental curves fall into a single universal curve, and (2) the dynamic contact angle, as the theory predicts, remains constant during the second spreading stage. 

Papermaking involves two stages. The first is to break up a raw material to form a suspension of individual fibers, and the second is to form sheets of paper by spreading the suspension on a suitable porous surface through which water can drain. 

In the second stage, the control of production and importation of chemicals is introduced, in response to wide spread use of various chemicals. Registration and evaluation of chemicals become an important part of the system. These kind of measures were taken around 1990 in Northeast Asia, except for Japan, where the first law of this type was introduced as early as 1973, as a response to a serious pollution incident with printed circuit boards (PCBs). 

---