A Dynamic Regions

DYNAMIC SURFACE TENSION REDUCTION IV.A. Dynamic Regions 

In many interfacial processes, such as in high-speed wetting of textile, paper, and other substrates (Chapter 6, Section IIC), or in foaming (Chapter 7), equilibrium 

FIGURE 5-6 Generalized dynamic surface tension, yt versus log time, t, curve region I, induction region II, rapid fall region HI, meso-equilibrium region IV, equilibrium. Reprinted with permission from X.Y. Hua and M. J. Rosen, J. Colloid Interface Sci. 124, 652 (1988). 

A is a constant related to the molecular structure of the surfactant. It has been suggested (Gao and Rosen, 1995) that n is related to the difference between the energies of adsorption and desorption of the surfactant. Some values of n are listed in Table 5-3. From the data, it is apparent that the value of n increases with increase in the hydrophobicity of the surfactant, thus increasing with (1) increase in the NaCl concentration of the solution for anionic surfactants (due to compression of the electrical double layer [Chapter 2, Section I]) (2) increase in the length of the hydrophobic group (3) increase in the pH of the solution for the amine oxide, Ci4H29N(CH3)20, which decreases its tendency to pick up a proton and become 

The time, f,-, for the induction period (region I) to end is an important factor in determining the surface tension as a function of time, since only when that period ends does the surface tension start to fall rapidly. The value of f,- has been shown (Gao, 1995 Rosen, 1996) to be related to the surface coverage of the air-aqueous solution interface and to the apparent diffusion coefficient, Dap, of the surfactant, calculated by use of the short-time approximation of the Ward-Tordai equation (Ward, 1946) for diffusion-controlled adsorption (equation 5.6)  

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The coastal ocean is a dynamic region where the rivers, estuaries, ocean, land, and the atmosphere interact. Coastlines extend over an estimated 350,000 km worldwide, and the coastal ocean is typically defined as a region that extends from the high water mark to the shelf break. 

Coastal ocean a dynamic region where the rivers, estuaries, ocean, land, and the atmosphere interact. 

Dynamic Measurements. Dynamic methods are requited for investigating the response of a material to rapid processes, studying fluids, or examining a soHd as it passes through a transition region. Such techniques impart cycHc motion to a specimen and measure the resultant response. 

The critical speed map shown in Figure 5-15 can be extended to include the second, third, and higher critical speeds. Such an extended critical speed map can be very useful in determining the dynamic region in which a given system is operating. One can obtain the locations of a system s critical speeds by superimposing the actual support versus the speed curve on the critical speed map. The intersection points of the two sets of curves define the locations of the system s critical speeds. 

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

A typical behavior of amplitude dependence of the components of dynamic modulus is shown in Fig. 14. Obviously, even for very small amplitudes A it is difficult to speak firmly about a limiting (for A -> 0) value of G, the more so that the behavior of the G (A) dependence and, respectively, extrapolation method to A = 0 are unknown. Moreover, in a nonlinear region (i.e. when a dynamic modulus depends on deformation amplitude) the concept itself on a dynamic modulus becomes in general not very clear and definite. 

The existence of the G (A) dependence even in the region of very small amplitudes is explained by a brittle pattern of fracture of a filler s structure, so that measuring virtually frequency (and amplitude) dependences of a dynamic modulus, a researcher always deals with a material in which the structure is partially fractured. 

Any polymer contains some inner free space free volume distributed in a dynamic manner between its molecular chains (see Section 23.2). When it is exposed to a fluid (liquid or gas) the physical possibility exists for fluid absorption by the polymer, if the fluid molecules or atoms are small enough to fit into local regions of this distributed space during kinetic movements. As this happens, subsequent kinetic chain motion must allow for the newly absorbed fluid molecules and, hence, the polymer s overall volume will adjust accordingly this action will coincide with the formation of more free space around these fluid molecules—so the polymer will swell a little. This process will be continued until an equilibrium is reached ( equilibrium swelling ), by which time the extent of swelling can be considerable. The amount of fluid taken up and the rate at which this happens are both important, and are discussed in this and following sections. 

We have seen that the cooperative region, which represents a nominal dynamical unit of liquid, is of rather modest size, resulting in observable fluctuation effects. Xia and Wolynes [45] computed the relaxation barrier distribution. The configurational entropy must fluctuate, with the variance given by the usual expression [77] 5Sc) ) = Cp barrier height for a particular region is directly related to the local density of states, and hence to... 

This condition of balanced motion is called dynamic equilibrium. Although a dynamic system contains objects that move continuously, a system at equilibrium shows no change in its observable properties. Our example of ink in water is dynamic because the water and ink molecules continually move about. The mixture is at equilibrium when the color is uniform and unchanging. In any part of the solution, ink molecules continue to move, but the number of ink molecules in each region does not change. 

INITIAL specifies the start of the INITIAL region specify the initial concentrations DYNAMIC specifies the start of the DYNAMIC region represent the model equations is a check on the total mass balance... 

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