Dynamics of the Triple Line

FIGURE 6.3. Dynamical contact angle On as a function of the capillary number Ca = T7V/7 (77 = viscosity, 7 = surface tension, V = velocity of the triple line) for various silicone oils in a glass tube (data from ref. 1). This particular case corresponds to total wetting 9e = 0) (a) Linear scale and (b) log scale, showing the V oc. 6% dependence. 

The dynamical properties of the triple line involve local phenomena—on a molecular scale—in the immediate vicinity of the line, as well as longer-range phenomena in the form of viscous flows in the overall liquid body. We shall see that both aspects are generally at play. Only in one particular case (when 0 is small) do macroscopic effects tend to dominate. 

The astute reader may well be startled by the assertion that the dynamical contact angle is 0 = J/U. As we know, the dynamical contact angle is usually determined by dissipation mechanisms in the vicinity of the triple line, and there is no reason why it should be equal to J/V. Nevertheless, detailed theoretical analyses suggest that the distortions of the profile associated with the line are restricted to a microscopic region near the line. The macroscopic angle is indeed 6 = J/V,... 

FIGURE 6.7. Dynamics of the relaxation of a triple line. At first, the line is pinched by a localized defect and takes on its equilibrium shape, as discussed in section 3.2.2. As the defect is eliminated at time t = 0, the line relaxes and reverts to a horizontal shape. Only a region of size ct is relaxed at time i. 

The Young-Dupre relation is the boundary condition that allows the determination of the shape of the surface between two fluids in contact with a solid wall, such as a liquid drop on a solid wall within a gas (dew) or an air bubble adhering to a sohd wall within a liquid. It is important to emphasize that the Young-Dupre law is applicable only to the case where the triple line is at static equilibrium on the sohd. When the triple line moves (if for example the dew drop slides down the wah), the concept of dynamic contact angle shoirld be substituted for that of static contact angle for better results. ... 

Figure 1. Density profiles for a droplet confined to a finite volume as predicted by YBG theoiy (solid line) are compared with the results of molecular dynamics simulations (7) ( ). The reduced temperature, kT/e=0.71, is near the triple point. The total number of atoms in each of the tems is indicated.

Figure 3. The time dependence of the friction f(r) (solid line) and the viscosity (r) (dashed line), for a Lennard-Jones liquid near its triple point (p = 0.844 and T = 0.728). The friction and the viscosity are normalized by their initial values to facilitate comparison of the dynamics. The time is scaled by the usual dimensionless time, xsc = (mo2 /IcbT)05. For more details see the text.

Supramolecular chemistry has experienced an extraordinary development in the last forty years or so, at the triple meeting point of chemistry with biology and physics. It has given rise to numerous review articles, special issues of journals and books [1-6]. The intention here is to provide a view emphasizing its development towards constitutional dynamic chemistry, together with some conceptual considerations and an outlook, along and beyond the lines earlier horizons, towards... 

Pressure and temperature are two important intensive properties that help determine the phase of a subsfan.ee. A phase diagram indicates the phases of a substance at different pressures and temperatures. Each section of a phase diagram represents a different phase. The lines marking the boundaries of each section represent temperatures and pressures where the corresponding phases are in equilibrium with each other. Like other equilibriums in chemistry, this equilibrium is a dynamic equilibrium, For instance, when water and steam are in equilibrium, water molecules are escaping from the liquid phase at the same rate that they are returning. Notice that there is only one point where a substance can exist in equilibrium as a solid, liquid, and gas. This point is called the triple point. 

As described below, the HAS-derived nitroxides in heterophasic polymer systems perform a triple role. First, they provide the contrast needed in the imaging experiments. Second, they enable the visualization of polymer morphology, based on the detection of two dynamically different components detected in the ESR spectra of the nitroxides in ABS, for example, the two sites, fast (F) and slow (S), have been assigned to location of nitroxides in butadiene-rich and styrene-acrylonitrile (SAN)-rich domains, respectively. Third, the spatial variation of the ESR spectra of nitroxides (in terms of intensity and line shapes) with treatment time, t, provides detailed information on the extent of degradation in the different miCTodomains. These experiments made possible the determination of the concentration profiles of the nitroxides from ID ESRl, and also of the spectral profiles from 2D spectral-spatial ESRI, both in a nondestructive way. In these studies the nitroxides, which are the contrast agents, are part of the systan therefore these studies represent the evolution of ESRl techniques beyond phantoms. 

Our steering results are demonstrated using an experimentally validated numerical model [20] of droplet motion inside the UCLA electrowetting system [21, 22], This model of EWOD fluid dynamics includes surface tensimi and electrowetting interface forces, viscous low Reynolds two-phase fluid flow, and the essential loss mechanisms due to contact angle saturatimi, triple point line pinning, and the related mechanism of contact angle hysteresis. 

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