Menisci, development

If the polymer in the latex is above its glass transition temperature, it may form a him on evaporation of the water. A simple example is the drying of a latex paint him on a wall. As the water evaporates, coalescence surface tension forces proceed from the presence of water menisci of very small radii of curvature. These menisci develop between the particles as the last traces of water are removed. The forces that these menisci generate drive the particles together. Interdiffusion of the polymer chains takes place, forming coherent hlms. 

There have been a number of attempts to revise and elaborate Brown s description of the film formation process [11,30]. For an overview of these approaches the reader is refmed to Mazur s review [25]. Perhaps the most important insight is that in a strict thermodynamic sense, there is no distinction betweai the osmostic pressure, II, and the mean capillaiy pressure, pc, which develops when the meniscus intercepts the surface of the particles. As the system becomes more concentrated, there will be some contribution of capillary forces to 11 before the particles come into contact and before the particle-water meniscus develops. Ultimately, n must converge to pc once the particles are in contact This continuity of n and Pc is the main point of the theoretical analysis by Crowley et al. [31], and they showed that when the osmotic pressure rises to little as 1% of the equilibrium vapour pressure of water, the force should be sufficirait to densify the film. 

The liquid phase distribution over time obtained from the numerical simulation is shown in Fig. 11 At the onset of evaporation, a curved meniscus develops inside the cylinder and recedes. Upon further evaporation, capillary effects become clearly visible large pores dry out earlier, while small pores stay saturated for a longer time. In order to study the effect of wettability, another simulation with the same particle packing but with a different value of the equilibrium contact angle has been performed, see Fig. 12. By comparing these two figures, one can see that the capillary effects are clearly more pronounced for smaller equilibrium contact angle. 

This report presents the results of investigations aimed at the creation of the surface wave transducer for the automated control. The basic attention is drawn to the analysis of the position of the front meniscus of the contact liquid when the surface waves excite through the slot gap and to the development of system for acoustic contact creation. 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

It is these kinds of uncertainties that have led to the development of mercury porosimetry, in which, since the meniscus is convex, the mercury has to be forced into the pores under pressure. Mercury porosimetry is the subject of Section 3.9. 

Kuppe,/. top, summit, tip, head meniscus. Kuppel,/. cupola, dome arch (of a furnace), kuppelartig, a. dome-like, dome-shaped, arched, kuppeln, v.t. [Pg.266]

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

To calculate the flow fields outside the evaporating meniscus we use the onedimensional model, developed by Peles et al. (1998, 2000, 2001). Assuming that the compressibility and the energy dissipation are negligible (a flow with moderate velocities), the thermal conductivity and viscosity are independent of the pressure and temperature, we arrive at the following system of equations ... 

In this section the influence of the pressure in the capillary and the heat flux fluctuations on the stability of laminar flow in a heated capillary tube is analyzed. All the estimations performed in the framework of the general approach and developed in the previous section are kept also in the present cases. Below we will assume that the single cause for capillary pressure oscillations is fluctuations of the contact angle due to motion of the meniscus, whereas heat flux oscillations are the result of fluid temperature fluctuations only. 

In addition to the sessile drop method which measures the contact angle directly, Neumann and Renzow (1969) have developed the Wilhelmy slide technique to measure it to 0.1° precision. As shown in Fig. 2.20, the meniscus at a partially immersed plate rises to a finite length, h, if the contact angle, 0, is finite. 6 is calculated from... 

A much easier method has been developed by Padday et al. (1975) (Faraday Trans. I, 71, 1919), which only requires measurement of the maximum force or weight on the rod as it is pulled upwards. It has been shown by using the Laplace equation to generate meniscus profiles that this maximum is stable and quite separate from the critical pull-off force where the meniscus ruptures. A typical force-height curve is shown in Figure 2.24. 

Figure D3.6.8 illustrates the different phases of drop development and detachment during the measurement. As shown in Figure D3.6.8, the drop does not detach at the exact tip of the capillary. Instead a neck is formed at which the liquid meniscus will eventually be disrupted. The radius of the neck is smaller than the radius of the capillary, rcap. A force balance on the drop yields ...

Transitions from steady-state to time-dependent surface-tension-driven motions are well known also and are important in meniscus-defined crystal growth systems. For example, the experiments of Preisser et al. (51) indicate the development of an azimuthal traveling wave on the axisymmetric base flow in a small-scale floating zone. 

In the JKR theory it is assumed that surface forces are active only in the contact area. In reality, surface forces are active also outside of direct contact. This is, for instance, the case for van der Waals forces. Derjaguin, Muller, and Toporov took this effect into account and developed the so-called DMT theory [206], A consequence is that a kind of neck or meniscus forms at the contact line. As one example, the case of a hard sphere on a soft planar surface, is shown in Fig. 6.19. 

At the craze tip, the advance mechanism would be by a Taylor meniscus instability leading to a series of void fingers occurring in the plastically deformed and strain-softened polymer formed at the craze tip. As the finger-like craze tip propagates, fibrils develop. 

Copies of Boris Cahan s thesis were circulated among many working in the fundamentals of the field in the 1970s. The thesis gave its readers access to the details of the elegant experimental studies it reported on the interplay between meniscus shapes and the thickness of the boundary layer, i0, electrolyte conductivity, and the local heat developed in porous electrodes used in fuel cells (and which tends to dry out thin menisci). 

---