Layer compression constant

Similarly, the layer compressibility constant, B, exhibits a critical variation in the vicinity of the transition. This pretransitional behavior above AN has been recognized by de Vries [32], who, by X-ray diffraction experiments, has shown the existence of small domains with a smectic... 

Yet another technique, measuring ultrasonic velocity anisotropies in the vicinity of the NA transition, however, also find anisotropies consistent with crossover behaviour. Sonntag et al [52] studied the divergence of three elastic constants, the bulk compression constant A, the layer compression constant B and the bulk-layer coupling constant C. B and C have critical exponents that are unequal and are in between that of the 3DXY values and anisotropic scaling values. 

The addition of a layer compression energy Wcomp such as those of the forms introduced at equations (6.147) and (6.148), can also be added to w. Some preliminary theoretical results involving the onset of layer undulations in a Helfrich-Hurault transition in SmC using such an energy obtained, for example, via (6.147), (6.299), (6.301) and (6.302), has been reported by Stewart [263]. Also, the smectic layer compression constant B has been measured for various materials that exhibit SmA and SmC phases see the comments and references on page 284. 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

The potential inside the brush layer is equal to the Donnan potential with the charge density ZeN h). We denote by i/ donC/i) the Donnan potential in the compressed brush layer, which is a function of h. Since the potential inside the compressed brush layers is constant independent x (but depends on the separation h) (Fig. 17.1b), the Poisson-Boltzmann equation in the brush layer becomes... 

For small-molecule thermotropic smectic-A phases, typical values of two elastic constants are K 10 dyn and B 10 dyn/cm (Ostwald and Allain 1985). For lyotropic smectics, such as those made from surfactants in oil or water solvents, the layer compression modulus B can be much lower (see Chapter 12). From B and K, a length scale A. = ( 1 /B) 1 nm is defined it is called the permeation depth and its magnitude... 

Assuming the Instrument is operating properly, obtaining reliable p values for the reference colloid also depends on the sample preparation conditions. First, our studies revealed that a solids loading greater than 0.005 vol% was required before a constant p could be obtained (Figure 2). Using different instrumentation (Pen Kern 3000), this has also been found for caldte powders. A decrease in the absolute value of p has been attributed to hydrodynamic interactions and colloidal phenomena sucn as double layer compression. In this experiment, however, the... 

The coefficient B is the elastic constant associated with the layer compressions. This represents the solid-like term along the layer normal. The second term (nematic-like) describes how much energy is required to bend the layers. In describing the SmA phase, both elastic constants K and B are very important. The former, which is higher order. 

Here Fq is tire free energy of the isotropic phase. As usual, tire z direction is nonnal to tire layers. Thus, two elastic constants, B (compression) and (splay), are necessary to describe tire elasticity of a smectic phase [20,19, 86]. 

Wlrile quaternary layers and stmctures can be exactly lattice matched to tire InP substrate, strain is often used to alter tire gap or carrier transport properties. In Ga In s or Ga In Asj grown on InP, strain can be introduced by moving away from tire lattice-matched composition. In sufficiently tliin layers, strain is accommodated elastically, witliout any change in the in-plane lattice constant. In tliis material, strain can be eitlier compressive, witli tire lattice constant of tire layer trying to be larger tlian tliat of tire substrate, or tensile. 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

Much higher shear forces than in stirred vessels can arise if the particles move into the gas-liquid boundary layer. For the roughly estimation of stress in bubble columns the Eq. (29) with the compression power, Eq. (10), can be used. The constant G is dependent on the particle system. The comparison of results of bubble columns with those from stirred vessel leads to G = > 1.35 for the floccular particle systems (see Sect. 6.3.6, Fig. 17) and for a water/kerosene emulsion (see Yoshida and Yamada [73]) to G =2.3. The value for the floe system was found mainly for hole gas distributors with hole diameters of dL = 0.2-2 mm, opening area AJA = dJ DY = (0.9... 80) 10 and filled heights of H = 0.4-2.1 m (see Fig. 15). 

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