Concentration gap

An air bath is a very cheap and convenient method of effecting even heating of small distillation flasks (say, 25 ml or 50 ml), where the use of a micro Bunsen burner, results in fluctuations in the level of heating due to air draughts. It may be readily constructed from two commercial tin cans (not aluminium) (those from tinned fruit or food are quite suitable), of such sizes that one fits into the other to provide a small concentric gap as an air insulator. The cleaned large can is cut to the same height as the small can, and the base is then removed. The... 

The concentric gap is c = r2 — r, and clearly a < c. The gap is very small, and locally we can assume flow between parallel plates. Thus we define a rectangular coordinate system X, YfZ located on the surface of the journal such that X is tangential to the journal, as indicated in Fig. E2.9a. The gap between the journal and bearing is denoted as B ) and is well approximated as a function of angle 6 by the following expression ... 

The phase transitions of liquid crystals in solutions occur normally through two mechanisms, i.e. lyotropic and thermotropic transitions. The lyotropic liquid crystal occurs upon addition of solvent into the crystalline phase, while the thermotropic liquid crystal occurs upon heating the crystalline phase, as illustrated by the two arrows in Fig. 10.3, respectively. The phase diagrams for the transition from the homogeneous solution to the liquid crystal are formed by two almost parallel curves, reflecting the concentration gap between the two coexisting phases. 

Yet, in most cases, soHd-state reactions proceed in diffusion couples with low mutual solubihty even in the metastable state (Figure 4.15b). In the case of phase 1 nucleating between a and p, in the absence of phase 1, these phases have metastable solubilities c and 1 — c . Interdiffusion must yield a steplike profile with a concentration gap (c, c ), which does not contain the concentration interval of phase 1. Here the polymorphic mode cannot be reaUzed. 

One procedure makes use of a box on whose silk screen bottom powdered desiccant has been placed, usually lithium chloride. The box is positioned 1-2 mm above the surface, and the rate of gain in weight is measured for the film-free and the film-covered surface. The rate of water uptake is reported as u = m/fA, or in g/sec cm. This is taken to be proportional to - Cd)/R, where Ch, and Cd are the concentrations of water vapor in equilibrium with water and with the desiccant, respectively, and R is the diffusional resistance across the gap between the surface and the screen. Qualitatively, R can be regarded as actually being the sum of a series of resistances corresponding to the various diffusion gradients present ... 

This subject has a long history and important early papers include those by Deijaguin and Landau [29] (see Ref. 30) and Langmuir [31]. As noted by Langmuir in 1938, the total force acting on the planes can be regarded as the sum of a contribution from osmotic pressure, since the ion concentrations differ from those in the bulk, and a force due to the electric field. The total force must be constant across the gap and since the field, d /jdx is zero at the midpoint, the total force is given the net osmotic pressure at this point. If the solution is dilute, then... 

Therefore, the locus of the values ( ) with a vanishing second derivative of A delimits the region of the miscibility gap in which spinodal decomposition occurs. This locus is referred to as the spinodal (figure C2.1.10 (bl). The length scale of the concentration fluctuations at the beginning of the separation process is controlled by... 

Germanium is very similar to Si, but its band gap is too small for many practical applications. Large crystals of ultra-high-purity Ge have been grown for use as gamma-ray detectors. In such crystals, the net concentration of... 

In a defect-free, undoped, semiconductor, tliere are no energy states witliin tire gap. At 7"= 0 K, all of tire VB states are occupied by electrons and all of the CB states are empty, resulting in zero conductivity. The tliennal excitation of electrons across tire gap becomes possible at T > 0 and a net electron concentration in tire CB is established. The electrons excited into tire CB leave empty states in tire VB. These holes behave like positively charged electrons. Botli tire electrons in the CB and holes in tire VB participate in tire electrical conductivity. 

A fluid of viscosity 17 is confined within the gap between two concentric cylinders as shown in Fig. 2.3b. Consider a cylindrical shell of radius r, length 1, and thickness dr located within that gap. 

The miscibility gap becomes progressively more lopsided as n increases. This means that c occurs at lower concentrations and that the tie line coordinates—particularly for the more dilute phase-are lower for large n. 

Data, for a 32% caustic concentration at 90°C and a current efficiency of 96.0%, obtained in laboratory cells using a DSA anode and an activated cathode, where the membrane is against the anode at a 3-mm gap. 

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