Free-molecule region

Consider first the case when the particle is much smaller than the mean free path of the gas molecules. This represents the condition where Kn > 1 and is often called the free molecule region. 

In the free molecule region, molecules colliding with a particle will travel on average many particle diameters away from the particle before colliding with another molecule. Thus it is extremely unlikely that the molecule and particle will ever meet again or that the molecule will affect other molecules which may collide with the particle. Therefore, the effect of the collision of the molecule with the particle is immediately lost, and the particle itself exerts virtually no influence on the velocities of the surrounding gas molecules. 

Forward scattering, 281-282, 291-293, 296-297 Fox, D. L., 233 Fractal geometry, 8-11 Fraunhofer diffraction, 296 Free energy and ions, 233-237 Free molecule region, thermophoresis in, 166-169... 

As the value of Kn increases, the value of y decreases and eventually the concentration dependence vanishes. For high enough values of the Knudsen number (roughly Kn > 10) we operate in the free molecule region and y equals ... 

The physicochemical reason why two regimes occur is as follows. In the free molecule region, the effective diffusion coefficient is determined by collisions of the molecules with the catalyst pore walls. Hence, the gas composition will not influence the effective diffusion coefficient. However, in the continuum region mutual collisions between the molecules are determining and the dependence of the effective diffusion coefficient on the concentration becomes most pronounced. 

SimUarity Solution Coagulation in the Free Molecule Region 215... 

SIMILARITY SOLUTION COAGULATION IN THE FREE MOLECULE REGION... 

For D dp (free molecule region), the integral Dvn dv is proportional to the average particle diameter (Chapter I). Hence this term represents the diffusion of a quantity proportional to the average particle diameter. 

Figures 8 and 9 shows a part of the bending region at low temperature containing the components of Vg (150-160 cm ) and Vs (190-200 cm ). The Vg vibration, IR active in the free molecule, has weak components in the Raman spectrum. According to theoretically calculated Raman intensities, which almost perfectly fit the experimental spectrum, the big component has a very low scattering cross-section [87] and is accidentally degenerate with the b2g component at ca. 188 cm. The IR active components of Vg cause strong absorptions in the IR spectrum even if the crystalline sample used for transmission studies is as thin as 400 pm [107, 109].

At high Re and Ma in the free-molecule regime, transfer rates for spheres have been calculated by Sauer (S4). These results, together with others for cylinders and plates, have been summarized by Schaaf and Chambre (Sll). The particles are subject to aerodynamic heating and the heat transfer coefficients are based upon the difference between the particle surface temperature and the recovery temperature (see standard aerodynamics texts). In the transitional region, the semiempirical result of Kavanau (K2),... 

In ionic micelles the hydrocarbon core is surrounded by a shell that more nearly resembles a concentrated electrolyte solution. This consists of ionic surfactant heads and bound counterions in a region called the Stern layer (see Chapter 11, Section 11.8). Water is also present in this region, both as free molecules and as water of hydration. 

Fig. 3 Example of the microdomains created by embedding luminescent indicator-loaded silica gel nanoparticles into poly(dimethylsiloxane) before cross-linking to fabricate films for oxygen optosensing. The largest circles represent the silica particles the black lines represent the PDMS polymer chains, while the smallest circles represent the indicator dye molecules (the black circles depict those located in the organic polymer-free silica regions and the gray circles stand for those adsorbed on silica regions in contact with the PDMS)...

A solute (additive) can be located in reverse micelles in different solubilization sites in the water core, in the interfacial region or in the bulk solvent. Solubilization into the water cores increases the inner volume at constant interfacial area, resulting in radial growth. If the micelle is too small to receive a solute molecule without deformation, e.g., at low water content, a segregation occurs between small free molecules and the large objects which are covered with surfactant (Chatenay et al., 1987 Encinas and Lissi, 1986 Pileni et al., 1985). 

Figure 1 Modes of diffusion of individual membrane proteins as revealed by single-molecule tracking techniques. The hypothetical trajectory of an individual plasma membrane protein as traced by single-particle tracking techniques is shown. An individual protein can switch between several different modes of over time, which include confined diffusion (region 1), free diffusion (region 2), and immobilization (region 3).

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