Hydrodynamic apparent

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

Certain hydrodynamical problems, as well as mass-transfer problems in the presence of surface-active agents, have been investigated theoretically under steady-state conditions (L3, L4, L10, R9). However, if we take into account the fact that in gas-liquid dispersions, the nonstationary term must appear in the equation of mass- or heat-transfer, it becomes apparent that an exact analysis is possible if a mixing-contacting mechanism is adopted instead of a theoretical streamline flow around a single bubble sphere. 

In the range of 500 to 900 rpm, Fig. 3 and 4 showed that impeller rotation speed does not affect significantly on reaction conversion for relatively long reaction time (above 60 minutes). Apparently, the hydrodynamic condition of liquid in the reactor was sufficiently turbulent by aeration. 

Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58-60, and references therein). A number of studies [58, 61-64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65-67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness... 

The rate of separation of the fragments depends on the functions A r), C(r), Fc> and the fragmentation number, while the rate of rotation depends only on the function B(r). Further, it is apparent that the separation between the fragments increases only when the hydrodynamic force exceeds the binding physicochemical force. The pair of fragments rotates as a material element in an apparent flow with an effective velocity gradient tensor... 

A (3 fibril formation an identifiable nucleating species has yet be isolated. Direct observation has been made difficult by the small size of the (3 peptide, which has an effective hydrodynamic radius of 4 nm [98-100], and by the apparent low abundance of nucleating species due to the low probability of their formation. Such species would be formally akin to an enzyme transition state that is usually kinetically inferred or sometimes trapped with certain kinds of inhibitor. In disaggregated, ultrafiltered (20 nm pore size) preparations, less than 1% of the molar peptide concentration is inferred to be present as seeds or nuclei determined by the kinetics of fibril formation [101]. 

Using two sets of data on water and one on methanol, which apparently fell in the hydrodynamic region, Ivey (1967) obtained the relation... 

Hydration can be an important factor in diffusion and mass transport phenomena in pharmaceutical systems. It may alter the apparent solubility or dissolution rate of the drug, the hydrodynamic radii of permeants, the physicochemical state of the polymeric membrane through which the permeant is moving, or the skin permeability characteristics in transdermal applications. 

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

Fig. 27 Apparent hydrodynamic radius (Rh) of the mesoglobules formed by quickly heated aqueous solutions of the homopolymer PVCL or the graft copolymers with varying concentrations. (Reprinted with permission from Ref. [180] copyright 2005 Elsevier)...

The dissolution rate of a solid from a rotating disc is governed by the controlled hydrodynamics of the system, and it has been treated theoretically by Levich [104]. This theory considers only forced convection due to rotation and ignores natural convection, which may occur at low speeds of rotation. Figure 16 shows the solvent flow held near the surface of the rotating disc. The apparent thickness, h, of the diffusion layer next to the surface of the disc is given by... 

We might properly refer to this value as the apparent Peclet number, because by many formal definitions the Peclet number accounts for the relative importance of advection and molecular diffusion, without mention of hydrodynamic dispersion. 

Regime of transport limitation, here

diffusion through the hydrodynamic boundary layer. The apparent activation energy under these conditions gets close to zero. Every educt molecule reacts instantaneously on the outer catalyst surface, no educt diffusion inside the catalyst particle takes place. 

Publication gravure printing inks apparently show elastic behavior at D = 105 s the modulus of shearing G is 103 Pa. This indicates that at high shear rates D, between 105 and 106 s gravure printing inks develop normal stress effects and thus show a hydrodynamic lubricating effect. These deductions are relevant to an... 

But p decreases with salt concentration with an apparent exponent of k which changes from 0 at low salt concentration to — at high salt concentrations. The N-independence of p arises from a cancellation between hydrodynamic interaction and electrostatic coupling between the polyelectrolyte and other ions in the solution. It is to be noted that the self-translational diffusion coefficient D is proportional to as in the Zimm model with full... 

An indirect indication of the presence of interactions between micellar phase and drugs is given by molecular and dynamic parameters of the drug and the micelles (ionic mobility, diffusion coefficient, hydrodynamic radius, apparent molecular mass), which are altered by the solubilization of lipophilic substances in a significant manner. 

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