Viscosity, microscopic macroscopic

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Thermodynamic, statistical This discipline tries to compute macroscopic properties of materials from more basic structures of matter. These properties are not necessarily static properties as in conventional mechanics. The problems in statistical thermodynamics fall into two categories. First it involves the study of the structure of phenomenological frameworks and the interrelations among observable macroscopic quantities. The secondary category involves the calculations of the actual values of phenomenology parameters such as viscosity or phase transition temperatures from more microscopic parameters. With this technique, understanding general relations requires only a model specified by fairly broad and abstract conditions. Realistically detailed models are not needed to un-... 

The influence of the lipophilic external phase on the production of xylan-based microparticles by interfacial cross-linking polymerization has been investigated (Nagashima et al., 2008). Three different external phases were investigated a 1 4 (v/v) chloroform cyclohexane mixture, soybean oil, and a medium chain triglyceride, with viscosities below 1, 24, and 52 cP, respectively. It was observed that the use of these different lipid phases results in different macroscopic and microscopic aspects of the system (Figure 10). 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

On the other hand, it was found that the microscopic parameter pH(c) exhibits close similarities to the macroscopic viscosity r (c)/r s of a low molecular mass (M 7.400 g/mol) PDMS/d-chlorobenzene system at 373 K. For that low molar mass the terminal Zimm time tz [see Eq. (80)] is comparable to the time scale of the NSE experiment. Thus, the macroscopic viscosity can relax towards... 

At the microscopic level, the liquid particles are in constant motion. The particles may exhibit short-range areas of order, but these usually do not last very long. Clumps of particles may form and then break apart. At the macroscopic level, a liquid has a specific volume but no fixed shape. Three additional macroscopic properties deserve discussion surface tension, viscosity, and capillary action. 

At the macroscopic level a solid is defined as a substance that has both a definite volume and a definite shape. At the microscopic level, solids may be one of two types—amorphous or crystalline. Amorphous solids lack extensive ordering of the particles. There is a lack of regularity of the structure. There may be small regions of order separated by large areas of disordered particles. They resemble liquids more than solids in this characteristic. Amorphous solids have no distinct, melting point. They simply get softer and softer as the temperature rises, leading to a decrease in viscosity. Glass, rubber, and charcoal are examples of amorphous solids. 

J. Quillet The swelling doesn t help you very much because it hasn t affected the mobility of the molecules. It has helped the macroscopic appearance of viscosity but not the microscopic. 

The only way to validate kinetic models is to measure experimentally the degree of cure as a function of time and temperature. It can be done on both macroscopic and microscopic levels by monitoring chemical, physical (refractive index [135], density [136], and viscosity [137]), electrical (electrical resistivity [138,139]), mechanical, and thermal property changes with time [140,141]. The most-used techniques to monitor cure are presented in the next two subsections. 

Because the quantitative analysis of transport processes in terms of the microscopic description of turbulence is difficult, Kdrmdn suggested (K2) the use of a macroscopic quantity called eddy viscosity to describe the momentum transport in turbulent flow. This quantity, which is dimensionally and physically analogous to kinematic viscosity in the laminar motion of a Newtonian fluid, is defined by... 

The first difficulty derives from the fact that given any values of the macroscopic expected values (restricted only by broad moment inequality conditions), a probability density always exists (mathematically) giving rise to these expected values. This means that as far as the mathematical framework of dynamics and probability goes, the macroscopic variables could have values violating the laws of phenomenological physics (e.g., the equation of state, Newton s law of heat conduction, Stokes law of viscosity, etc.). In other words, there is a macroscopic dependence of macroscopic variables which reflects nothing in the microscopic model. Clearly, there must exist a principle whereby nature restricts the class of probability density functions, SF, so as to ensure the observed phenomenological dependences. 

Time-dependent correlation functions are now widely used to provide concise statements of the miscroscopic meaning of a variety of experimental results. These connections between microscopically defined time-dependent correlation functions and macroscopic experiments are usually expressed through spectral densities, which are the Fourier transforms of correlation functions. For example, transport coefficients1 of electrical conductivity, diffusion, viscosity, and heat conductivity can be written as spectral densities of appropriate correlation functions. Likewise, spectral line shapes in absorption, Raman light scattering, neutron scattering, and nuclear jmagnetic resonance are related to appropriate microscopic spectral densities.2... 

The question about the difference between the macroscopic and microscopic values of the quantities characterizing the translational mobility (viscosity tj, diffusion coefficient D, etc.) has often been discussed in the literature. Numerous data on the kinetics of spin exchange testify to the fact that, with the comparable sizes of various molecules of which the liquid is composed, the microscopic translational mobility of these molecules is satisfactorily described by the simple Einstein-Stokes diffusion model with the diffusion coefficient determined by the formula... 

On the basis of these considerations it can be expected that the Einstein Stokes model will be applicable for vitrified solutions consisting of the particles with comparable sizes. In other words, for the order of magnitude estimations of the microscopic translational mobility of molecules in such solutions, the value of the diffusion coefficient, which is obtained by using the macroscopic viscosity t] in eqn. (1), can be used. 

It is to be noted that in the above discussion although the numerical values of the prefactor is close to 6n, it does not in any way imply the stick boundary condition. The above calculation is based only on microscopic considerations on the other hand, the boundary condition can only be obtained by studying the somewhat macroscopic velocity profile of the solvent. Thus, the main point here is that in the high-density liquid regime, the ratio of the friction to the viscosity attains a constant value independent of the density and the temperature. 

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