International length

The data indicated that droplet-size changes are primarily influenced by injection pressure and orifice size while secondary changes can be attributed to fluid properties, orifice shape, and the nozzle s internal length diameter ratio. This last point was not observed by Dombrowski and Wolfsohn (8) for more conventional swirl spray nozzles. Nevertheless, they present a useful correlation between Sauter mean diameter and operating conditions. 

The aspect ratio of a pressure vessel, defined as the ratio of the internal length to the internal diameter, is also important for improved mixing and heat transfer. As important as these factors may be, they must often be balanced with the cost of the pressure vessel. As the diameter of a vessel increases, the thickness of the wall must increase proportionally for safe operation at the same pressure. The heat transfer rate can become limited because of the thicker wall and because of the decreased surface to volume ratio of vessels with larger diameters. 

In fact, this shorter length scale is imposed on the problem by the physical necessity of retaining viscous terms in order to satisfy the no-slip condition at z = 0. To say the same thing in another way, an internal length scale is generated by the physics that has just the correct value to maintain viscous effects where they are needed in the domain in order to satisfy all of the physical conditions of the original problem. 

The formulation of extended continua can be traced back to the Cosserat brothers [13], who enriched the standard continuum by rotational degrees of freedom. As a consequence, such a continuum does not only transfer stresses but also couples stresses. The Cosserat or micropolar theory is well established now [17, 22, 32]. It is successfully applied if materials with microstructure are modeled on the macroscale, e.g., the equivalence of the Cosserat model is shown for materials with lattice-Hke microstractures [1, 2, 16, 25, 34, 35, 41] and with granular materials [3-5, 8, 15]. Furthermore, the micropolar approach is taken into account if strain localization arises which in the framework of the standard continuum would lead to a mesh dependence in the numerical solution (see, e.g.. Ref [29]). The Cosserat model introduces a so-called internal length A in the theory which allows for the existence of solutions of the bound-... 

The internal length scale of the CPs was also examined using the following procedure if r denotes the coordinates of the ith bead, then the internal distribution of distances between beads (i.e., the internal length scale) is obtained by examining... 

A capillary-tube method to analyze binary liquid diffusivity was reported in Mickley et al. (1957) a straight, narrow bore capillary tube of known internal length has one end sealed and is filled with a binary solution of known composition. The capillary is maintained in a vertical position with the open end pointed upward. A slow stream of pure solvent is allowed to continuously sweep past the open mouth of the capillary tube. We shall designate species A as solute and species B as solvent. After an elapsed time, t, the capillary is removed and the solution it contains is well mixed and then analyzed for composition, to find how much solute A was extracted. Generally, several such experiments are conducted at different values of r. 

Mile (nautical international) Length mi 1.852 kilometers 1.151 statute imles 0.999 U.S. nautical imles... 

As we can see in Sect. 5.2, formula (90), the introduced time of correlation appears to be connected with the internal length or (as we shall see in Sect. 6.6, formula (136)) with the length of the macromolecule between adjacent entanglements Me... 

Hydrocarbon chains snch as n-tetradecane (C14) that are longer than the internal length of the capsule cavity form encapsulation complexes by assuming helical conformations as confirmed by through-space nuclear Overhauser effect (NOE) cross peaks along their chains (Figure 8.10). Apparently, the unfavorable gauche interactions are compensated by attractive CH- n interactions. 

For better understanding the diverse relaxation behavior of confined polymers, researchers have utilized models or simulation tools to capture the kinetic features of the material at the molecular level, aiming to represent the results observed in experiments. The FVHD model, which has been widely employed in characterizing physical aging in bulk polymers, is reformulated to describe the relaxation behavior of polymers under nanoconfinement. A dual mechanism combines the effect of vacancy diffusion and lattice contraction, and was recently applied with time-dependent internal length scales to characterize the free volume reduction in the aging process [169]. The dual mechanism model (DMM) fits the data of thin film permeability fairly well. The potential predictive capability of the DMM model depends on the accuracy of the relationship between the internal length and time scale on the description of complex material dynamics [161]. 

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