Micropolarization

From experimental results, the variation of film thickness with rolling velocity is continuous, which validates a continuum mechanism, to some extent in TFL. Because TFL is described as a state in which the film thickness is at the molecular scale of the lubricants, i.e., of nanometre size, common lubricants may exhibit microstructure in thin films. A possible way to use continuum theory is to consider the effect of a spinning molecular confined by the solid-liquid interface. The micropolar theory will account for this behavior. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

Size-dependent effects will be seen in fluids with micro-structure, and the thinner the gap is, the greater the effect will be. During lubrication when the him approaches molecular dimensions, the microstructure will play a dominant role. In the present paper, micropolar theory is incorporated into the theory accounting for very thin him EHL. The effects of coupling number and characteristic length are analyzed for specihc conditions. 

The point contact thin him lubrication problem with micropolar fluids requires the simultaneous solution of several governing equations as described below. 

Being compared to conventional Reynolds equations, /12 can be regarded as a modification coefficient of the micropolar effects on viscosity, and its effects are shown in Fig. 8. This shows that the microstructure and microrotation will add an increase in lubricant viscosity. When the ratio hH increases, the viscosity enhancement decreases further increasing the ratio, the modiflcation approaches unit. Because I is related to the molecular size, and h is the film gap, this means that if the problem scale is much larger than the molecular dimension, microrotation and the microstructure of particles will contribute msignrhcantly to the macroscopic properties. The larger N is, the more the increase is, as also evidenced by Fig. 8. 

The pressure profile and film shape with or without micropolarity are shown in Figs. 10-17. The polarity does not alter the positions of the second pressure spike and the minimum thickness, and it has a minor influence on the pressure profile and the film shape. In the case of the pressure profile, the micro-polarity affects the pressure distribution in the vicinity of the second pressure spike. It should be noted that, in Figs. 10 and 12, the second pressure spikes are not clear enough due to low velocities. With an increase in character-... 

The effective viscosity is also affected by the microrotation of the rigid particles. If the gap is much larger than the molecular dimensions, the boundary walls will have little influence on the microrotation motion. This means that if the gap between the solid walls is sufficiently large, the micropolarity can be reasonably taken out of consideration without losing precision. The microrotation in thin film lubrication will result in viscosity-enhancements and consequently higher film thicknesses, which contribute to a better performance of lubrication. 

The effective viscosity predicted with micropolar theory is in very close agreement with that found by experimental results in a previous work. This does not adequately assure that it is the only possible way to explain the traits of thin him lubrication, but it shows the roles the microstructure and microrotation of the particles will play in the lubrication process in the very thin him EHL situation. 

Brului, O., and Hsieh, R. K. T, "Mechanics of Micropolar Media, World Scientific, Singapore, 1982. 

Singh, C., and Suiha, P., The Three-Dimensional Reynolds Equation for Micropolar-Fluid Lubricated Bearings, Wear, Vol. 76, No. 2,1982,pp. 199-209. 

Lin, T. R., Analysis of Film Rupture and Reformation Boundaries in a Finite Journal Bearing with Micropolar Fluids, Wear, Vol. 161,1993,pp. 145-153. 

Basic concepts and the methods for determining DD sites in lipid bilayer membranes have been developed by NMR on the atomic site level. Lipid bilayer interfaces as delivery sites can be specified by taking advantage of the site selectivity of NMR. DD sites can be generally classified into the three categories in Fig. 6. The distinction is based on the difference in the micropolarity in membranes around the drug. It has been briefly mentioned how to evaluate dynamic properties of drugs in membranes. 

Lessard, J. G. Fragata, M., Micropolarities of lipid bilayers and micelles. 3. Effect of monovalent ions on the dielectric constant of the water-membrane interface of unilamellar phosphatidylcholine vesicles, J. Phys. Chem. 90, 811-817 (1986). 

A) tracts, whereas conformation of the probe changed in the presence of an RNA poly(A)tract (alteration on the micropolarity around a pyrenecarboxamide chromo-phore caused by hybridization with the targeted RNA) and a much higher fluorescence was observed. 

Berezin MY, Lee H, Akers W, Achilefu S (2007) Near infrared dyes as lifetime solvato-chromic probes for micropolarity measurements of biological systems. Biophysical J 93 2892-2899... 

The plots of h/h vs. copolymer concentration also reveal differences in the micropolarity of the hydrophobic domains created upon association of the various copolymers in water. A qualitative assessment of this property is given by the h/h value determined in the copolymer solutions of highest concentration when the plateau value is attained (Fig. 25). This value depended significantly on the grafting level the solution of the most densely grafted copolymer yielded the lowest h/h value (1.40) and the pure homopolymer the highest. In all cases, this value is higher than the value (1.20) recorded for micellar solutions of the macromonomer. It can be concluded... 

A. Itaya, T. Yamada, K. Tokuda, and H. Masuhara, Interfacial characteristics of poly(methyl methacrylate) film Aggregation of pyrene and micropolarity revealed by time-resolved total internal reflection fluorescence spectroscopy, Polym. J. 22, 697-704 (1990). 

Less frequently used at present is electron spin resonance spectroscopy, which is based on the use of spin probes as model componnds or covalent spin labeling of drugs. Microviscosity and micropolarity of the molecnlar environment of the probe can be derived from electron spin resonance spectra. Moreover, the spectra allow us to differentiate isotropic and anisotropic movements, which result from the incorporation of the probe into liposomal structures. Quantitative distribution of the spin probes between the internal lipid layer, the snrfactant, and the external water phase is to be determined noninvasively. On the basis of the chemical degradation of drugs released from the lipid compartment, agents with reductive features (e.g., ascorbic acid) allow us to measure the exchange rate of the drugs between lipophilic compartments and the water phase [27,28]. 

Habicher T, Diederich F, Gramlich V. Catalytic dendrophanes as enz3mie mittfics. Synthesis, binding properties, micropolarity effect, and catal3ftic activity of dendritic thiazolio-cyclophanes. Helv Chim Acta 1999 82 1066-1095. 

Fig. 22 Comparison of critical aggregate concentration, determined by excimer formation of covalently labeled polymer and micropolarity response of free pyrene...

The polarity within a surfactant assembly will be quite different from that of the bulk solution. It is useful to know the micropolarity of these assem-bhes for such applications where different substrates are compartmentalized inside these surfactants. The micropolarity of the surfactant assembhes can be determined using any fluorescence probe whose emission characteristics change with solvent polarity. The emissions of the probe are measured in solvents of known polarities and the polarity of the surfactant assembhes is determined by comparison. 

Pyrene carboxaldehyde and a series of pyrene carboxylic acids were found useful as fluorescence probes in describing the constitution of inverted micelles of certain calcium alkarylsulfonates in hydrocarbon media. 1-Pyrene carboxaldehyde is a convenient probe for studying the particle sizes of micelles in the region of lOOA. A series of graded probes, pyrene carboxylic acids with varying alkyl chain length, have been used to determine internal fluidity and micro-polarity as a function of distance from the polar core of these Inverted micelles. Pyrene exclmer to monomer fluorescence intensity ratio and fluorescene lifetime provided the means of measurement of internal fluidity and micropolarity, respectively. 

The present study demonstrates the utility of the above probe in describing the constitution of aggregates of certain alkarylsulfonates in hydrocarbon media. It also demonstrates the use of the probe technique in measuring the micropolarity of these same aggregates as a function of distance from the polar core. The micro-viscosity of inverted or normal micelles in the past has been estimated only as an average value of either the polar or non-polar regions (6). 

Hooke s law relates stress (or strain) at a point to strain (or stress) at the same point and the structure of classical elasticity (see e.g. Love, Sokolnikoff) is built upon this linear relation. There are other relationships possible. One, as outlined above (see e.g. Green and Adkins) involves the large strain tensor Cjj which does not bear a simple relationship to the stress tensor, another involves the newer concepts of micropolar and micromorphic elasticity in which not only the stress but also the couple at a point must be related to the local variations of displacement and rotation. A third, which may prove to be very relevant to polymers, derives from non-local field theories in which not only the strain (or displacement) at a point but also that in the neighbourhood of the point needs to be taken into account. In polymers, where the chain is so much stiffer along its axis than any interchain stiffness (consequent upon the vastly different forces along and between chains) the displacement at any point is quite likely to be influenced by forces on chains some distance away. 

Comprehensive accounts of polar field theories (micropolar and micromorphic) and of non-local field theories are given in the book edited by Eringen4). We return to Hooke s law, oy = C e. ... 

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