Order viscosity coefficients

Note 1 The rotational viscosity coefficients are of the order of lO -lO" Pa s for low-molar-mass liquid crystals for polymeric liquid-crystals their values depend strongly on the molar mass of the polymer. 

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

The last formula written for the coefficient of viscosity [Eq. (VIII.3.11)] indicates that y should be independent of the pressure and should vary as the square root of T. This rather surprising result with respect to pressure independence has been strikingly confirmed. Thus from 1 X 10 up to 20 atm pressure the change in the viscosity coefficient for most gases is less than 10 per cent. At very high pressures (above 100 atm) the viscosity becomes almost proportional to density, but here the mean free paths are of the same order of magnitude as the molecular diameters, and the whole treatment breaks down. 

Sarman and Evans [24, 32] performed a comprehensive study of the flow properties of a variant of the Gay-Beme fluid. In order to make the calculations faster the Lennard-Jones core of the Gay-Beme potential was replaced by a 1/r core. This makes the potential more short ranged thereby decreasing the number of interactions and making the simulation faster. The viscosity coefficients were evaluated by EMD Green-Kubo methods both in the conventional canonical ensemble and in the fixed director ensemble. The results were cross checked by shear flow simulations. The studies covered nematic phases of both prolate ellipsoids with a length to width ratio of 3 1 and oblate ellipsoids with a length to width ratio of 1 3. The complete set of potential parameters for these model systems are given in Appendix II. 

Note that the viscosity // will appear linearly in each of the second-order tensor coefficients in (7 20) and (7 21) and thus has been factored out in (7 22) that is, A = // A,... 

It will be noted that a function analogous to ipz which arises in the shear viscosity, does not appear in the thermal conductivity. Its absence, of course, is due to the lack of second order surface harmonic perturbation of the radial distribution function g0m in the case of heat conduction. It may be anticipated that this difference in the form of the number density perturbation might lead to the thermal conductivity coefficient leaving a functional dependence on the temperature which is quite different from that of the shear viscosity coefficient. However, the exact temperature dependence of the two coefficients (Eqs. 42 and 47) has not yet been explored. 

Table II presents a comparison of the values for the shear viscosity coefficients calculated from Eqs. 69 and 72 with those obtained experimentally for a few liquids. While the calculated results are of the correct order of magnitude, they are significantly...

The order parameter S is a very important quantity in a partially ordered system. It is the measure of the extent of the anisotropy of the liquid crystal physical properties, e.g., elastic constants, viscosity coefficients, dielectric anisotropy, birefringence, and so on. S is temperature dependent and decreases as the temperature increases. The typical temperature dependence of S is shown in Figure 1.16. 

A recent study of iodine atom recombination in solution by Luther et al. [294] used a dye laser (wavelength 590nm, pulse duration 1.5ps) to photodissociate iodine molecules in n-heptane, -octane or methyl cyclohexane at pressures from 0.1 to 300 MPa. Over this pressure range, the viscosity increases four-fold. The rate of free-radical recombination was monitored and the second-order rate coefficient was found to be linearly dependent on inverse viscosity. This provides good reason to believe that the recombination of free iodine atoms is diffusion-limited, especially as the rate coefficient is typically 10 °dm mol s . The recombination of primary and secondary pairs is too rapid to be monitored by such equipment as was used by Luther etal. [294] (see below). Instead, the depletion of molecular iodine absorption just after the laser pulse was used to estimate the yield of (free) photodissociated iodine atoms in solution. They found that the photodissociation quantum yields (survival probability) were about 2.3 times smaller than had been measured by Noyes and co-workers [291, 292] and also by Strong and Willard [295]. This observation raises doubts as to the accuracy of the iodine atom scavenging method used by Noyes et al. or perhaps points to the inherent difficulties of doing steady-state measurements. In addition, Luther et al. 

The viscosity coefficient of gases may be determined from measurements of the rate of fiow through a capillary tube of known radius under a given pressure difference, and from the result the mean free path, I, may be calculated. For simple gases at atmospheric pressure it is of the order 10- cm. It varies inversely as the pressure, and long before the highest vacuum given by a modern pump is reached it exceeds the dimensions of ordinary small-scale laboratory apparatus. 

The isothermal flow of incompressible liquid is described by equations (5.13) and (5.21), and the viscosity coefficient n = const. Hence, there are four equations for four unknowns - the pressure p and three velocity components u, v, and w. Thus, the system of equations is a closed one. For its solution it is necessary to formulate the initial and boundary conditions. Let us discuss now possible boundary conditions. Consider conditions at an interface between two mediums denoted as 1 and 2. The form and number of boundary conditions depends on whether the boundary surface is given or it should be found in the course of solution, and also from the accepted model of the continuum. Consider first the boundary between a non-viscous liquid and a solid body. Since the equations of motion of non-viscous liquid contain only first derivatives of the velocity, it is necessary to give one condition of the impermeability u i = u 2 at the boundary S, where u is the normal component of the velocity. The equations of motion of viscous liquid include the second-order derivatives, therefore at the boundary with a solid body it is necessary to assign two conditions following from the condition of sticking u i = u 2, Wii = u i where u is the tangential to S component of the velocity. If the boundary S is an interface between two different liquids or a liquid and a gas, then it is necessary to add the kinematic condition Ui = U2 =... 

Thus, in spite of the difference in molecular-kinetic approaches of Frenkel and Eyring to the analysis of the viscosity coefficient for simple liquids, they lead to the ratios containing the same phenomenological value RTt/V. The difference between Eqs. (15) and (16) is visualized in numerical coefficient and physical interpretation of Tq determined by the Eqs. (9) and (13). This difference is quite substantially, since Tq of the translational movement is on two orders higher than the Tq of the oscillat-... 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

It may be noted that the coefficients that appeared in the IP-based viscosity coefficient model similarly reappear in the IP-based slip coefficient expression. For the general second-order boundary condition given by Eq. 11,... 

If the above equation (IP-based viscosity coefficient model) was further incorporated with the second-order slip velocity expression, i.e., Eq. 13... 

Here a22 is the tangential momentum accommodation coefficient, a2g and are "second-order" coefficients, is the Chapman-Enskog first-order approximation to the viscosity coefficient. Equation (2.68) is, of course, valid for general gas-surface scattering kernels (2.49). Equation (2.68) reduces approximately to... 

The normal solution method just outlined leads to two principal results, both of which can be tested experimentally. These are (i) explicit expressions for the coefficients of viscosity 17 and thermal conductivity A for dilute monatomic gases, in terms of the intermolecular potential < (r), and (ii) an explicit form for the Burnett and higher-order corrections to the Navier-Stokes equation, together with expressions for the associated (higher-order) transport coefficients in terms of the intermolecular potential. 

Chapter 6 heralds the second part of the book and introduces the reader to anisotropy of the magnetic and electric properties of mesophases. Following in Chapter 7 there is a focus on the anisotropy of transport properties, especially of electrical cOTiductivity. Without these two chapters (Chapters 6 and 7), it would be impossible to discuss electro-optical properties in the third section of the book. Further, Chapters 7 and 8 deal with the anisotropy of the properties of elasticity and viscosity. Chapter 8 is more difficult than the others, and in order to present the theoretical results as clearly as possible, the focus is on the experimental methods for the determinatimi of Leslie viscosity coefficients from the viscous stress tensor of the nematic phase. Chapter 9 terminates the discussion of the anisotropy of... 

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