Temperature effect, viscosity coefficients

Here, a is the characteristic size of the structural element, p is the density, which is approximately equal to 1 g/cm3, rj is the effective viscosity coefficient of the medium which is 10 2-10 Ps, and u is the characteristic velocity of motion of the particle, which is not more than the mean thermal velocity (T/to)1/2. It is easy to see that, at room temperature and with the above values of the parameters, condition (8.22) is valid if a 3> 10 7 10 6 cm. 

Physical characteristics Molecular weight Vapour density Specific gravity Melting point Boiling point Solubility/miscibility with water Viscosity Particle size size distribution Eoaming/emulsification characteristics Critical temperature/pressure Expansion coefficient Surface tension Joule-Thompson effect Caking properties... 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

It is apparent from early observations [93] that there are at least two different effects exerted by temperature on chromatographic separations. One effect is the influence on the viscosity and on the diffusion coefficient of the solute raising the temperature reduces the viscosity of the mobile phase and also increases the diffusion coefficient of the solute in both the mobile and the stationary phase. This is largely a kinetic effect, which improves the mobile phase mass transfer, and thus the chromatographic efficiency (N). The other completely different temperature effect is the influence on the selectivity factor (a), which usually decreases, as the temperature is increased (thermodynamic effect). This occurs because the partition coefficients and therefore, the Gibbs free energy difference (AG°) of the transfer of the analyte between the stationary and the mobile phase vary with temperature. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

Much of the recent impetus for temperature control has focused on exploiting the effects of elevated temperature on viscosity and diffusion coefficients [2], These lead to faster separations and also allow smaller particle diameters to be employed with conventional HPLC hardware. As the viscosity of solvents decreases, the column pressure drops. This can be exploited by using faster flow rates and smaller particle diameters. All of this leads to faster separations. In one experiment in this laboratory, a separation which required 8 min at room temperature was reduced to 2 min at 50°C without changing the column. Speed enhancements of as much as 50-I00-fold have been reported [13] as shown in Figure 9.1. 

Second, the properties of such liquids are well determined by the stationary dependence of effective viscosity r eff on shear rate y (at large y, the lowest Newtonian viscosity is attained at T <, 40-60 °C). At higher temperatures, together with t eff(y), one has to known the dependence of t x on time as well. This dependence is linear, and its coefficients are exponentially dependent on temperature. 

The physical factors include mechanical stresses and temperature. As discussed above, IFP is uniformly elevated in solid tumors. It is likely that solid stresses are also increased due to rapid proliferation of tumor cells (Griffon-Etienne et al., 1999 Helmlinger et al., 1997 Yuan, 1997). The increase in IFP reduces convective transport, which is critical for delivery of macromolecules. The temperature effects on the interstitial transport of therapeutic agents are mediated by the viscosity of interstitial fluid, which directly affects the diffusion coefficient of solutes and the hydraulic conductivity of tumor tissues. The temperature in tumor tissues is stable and close to the body temperature under normal conditions, but it can be manipulated through either hypo- or hyper-thermia treatments, which are routine procedures in the clinic for cancer treatment. 

The proper choice of a solvent for a particular application depends on several factors, among which its physical properties are of prime importance. The solvent should first of all be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapour pressure, and their temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity also need to be considered. Electrical, optical and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant too. Furthermore, molecular characteristics, such as the size, surface area and volume, as well as orientational relaxation times have appreciable bearing on the applicability of a solvent or on the interpretation of solvent effects. These properties are discussed and presented in this Chapter. 

The effects of temperature on a CE separation are severalfold. With increasing temperature, the viscosity of the running electrolyte decreases and analysis times are shorter. The high currents associated with elevated temperatures generates additional heat thus, the efficiency and resolution may be altered. Changes in selectivity are often observed with different temperatures because solute mobilities are a function of diffusion coefficients, which are, in turn, dependent on temperature. Changes in selectivity may result from alteration of solute pKa values with temperature changes. 

It should be noted again that the numerical coefficient above has units of mole. According to this equation, the gas viscosity coefficient should be independent of pressure and should increase with the square root of the absolute temperature. The viscosities of gases are in fact found to be substantially independent of pressure over a wide range. The temperature dependence generally differs to some extent from because the effective molecular diameter is dependent on how hard the molecules collide and therefore depends somewhat on temperature. Deviation from hard-sphere behavior in the case of air (diatomic molecules, N2 and O2) is demonstrated by Eq. (4-19). 

Transport processes are concerned with the flow of mass, momentum, and energy in fluids in nonuniform states. For normal liquids near equilibrium, the transport rates are proportional to the gradients of concentration, mass velocity, and temperature and the coefficients of diffusion, viscosity, and thermal conductivity are the respective proportionality constants. Various cross coefficients such as those of binary and thermal diffusion arise in Reciprocal processes expressing the effects of combined gradients of concentration and temperature. 

In heat transfer, the fluid at the wall has the same temperature as the wall, different from the bulk temperature. While all fluid properties are to some degree functions of temperature, the viscosity is most strongly affected. If the viscosity at the wall is lower than the bulk value, the boundary layer is thinner than for the isothermal case, and the heat-transfer coefficient is higher than that predicted for the constant property case. Correspondingly, the coefficient is reduced if the viscosity at the wall is higher than the bulk value. The effect is usually small (5 to 10%) but can be much larger with viscous fluids or large temperature differences. 

Lubricants have a nonlinear viscosity coefficient against temperature. At very low or very high temperature this nonlinearity can create significant measurement failures. A careful analysis will show this effect within the transmission chain. Sticking is the worst case. It can happen that frozen water makes a short cut in torque sensors. In most cases damping factors are based on the electrical filter circuits (Fig. 7.12.13). 

Temperature coefficient, 205, 206, 335, 495, 506, 509, 511, 512 Temperature factor, 303 Temperature, effect on viscosity, 633 Tensile modulus of elasticity of composite materials, 329... 

Since sedimentation rate studies may be performed using a wide variety of solvent-solute systems, the measured value of the sedimentation coefficient which is affected by temperature, solution viscosity and density, is often corrected to a value that would be obtained in a medium with a density and viscosity of water at 20°C, and expressed as the standard sedimentation coefficient or S20, to. For many macromolecules including nucleic acids and proteins the sedimentation coefficient usually decreases in value with increase in the concentration of solute, this effect becoming more severe with increase both in molecular weight and the degree of extension of the molecule. Hence s2o, to is usually measured at several concentrations and extrapolated to infinite dilution to obtain a value of s2o, to at... 

Because of distortions in the flow field from the effects of temperature on viscosity and density, Eq. (12.16) does not give accurate results. The heat-transfer rates are usually larger than those predicted by Eq. (12.16), and empirical correlations have been developed for design purposes. These correlations are based on the Graetz number, but they give the film coefficient or the Nusselt number rather than the change in temperature, since this permits the fluid resistance to be combined with other resistances in determining an overall heat-transfer coefficient. 

Molecular Meaning of aT. The effect of temperature on viscosity is related to its effect on the friction coefficient, which, in turn, depends on the fractional free volume according to the equation ... 

All physical parameters mentioned above are material specific and temperature dependent (for a detailed discussion of the material properties of nematics, see for instance [4]). Nevertheless, some general trends are characteristic for most nematics. With the increase of temperature the absolute values of the anisotropies usually decrease, until they drop to zero at the nematic-isotropic phase transition. The viscosity coefficients decrease with increasing temperature as well, while the electrical conductivities increase. If the substance has a smectic phase at lower temperatures, some pre-transitional effects may be expected already in the nematic phase. One example has already been mentioned when discussing the sign of Ua- Another example is the divergence of the elastic modulus K2 close to the nematic-smecticA transition since the incipient smectic structure with an orientation of the layers perpendicular to n impedes twist deformations. 

Mathematical description of the process of polymer melting in the extrusion channel is complex when ultrasound is used. The description requires firstly, consideration of the mass flow of the polymer, knowledge of the flow characteristics of the melt, the temperature and pressure of extrusion, sizes of the channel and frequency of ultrasonic oscillations. Secondly, coefficient of swelling of the extrudate, effective viscosity of polymer, pressure of melt, and frequency of oscillations. 

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