The Effect of Viscosity

When the QCM was first introduced, it was not clear if this device could operate in condensed media, and, specifically, in aqueous solutions. This possibility was only implemented in 1980. It was shown that the interaction of vibrating QCM in a liquid leads to an added term in the change in resonance frequency, which depends primarily on the square root of the product of the viscosity and density of the fluid, namely 

Equation (17.6) is also important when considering the effect of temperature on the shift of the resonance frequency, because the viscosity of liquids is temperature 

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Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

However, more accurate predictions for the spin velocity may be obtained with allowance made for the effect of viscosity in the governing equation for the spin velocity. According to the experimental data of Keisall," which indicates that the spin velocity in a cyclone is a function of R only, the A component of Eq. (13.1) in the cylindrical polar coordinate sy stem may reduce to... 

The effect of viscosity ratio on the morphology of immiscible polymer blends has been studied by several researchers. Studies with blends of LCPs and thermoplastics have shown indications that for good fibrillation to be achieved the viscosity of the dispersed LCP phase should be lower than that of the matrix [22,38-44]. 

In an earlier study (44) on the effect of viscosity ratio on the morphology of PP-LCP blends we found that the viscosity ratio is a critical factor in determining the blend morphology. The most fibrillar structure was achieved when the viscosity ratio (i7lcp i7pp) ranged from about 0.5-1. At even lower viscosity ratios the fiber structure was coarser, while at viscosity ratios above unity, the LCP domains tended to be spherical or clusterlike (Fig. 1)=... 

For proper selection and corresponding operation, a pump capacity must be identified with the actual pumping temperature of the liquid in order to determine the proper power requirements as well as the effects of viscosity. 

There are several similar relationships for centrifugal pumps that can be used if the effects of viscosity of the pumped fluid can be neglected. These relate the operating performance of any centrifugal pump for one set of operating conditions to those of another set of operating conditions, say conditions, and conditions 2. 

Two effects on pump performance must be discussed viscosity and gas content. Figures 32.23 and 32.24 illustrate the effects of viscosity change on centrifugal and... 

Figure 7.4 The effect of viscosity on oxygen transfer rates. Adapted from Biochemical and Biotechnology Handbook. B Atkinson and F Mavituna, (Eds) 1991, Stockton press.

Nevertheless, from a practical viewpoint physical reasons for viscosity reduction during the surface treatment of the filler play a minor role first of all the effect of viscosity reduction itself is significant. 

Reynold s number It is a dimensionless number that is significant in the design of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. It is equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity. This value or ratio is used to determine whether the flow of a fluid through a channel or passage, such as in a mold, is laminar (streamlined) or turbulent. 

Thus, the enhancement of heat transfer may be connected to the decrease in the surface tension value at low surfactant concentration. In such a system of coordinates, the effect of the surface tension on excess heat transfer (/z — /zw)/ (/ max — w) may be presented as the linear fit of the value C/Cq. On the other hand, the decrease in heat transfer at higher surfactant concentration may be related to the increased viscosity. Unfortunately, we did not find surfactant viscosity data in the other studies. However, we can assume that the effect of viscosity on heat transfer at surfactant boiling becomes negligible at low concentration of surfactant only. The surface tension of a rapidly extending interface in surfactant solution may be different from the static value, because the surfactant component cannot diffuse to the absorber layer promptly. This may result in an interfacial flow driven by the surface tension gradi-... 

Fixed-bed reactors employed for lipase-catalyzed hydrolysis and interesterification reactions are highly efficient and have been used on a large scale (Table 5). The two phases may flow through the reactor in the opposite or same directions. If no solvents are used, the effect of viscosity of some substrates (i.e., oil) may be minimized by employing high temperatures which lead to faster rates of inactivation of lipases. 

Fig. 7. Dependence of uncorrected (A) diffusion coefficient (D) and (B) number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The data shown here are not corrected for the effect of viscosity and refractive indices of the urea solutions. Experimental condition is the same as in Figure 6. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

In addition to the effect of viscosity on some physical properties, the oil s composition can also determine the level of some physical properties. In normal length mixing cycles, the tensile... 

Photosensitization of diaryliodonium salts by anthracene occurs by a photoredox reaction in which an electron is transferred from an excited singlet or triplet state of the anthracene to the diaryliodonium initiator.13"15,17 The lifetimes of the anthracene singlet and triplet states are on the order of nanoseconds and microseconds respectively, and the bimolecular electron transfer reactions between the anthracene and the initiator are limited by the rate of diffusion of reactants, which in turn depends upon the system viscosity. In this contribution, we have studied the effects of viscosity on the rate of the photosensitization reaction of diaryliodonium salts by anthracene. Using steady-state fluorescence spectroscopy, we have characterized the photosensitization rate in propanol/glycerol solutions of varying viscosities. The results were analyzed using numerical solutions of the photophysical kinetic equations in conjunction with the mathematical relationships provided by the Smoluchowski16 theory for the rate constants of the diffusion-controlled bimolecular reactions. 

A series of steady-state fluorescence experiments were performed in mixtures of propanol and glycerol to investigate the effect of viscosity on the effective second order photosensitization rate constant, k2. Figure 3 illustrates that the effective rate constant decreases as the viscosity of the system is increased. For example, as the reaction solvent is changed from pure propanol to pure glycerol, the viscosity of the system rises by three orders of magnitude, while the effective reaction rate coefficient, k2, decreases by approximately one order of magnitude. 

When all three components of the vorticity are zero the flow is said to be irrotational. In irrotational flow the effects of viscosity disappear as will be... 

In the following four years Mark successively reported on the viscosity and molecular weight of cellulose (40), Staudinger s Law (41), high polymer solutions (42), and the effect of viscosity on polymerization rates (43). Confident of his findings, he proposed (at the same time as R. Houwink) the general viscosity equation now known as the Mark-Houwink Equation (44, 45). 

To minimize the effects of viscosity for purposes of comparing data between solvents, plots areoften made using the product of the ion mobility and the viscosity (Walden product) in place of mobility alone. A plot of the Walden product against the reciprocal of the crystallographic radii for several solvents is shown in Fig. 6. Arbitrary curves have been drawn to indicate general trends. Values in solvents for which precise transference numbers and conductance data are available, such as acetonitrile and nitromethane, give smooth curves. 

The above results seem to be contradictory and irreconcilable. This is not so because the effect of viscosity is associated with those of flow rate, surface tension, and orifice diameter. Since the effect of viscosity is negligible when the flow rate tends to zero, even a large difference in the viscosities of the two fluids under consideration does not, at small flow rates, show the influence of viscosity. This is precisely the case in the investigations of Datta et al. (D4). What was mistakenly interpreted as the influence of viscosity, was probably, in reality, the influence of the reduced surface tension though the viscosity had been increased a hundredfold, the surface tension was simultaneously reduced by about 5 dynes per centimeter. At the extremely small flow rates (<0.1 cm3/sec) employed, the effect of viscosity was presumably negligible. 

To recapitulate the discrepancies in literature, Datta et al. (D4) varied the viscosity of water from 0.012 to 1.108 poise and found that with an increase in the viscosity, the bubble volume decreased for all the nozzles used. This is in apparent contradiction to the observations of most of the other investigators. An effort can now be made to explain this discrepancy on the basis of the present model. Note is to be made of the extremely small volumetric flow rates employed by Datta et al. (D4). In fact, they are in the range where effects due to viscosity are negligible when compared to the effects of surface tension. Thus, though there is a hundredfold increase in the viscosity, it is accompanied by a large variation in the surface tension, which decreases from 72.8 to 65.7 dyn per centimeter. At the very small flow rates employed, the decrease in the bubble volume observed by Datta et al. (D4) seems more likely to be due to this decrease in the surface tension rather than to the hundredfold increase in the viscosity. Thus, the influence of surface tension has been mistakenly attributed to the effect of viscosity. The actual values of the bubble volumes obtained by these authors for a typical nozzle are given in Table VI along with those obtained by the application of the present model. 

On the other hand, Coppock and Meiklejohn (C8) find that the viscosity has negligible influence on the bubble volume. These authors have used liquids of very low viscosity and extremely small flow rates where the effect of viscosity is negligible. Calculations made for a set of data of Datta et al. (D4) are presented in Table VI. The predictions made by the general model are again seen to bear with the trends found experimentally. 

The above discussion dealt with only that particular situation where the continuous phase approximated to an inviscid fluid. However, the equations thus derived can be easily modified to include the effects of viscosity of the of the continuous phase. Under constant pressure conditions also, viscosity of the continuous phase tends to increase the bubble volume by increasing the drag during both the expansion and detachment stages. 

Such is the newness of appreciation of near-IR fluorescence techniques that there is a dearth of examples in the literature of implementations of many of the classic fluorescence methods in the IR. Anisotropy is one striking example of this. However, in a comprehensive study of the anisotropy decay of dyes, including oxazine fluorescence at 720 nm, in mixed isotropic solvents Dutt et al.( T7 TS) have investigated the effects of viscosity on molecular rotation. 

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