Effective volume viscosity

Hellmann, R., Bich, E., Vogel, E., Dickinson, A. S., and Vesovic, V, Calculation of the Transport and Relaxation Properties of Methane. II. Thermal Conductivity, Thermomagnetic Effects, Volume Viscosity, and Nuclear-Spin Relaxation, / Chem. Phys. 130, 124309, 2009. 

Viscosity. Because a clump of particles contains occluded Hquid, the effective volume fraction of a suspension of clumps is larger than the volume fraction of the individual particles that is, there is less free Hquid available to faciHtate the flow than if the clumps were deagglomerated. The viscosity of a suspension containing clumps decreases as the system becomes deagglomerated. This method is not very sensitive in the final stages of deagglomeration when there are only a few small clumps left. 

Whilst temperature rises at constant pressure cause a decrease in viscosity, pressure rises at constant temperature cause an increase in viscosity since this causes a decrease in free volume. It is in fact found that within the normal processing temperature range for a polymer it is possible to consider an increase in pressure as equivalent, in its effect on viscosity, to a decrease in temperature. 

Experimental measurements of viscosity almost always are recommended when dealing with slurries and extrapolations should be made with caution. Most theoretically based expressions for liquid viscosity are not appropriate for practical calculations or require actual measurements to evaluate constants. For nonclustering particles, a reasonable correlation may be based on the ratio of the effective bulk viscosity, /ig, to the viscosity of the liquid. This ratio is expressed as a function of the volume fraction of liquid x in the slurry for a reasonable range of compositions ... 

Increasing the bound mbber content increases the effective volume fraction of filler by intimately bonding polymer to the filler. This polymer is no longer available to contribute to viscous flow. As a consequence, the viscosity of the compound increases. 

Tjo is the viscosity of the unfilled polymer ( eff is the effective volume fraction of filler... 

According to the interpretation given above, the intrinsic viscosity is considered to be proportional to the ratio of the effective volume of the molecule in solution divided by its molecular weight. In particular (see Eq. 23), this effective volume is represented as being proportional to the cube of a linear dimension of the randomly coiled polymer chain,... 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

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.

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. 

Fig. 22. Effect of viscosity of continuous phase on drop volume.

In the mucosal environment, effects of salt, pH, temperature, and lipids need to be taken into consideration for possible effects on viscosity and solubility. A pH range of 4-7 and a relatively constant temperature of 37°C can generally be expected. Observed solution properties as a function of salt and polymer concentration can be referred to as saline compatibility. Polyelectrolyte solution behavior [27] is generally dominated by ionic interactions, such as with other materials of like charge (repulsive), opposite charge (attractive), solvent ionic character (dielectric), and dissolved ions (i.e., salt). In general, at a constant polymer concentration, an increase in the salt concentration decreases the viscosity, due to decreasing the hydrodynamic volume of the polymer at a critical salt concentration precipitation may occur. 

Figure I 1.7. Variation of viscoelastic scaling factors with gas content for PS-C02 and PDMS-C02 systems. Lower scaling factor values for PS-C02 system, compared with PDMS-C02 system, are due to the closer proximity of the experimental temperatures to Tg of the pure polymer. The top curve displaying results for iso-free volume dilution of high-Mw polystyrene by low-Af polystyrene represents the effect on viscosity of volumetric dilution of high-Mw chains. Viscosity reductions for polymer-gas systems are significantly lower than the iso-free volume dilution curve, indicating that viscosity reduction is primarily due to free volume contributed by dissolved gas.

Apart from physical barriers, topical drug delivery to eye is also affected by the volume, viscosity, pH, tonicity of vehicle, and type of drug. Constant drainage by tear fluid minimizes topical drug absorption and increases systemic absorption. As a result, only about 5 percent of total dose is effectively absorbed through the intraocular route,... 

In the case of non-interacting anisometric aggregates, the situation becomes more complex. Such aggregates rotate in a shear flow with the consequence that their effective volume is much larger than the volume fraction of the micelles. Hence, the viscosity as a function of concentration increases with a larger slope once rod-like micelles are formed. 

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