Viscosity ratio

Critical capillary number versus viscosity ratio in simple shear and plane hyperbolic (two-dimensional elonga-tional) flow. (From H. P. Grace, Chem. Eng. Commun. 14,225,1982. With permission.) 

---

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

Koch/Sul2er SMX has a correlation factor for design based onlog(viscosity ratio of the two Hquids). 

The viscosity ratio or relative viscosity, Tj p is the ratio of the viscosity of the polymer solution to the viscosity of the pure solvent. In capillary viscometer measurements, the relative viscosity (dimensionless) is the ratio of the flow time for the solution t to the flow time for the solvent /q (Table 2). The specific (sp) viscosity (dimensionless) is also defined in Table 2, as is the viscosity number or reduced (red) viscosity, which has the units of cubic meters per kilogram (m /kg) or deciUters per gram (dL/g). The logarithmic viscosity number or inherent (inh) viscosity likewise has the units m /kg or dL/g. For Tj g and Tj p, the concentration of polymer, is expressed in convenient units, traditionally g/100 cm but kg/m in SI units. The viscosity number and logarithmic viscosity number vary with concentration, but each can be extrapolated (Fig. 9) to zero concentration to give the limiting viscosity number (intrinsic viscosity) (Table 2). 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

Many investigators have also measured the trace metal content of asphalts (68). The catalytic behavior of vanadium has prompted studies of the relation between vanadium content and an asphalt s sensitivity to oxidation (viscosity ratio). The significance of metals in the behavior of asphalts is not yet well understood or defined. 

As an approximate rule, break-up of droplets occurs for a Weber number in excess of one, a rule of thumb that is actually valid for the range of viscosity ratios of the dispersed phase to the continuous phase of less than approximately five. Higher viscosities of the disperse phase lead to serious difficulties with emulsification because the shear energy is then dispersed in rotation of the droplets. 

The classical (and perhaps more famihar) form of dimensionless expressions relates, primarily, the Nusselt number hD/k, the Prandtl number c l//c, and the Reynolds number DG/ I. The L/D and viscosity-ratio modifications (for Reynolds number <10,000) also apply. 

Motionless mixers continuously interchange fluid elements between the walls and the center of the conduit, thereby providing enhanced heat transfer and relatively uniform residence times. Distributive mixing is usually excellent however, dispersive mixing may be poor, especially when viscosity ratios are high,... 

Apparent viscosity Ratio of shear stress to shear rate. It depends on the rate of shear. 

To understand how the dispersed phase is deformed and how morphology is developed in a two-phase system, it is necessary to refer to studies performed specifically on the behavior of a dispersed phase in a liquid medium (the size of the dispersed phase, deformation rate, the viscosities of the matrix and dispersed phase, and their ratio). Many studies have been performed on both Newtonian and non-Newtonian droplet/medium systems [17-20]. These studies have shown that deformation and breakup of the droplet are functions of the viscosity ratio between the dispersity phase and the liquid medium, and the capillary number, which is defined as the ratio of the viscous stress in the fluid, tending to deform the droplet, to the interfacial stress between the phases, tending to prevent deformation ... 

The mechanism of droplet deformation can be briefly summarized as follows. The factors affecting the droplet deformation are the viscosity ratio, shear stress, interfacial tension, and droplet particle size. Although elasticity takes an important role for general thermoplastics droplet deformation behavior, it is not known yet how it affects the deformation of TLCP droplet and its relationship with the processing condition. Some of... 

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)=... 

In manufacturing and processing polymer blends, it is thus important that the viscosity ratio be within the optimal range in the actual processing conditions. Not only the polymers to be blended but also the temperature and processing conditions (shear, elongation) should be carefully selected. Other factors, such as interfacial tension [46,47] and elasticity of the blended polymers, may also influence the blend morphology. 

Figure 1 Optical micrographs in the flow direction of the extruded strands of the PP-LCP blends exhibiting viscosity ratios of (a) t7lcp i7pp = 0,6, and (b) 2.8 [44].

ABS at high shears [142]. D also increases with the increase of the viscosity ratio of the phases [143]. 

Finally, a generalized viscosity function in the form of a weight fraction-dependent viscosity ratio, r]Q/r], could be derived as follows ... 

The influence of the vi.scosity ratio 8 on the flow behavior in a capillary was discussed by Rumscheidt and Mason [lOj. They pointed out that when the viscosity ratio is small, the dispersed droplets are drawn out to great lengths but do not burst, and when the viscosity ratio is of the order of unity, the extended droplets break up into smaller droplets. At very high viscosity ratios, the droplets undergo only very limited deformations. This mechanism can explain our observations and supports our theoretical analysis assumptions, summarized previously as points 2, 3, and 4. 

Figure 1 Theoretical viscosity function patterns by varying the viscosity ratio 6.

As demonstrated, Eq. (7) gives complete information on how the weight fraction influences the blend viscosity by taking into account the critical stress ratio A, the viscosity ratio 8, and a parameter K, which involves the influences of the phenomenological interface slip factor a or ao, the interlayer number m, and the d/Ro ratio. It was also assumed in introducing this function that (1) the TLCP phase is well dispersed, fibrillated, aligned, and just forms one interlayer (2) there is no elastic effect (3) there is no phase inversion of any kind (4) A < 1.0 and (5) a steady-state capillary flow under a constant pressure or a constant wall shear stress. 

As mentioned previously, and as expected, the mixtures containing a TLCP component exhibited shear viscosities lower than those of their original components, whether the TLCP weight fraction was 10% or 30%. The higher the TLCP weight fraction, the lower the blend viscosity. The viscosity curves of the two pure components crossed each other at a shear rate about 25 s , i.e., at this point the viscosity ratio was 1. 

Figure 6 Theoretical viscosity function versus viscosity ratio 8 = 771/770 at different blending ratios .

Figure 9 We - 8 plot comparison of effect of viscosity ratio 8 on critical shear We.cn in rotational and irrotational shear fields [18].

Both dimensionless Weber number and viscosity ratio are defined by ... 

Grace [18] evaluated t% as a function of 8 for viscoelastic matrices. His results are shown in Fig. 10. The reduced time increases as the viscosity ratio increases. If the residence time during a processing is less than... 

The purpose of our calculation was to quantitatively evaluate the deformational behavior of the TLCP droplets and their fibrillation under the processing conditions, and finally, to establish a relationship among the calculated Weber number, the viscosity ratio, and the measured aspect ratio of the fibers. Figure 13 illustrates this procedure. All calculated results were plotted as... 

From the y(jc) functions and the two melt temperatures used, and by using the viscosity curves from rheological examinations (Fig. 11), viscosity distributions T](jc) of the two pure components were easily determined, as shown in Figs. 15a and 15b. Subsequently, the viscosity ratio functions 6(jc) were also calculated (Fig. 16). All four curves fall slightly from the core to the outside. 

Figure 16 Calculated viscosity ratio as function of the halved sample thickness for the four sample groups.

---