Capillary flow viscosity

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

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. 

Viscosity is a measurement of resistance to flow. Although the unit of absolute viscosity is poise, its measurement is difficult. Instead, kinematic (flowing) viscosity is determined by measuring the time for a given flow through a capillary tube of specific diameter and length. The unit of kinematic viscosity is the stoke. However, in general practice, centistoke is used. Poise is related to stoke by the equation ... 

The greater the viscosity of a liquid, the more slowly it flows. Viscosity usually decreases with increasing temperature. Surface tension arises from the imbalance of intermolecular forces at the surface of a liquid. Capillary action arises from the imbalance of adhesive and cohesive forces. 

In the capillary method, the time required for a liquid to flow through a capillary tube is determined. The melt under investigation flows with a constant rate through a tube with a small, definite cross-sectional area, such as a cylindrical capillary. The viscosity can be measured in an absolute way from the pressure drop. This method can yield the most reliable absolute data, the viscosity being given by a modified Hagen-Poiseuille equation ... 

There are commercially available in-line or on-line viscometer devices. In-line devices are installed directly in the process while on-line devices are used to analyze a side stream of the process. Most devices are based on measuring the pressure drop and flow rate through a capillary. The viscosity is either determined at a single shear rate or, at most, a few shear rates. Complex fluids, on the other hand, exhibit a viscosity that cannot be so easily characterized. In order to capture enough information that allows, for example, a molecular weight distribution to be inferred, it is necessary to determine the shear viscosity over reasonably wide ranges of shear rates. 

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

Note 4 Some experimental methods, such as capillary flow and flow between parallel plates, employ a range of shear rates. The value of tj evaluated at some nominal average value of Y is termed the apparent viscosity and given the symbol /app. It should be noted that this is an imprecisely defined quantity. 

Fig. 50 Monomer to excimer ratio (h/Im) of DNP in ethanol-glycerol mixtures (viscosities of the solvent measured by capillary flow method)...

A number of instruments are based on the extmsion principle, including slit flow and normal capillary flow (Table 6). These instruments are useful when large numbers of quality control or other melt viscosity test measurements are needed for batches of a single material or similar materials. When melt viscosities of a wide range of materials must be measured, rotational viscometers are preferable. Extmsion rheometers have been applied to other materials with some success with adhesives and coatings (10,161). 

Here kH is the Huggins coefficient. The intrinsic viscosity decreases and the Huggins coefficient increases, as micelles become smaller. On micellization, ijsp/c has been observed to increase for some systems but to decrease for others, and unfortunately there are no firm rules governing which case will prevail for a given block copolymer solution. The viscosities of polymer solutions are measured in capillary flow viscometers, which are described in detail by Macosko (1994). 

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

By assuming only that the polymer melt is viscous and time independent, and that the viscosity is a function of the shear rate, //( >), without the need to specify any specific viscosity function, we can state that for capillary flow at the wall,... 

This equation shows that the capillary flow velocity increases with capillary radius rc and surface tension y it decreases, as do all flow velocities, with viscosity 17. The equation also shows that (v) decreases with the length Xf of penetration of liquid into the capillary space that is, flow diminishes as the liquid progresses further and further into the pore space. This diminution can be calculated as a function of time as follows. 

The viscosity as calculated according to Eq. (44) is meaningful only if the flow is laminar. For a capillary flow the rate of flow should not exceed a critical velocity which can be determined from its Reynolds number (Rk) ... 

In some foods, a thin layer of low-viscosity fluid forms at the solid-fluid interface that in turn contributes to lower viscosity values. The boundary condition that at the solid-fluid interface the fluid velocity is that of the wall is not satisfied. This phenomenon is known as slip effect. Mooney (1931) outlined the procedures for the quantitative determination of slip coefficients in capillary flow and in a Couette system. The development for the concentric cylinder system will be outlined here for the case of the bob rotating and details of the derivation can be found in Mooney (1931). 

If indeed one of the phases has broken up into droplets, then slow diffusive processes are the only coarsening mechanisms possible. However, if both phases are still interconnected and are both fluids, then coarsening can occur by the faster process of capillary flow, which is driven by the interfacial tension acting on the curved surfaces between the two fluids (Siggia 1979). The typical pressure drop Ap produced by capillarity is Ap Tja. The velocity produced by this pressure drop is V aApfrj Y/t], where is an average viscosity. The domains grow at a rate da/dt jr] hence... 

Bentley and Leal have measured droplet shapes and critical conditions for droplet breakup over a wide range of capillary numbers, viscosity ratios, and flow types. The flow type is conveniently controlled in an apparatus called a four-roll mill, in which a velocity field is generated by the rotation of four rollers in a container of liquid (see Fig. 1-15). By varying the rotation rate of one pair of rollers relative to that of a second pair, velocity fields ranging from planar extension to nearly simple shear can be produced near the stagnation point. 

Another source of error in the determination of the apparent viscosity in capillary flow lies in the fact that as the polymer liquid converges from the barrel to the capillary, the convergence of the flow requires a sharp pressure drop due to the elongational viscosity flow. This effect is illustrated in Figure 13,12. The drop in pressure is not P2 — P )/L but rather (P2 — P )/L, in which L is related to L by... 

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