Interfacial elongational viscosities

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. 

Furtheron, the dispersed droplets are the smaller the closer to unity the viscosity ratio of the components is (62-64). Their sizes decrease also if the first normal stress difference of the dispersed phase becomes smaller than that of the matrix (61). The droplet size, moreover, is influenced by the tendency to further break down of elongated particles due to capillary instabilities (61) as well as by coalescence via an interfacial energy driven viscous flow mechanism. All these procedures and dependences affect the structure formation within their typical time scales (61,62). 

The microrheology makes it possible to expect that (i) The drop size is influenced by the following variables viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillarity number, composition, flow field type, and flow field intensity (ii) In Newtonian liquid systems subjected to a simple shear field, the drop breaks the easiest when the viscosity ratio falls within the range 0.3 < A- < 1.5, while drops having A- > 3.8 can not be broken in shear (iii) The droplet breakup is easier in elongational flow fields than in shear flow fields the relative efficiency of the elongational field dramatically increases for large values of A, > 1 (iv) Drop deformation and breakup in viscoelastic systems seems to be more difficult than that observed for Newtonian systems (v) When the concentration of the minor phase exceeds a critical value, ( ) >( ) = 0.005, the effect of coalescence must be taken into account (vi) Even when the theoretical predictions of droplet deformation and breakup... 

From the above equations it is possible to calculate the size of the largest drop that exists in a fluid undergoing distortion at any shear rate. In these equations, the governing parameters for droplet breakup are the viscosity ratio p (viscosity of the dispersed phase to that of the matrix) the type of flow (elongational, shear, combined, etc.) the capillary number Cfl, which is the ratio between the deforming stress (matrix viscosity x shear rate) imposed by the flow on the droplet and the interfacial forces a/R, where ais the interfacial... 

H. M. Laun and H. Munstedt, Elongational behavior of a LDPE melt. I. Strain rate and stress dependence of viscosity and recoverable strain in the steady state. Comparison with shear data. Influence of interfacial tension, Rheol. Acta 17, 415-425 (1978). 

Using Eqs. (15.12) and (15.13) one can obtain the droplet diameter from a knowledge of the stress acting on each drop (in elongational flow) and the interfacial tension at the oil/saliva interface. Alternatively, one can measure the droplet diameter of the oil drops produced in the saliva and, from a knowledge of the viscosity of the saliva and the interfacial tension of the oil/saliva interface, estimate the stress in the flowing saliva. This is illustrated below. 

Taylor s work with Newtonian liquids showed that elongation of a droplet is favoured by low interfacial tension, larger particle diameter, matrix viscosity and high shear rates. Flumerfelt [17], using non-Newtonian fluids, showed that in a simple shear field, a spherical drop becomes ellipsoidal with the major axis and inclined at about 45° from perpendicular to the shear field. Depending on relative viscosities, a critical shear rate was reached in which the droplet broke up into smaller droplets. A minimum size was eventually reached below which break-up could not be achieved regardless of shear rate. 

Where t = rate of shear or elongation of the matrix pm = the viscosity of the matrix o = the coefficient of the interfacial tension R = radius of the undeformed droplets... 

For lower viscosity fluids, an alternate to rod pulling is to use a buoyancy fluid to squeeze the sample radially. Hsu and Flummer-felt (1975) have adapted the spinning drop tensiometer (Joseph et al., 1992) shown in Figure 7.2.9 to extensional measurements. If the surrounding fluid is more dense, P2 > Pi > then the test fluid will move to the center when rotation starts. It will elongate until interfacial tension balances the inertial forces. 

---