Ellipsoidal drop

For an oblate ellipsoidal drop with the major axis Dh in a horizontal... 

In order to allow for a variation of interfacial area from that of an equivalent sphere, the eccentricity of the ellipsoidal drop must be taken into account. The area ratio of Eq. (44) does not exceed unity by a serious amount until an eccentricity of 1.5 is attained. An experimental plot of eccentricity as ordinate vs. equivalent spherical drop diameter as abscissa may result in a straight line (G7, Kl, K3, S12). A parameter is yet to be developed by which the lines can be predicted without recourse to experiment. Eccentricity is not an accurate shape description of violently oscillating drops and should therefore be used only for drop size below the peak diameter (region B of Fig. 5). 

Drop evaporation theory for spherical and ellipsoidal drops... 

The dependence of drop deformation on the Weber number and the vorticity inside the drop was studied in [336]. It was shown that the drop is close in shape to an oblate ellipsoid of revolution with semiaxis ratio > 1 If there is no vortex inside the drop, then this dependence complies with the function We(x) given in (2.8.3). The ratio x decreases as the intensity of the internal vortex increases. Therefore, the deformation of drops moving in gas is significantly smaller than that of bubbles at the same Weber number We. The vorticity inside an ellipsoidal drop, just as that of the Hill vortex, is proportional to the distance TZ from the symmetry axis,... 

At low viscosity ratios, R < 0.2, drops in shear flow first align themselves at 45 to the flow in the form of ellipsoidal drops. Increasing flow and hence shear creates drops with pointed tails that break off to create satellite drops. Drops with viscosity ratios of 1.0 form dumb-bells that with increases shear burst into two spherical drops with some satellite drops. Increasing R tends to produce long slender drops, / > 3.8 drops do not break but form ellipsoidal drops aligned with the shear field. 

In elongational flow Figure 14.7) and small R, ellipsoidal drops parallel to the flow and with trailing ends are formed, sometimes accompanied with smaller satellite drops. Drops with large R in elongational flow give ellipsoidal drops aligned with the flow and no breakup. 

The deformed drop retraction method (DDRM) has been recently proposed. It makes it possible to determine Vj2 from the time evolution of deformed ellipsoidal drops toward its spherical equilibrium form (Luciani et al. 1997). Assuming an elhpsoidal shape for a drop of initial radius Rq deformed under simple shear, the following relation was found ... 

A. Luciani, L.A. Utracki, The extensional flow mixCT, EFM. Int. Polym. Process. 11,299-309 (1996) A. Luciani, ME. Champagne, L.A. Utracki, Interfacial tension determination by retraction of ellipsoidal drops. J. Polym. Sd. B. Polym. Phys. Ed. 35(9), 1393-1403 (1997)... 

J. Lyngaae-J0rgensen, K. S0ndergaard, L.A. Utracki, A. Valenza, Formation of ellipsoidal drops in simple shear flow transient behavior. Poly. Netw. Blends 3(4), 167-181 (1993)... 

Maffettone, P.L. and Minale, M. (1998) Equation of change for ellipsoidal drops in viscous flow. /. Non-Newtonian Fluid Mech., 78 (2-3), 227-241. 

Lyngaae-Jorgensen, J., Sondergaard, K., Utracki, L.A., and Valenza, A. (1993) Formation of ellipsoidal drops... 

Minale M. Models for the deformation of a single ellipsoidal drop A review. Rheol Acta 2010 49(8) 789-806. 

Maffettone PL, Minale M. Equation of change for ellipsoidal drops in viscous flows (vol. 78, p. 227, 1998). J Non-Newtonian Fluid Mech 1999 84(1) 105-106. 

Luciani A, Champagne MF, Utracki LA. Interfacial tension coefficient from the retraction of ellipsoidal drops. J Polym Sci PartB 1997 35(9) 1393-1403. 

Maffettone PL et al. Analysis of start-up dynamics of a single drop through an ellipsoidal drop model for non-Newtonian fluids. J Non-Newtonian Fluid Mech 2005 126(2—3) 145-151. 

Minale M. A phenomenological model for wall effects on the deformation of an ellipsoidal drop in viscons flow. Rheol Acta 2008 47(5-6) 667-675. 

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