Download e-book for iPad: A Bridge Principle for Harmonic Maps by Ynging Lee, Al Nungwang, Derchyi Wu
By Ynging Lee, Al Nungwang, Derchyi Wu
We end up a bridge precept for harmonic maps among normal manifolds.
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Extra info for A Bridge Principle for Harmonic Maps
Fkinetic is derived based on the assumption that all fluid energy is transmitted in vertical direction. The drag force of the quiescent continuous phase, Fdrag , decelerates the growing drop and is evaluated when considering the forming droplet as a solid sphere. 2 Drop formation at a capillary tip is lost. The result shows an improvement to previous theories in predicting drop sizes at varying flow rates of the disperse phase, but still large deviations of theory and experiment were observed at high disperse flow rates where the assumption of static conditions fails.
Taylor (1934) derived an expression where the drop deformation, D, is described as a function of the applied stresses in terms of the Capillary number, Ca, and the viscosity ratio, λ: 19λ + 16 . 26) 16λ + 16 According to Eq. 26 the deformation D is linear in Ca and the effect of viscosity is small. The applicability of Eq. 26 is limited to small Capillary numbers where the deformations are small. g. Chaffey and Brenner, 1967; Cox, 1969; Barth`es-Biesel and Acrivos, 1973; Rallison, 1980). 27) λ)2 and θ= π 1 19λ · Ca + · arctan .
1994) developed a dispersion equation describing the instability of liquid jets at low velocity using an integro-differential approach based on the conservation of energy of the jet for Stokes flow. The derived explicit equation agrees well with the limiting solutions to Tomotika’s implicit, complex dispersion relationship, which were introduced by Meister and Scheele (1967). All previous liquid-liquid stability theories are based on simplifying assumptions which have to be accounted for when performing experiments.
A Bridge Principle for Harmonic Maps by Ynging Lee, Al Nungwang, Derchyi Wu