Taylor’s theory

Gas-liquid interfacial areas, a, and volumetric liquid-side mass transfer coefficients, kLa, are measured in a high pressure trickle-bed reactor. Increase of a and kLa with pressure is explained by the formation of tiny bubbles in the trickling liquid film. By applying Taylor s theory, a model relating the increase in a with the increase in gas hold-up, is developed. The model accounts satisfactorily for the available experimental data. To estimate kLa, contribution due to bubbles in the liquid film has to be added to the corresponding value measured at atmospheric pressure. The mass transfer coefficient from the bubbles to the liquid is calculated as if the bubbles were in a stagnant medium. 

Taylor s Theory. To explain the behavior of in Figures 3 and 4 we borrow from G. I. Taylor s theory of continuous movements, one of the pioneering works in the representation of turbulence. Casting Taylor s equation over into our notation and restricting the theory to an exponentially-declining correlation function, as seems appropriate from Figure 5, yields the following for the dependence of... 

Cox [1969] extended Taylor s theory to systems with the full range of viscosity ratios ... 

Taylor s theory makes it also possible to predict the retraction of slightly deformed drops toward an equilibrium spherical form ... 

During mixing, the dispersed phase progressively breaks down until a rninimum drop diameter is reached. As the drop diameter decreases, further breakup becomes increasingly difficult. For emulsions, the size of the smallest drop that can be broken can be calculated from Taylor s theory, but experiments have shown that in most cases the equUibrium droplet size is larger than predicted. Furthermore, the deviation increases with concentration of the dispersed phase, ( ) - ( ), where experimentally the smallest value for which the deviation occurs, ( ) 0.005 [Utracki and Shi, 1992]. 

A set of empirical equations was obtained by Wu to describe the dispersed phase average particle size obtained after dispersive mixing in an extruder (13). The equations were based on the case of a Newtonian drop suspended in a Newtonian matrix, that is, Taylor s theory (16,17) with an extension to the case of a viscoelastic drop in a viscoelastic matrix. The empirical data employed were for blends containing 15 wt% dispersed phase and 85 wt% matrix phase. The particle size was found to be critically dependent on the ratio of the dispersed phase to the matrix phase melt... 

In contrast and for comparison, the theoretical equation from Taylor s theory (16, 17) for a Newtonian drop suspended in a Newtonian matrix with the concentration of the dispersed phase particle assumed to be vanishingly small is... 

The growing importance of catalysis was reflected in the formation of the Committee on Contact Catalysis in the Division of Chemistry and Chemical Technology of the National Research Council in 1922 (21). The committee, chaired by Cornell physical chemist Wilder Bancroft, published periodic review articles although some of the early ones mainly summarized the theories of the author. In the Fifth Report (1927), Emmett Reid of Johns Hopkins criticized the previous reviewer, Taylor, for giving his own theories instead of surveying the literature (22). The author of the Eighth Report (1930), J. C. W. Frazer, pointed out that Taylor s theory had been anticipated by Fusineri in 1825 (23). 

Taylor s theory [4] for the break-up of individual droplets for Newtonian fluids has been found applicable to better understand the morphology formed in polymer blends. The stable size of a drop against break-up in a simple shear field is given by... 

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