In this work a study has been made of the Stuart (1960)–Watson (1960) formalism as applied to plane Poiseuille flow. In particular, the higher-order Landau coefficients have been calculated for the Reynolds & Potter (1967) method and for the Watson (1960) method. The results have been used to study the convergence of the Stuart–Landau series. A convergence curve in the (α, R)-plane has been obtained by using suitable Domb–Sykes plots. In the region of poor convergence of the series, and also in a part of the divergent region of the series, it has been found that the Shanks (1955) method, using the em1 transformation, serves as a very effective way of finding the proper sum of the series, or of finding the proper antilimit of the series. The results for the velocity calculations at R = 5000 are in very good agreement with Herbert's (1977) Fourier-truncation method using N = 4. The Watson method and the Reynolds & Potter method have also been compared inthe subcritical and supercritical regions. It is found in the supercritical region that there is not much difference in the results by the ‘true problem’ of Watson and the ‘false problem’ of Reynolds & Potter when the respective series in both methods are summed by the Shanks method. This fact could possibly be capitalized upon in the subcritical region, where the Watson method is difficult to apply.
Motion of liquid drops in immiscible liquids is important in liquid-liquid extractors, in separators used with distillation columns, and in packed towers when the packing is not wetted by the disperse phase. A knowledge of the factors which influence their motion is essential for the design and evaluation of performance of equipment used in process industries. The terminal velocities of single liquid drops falling under steadystate conditions in a stationary continuous medium of water with no mass transfer are reported.Twenty-five pure liquids and six mixtures were studied in the following ranges.Drop diameter, 0.0636 to 4.24 cm. Drop liquid density, 1.016 to 2.939 grams per cc. Drop liquid viscosity, 0.653 to 27.06 centipoises Interfacial tension, 4.13 to 45.67 dynes per cm. Reynolds number, 2.5 to 4,158
PREVIOUS WORKThe theoretical equations of Hadamard (4), Rybzynski (77) and Boussinesq (3) and the experimental investigations of Bond (7), and Bond and Newton (2) are limited to the Stokes' law region of Reynolds number less than 1.
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