STRATIFIED THREE PHASE FLOW IN PIPES - STABILITY AND TRANSITION

The stability of stratified three phase flow (water-oil-gas) was analyzed using two approaches: A straight forward Kelvin-Helmholtz stability analysis on the two interfaces termed here the “exact” approach and a simplified approach. 1 n the “exact” approach the two interfaces (water-oil and oil-gas) are perturbed, while in the simplified approach the perturbed interface is only the upper oil-gas interface. Both approaches include the viscous Kelvin-Helmholtz analysis in which the shear stresses are laken into account and the inviscid K H analysis where the shear stresses are neglected.

Comparison with some experimental results suggests that the simplified method is a better predictor of the transition from stratified flow than the “exact” approach, suggesting, perhaps, that the stability analysis on the upper interface alone is preferred.     

Analysis of supply contracts with total minimum commitment

In this paper we analyze a supply contract for a single product that specifies that the cumulative orders placed by a buyer, over a finite horizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer places orders periodically. We derive the optimal purchase policy for the buyer for a given total minimum quantity commitment and a discounted price. We show that the policy is characterized by the order-up-to levels of the corresponding finite horizon and a single-period standard newsboy problem with no commitment but with discounted price. We show that this policy can be computed easily. We can use this to evaluate any discount schedule characterized by a set of (price discount, minimum commitment) pairs.     

Thin-Layer Chromatographic Study on the Lipid Components of Cocoa Beans and Cocoa Butter

SUMMARY— After thin-layer chromatography, cocoa bean cotyledon section presented only one chromatographic spot whereas cocoa butter showed five spots. Apparently, the lipids naturally occurring in cocoa beans are not modified during farm fermentation.