ABSTRACT
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
II. Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
III. Transport at Low Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A. Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
B. Heat or Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
IV. Transport at Higher Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A. Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
B. Heat or Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
V. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
The knowledge of the basic phenomena involved between a fluid sphere and an external flow is
important for the comprehension of liquid-liquid, solid-liquid, and gas-liquid systems in the
fields of chemical, petrochemical, or environmental engineering. The system considered here is
a rigid or a fluid sphere of radius a moving with a constant velocity U1 in another immiscible fluid of infinite extent, which is at a different temperature. Some of the early works on the
motion and heat or mass transfer from a fluid sphere, as well as recent advances, are exposed.
Particular emphasis is placed on drag coefficients and Nusselt and Sherwood numbers. This
information should be useful for the study of the dispersed systems (liquid-liquid, gas-liquid,
or solid-liquid), particularly for the design of liquid-liquid contactors (in the field of chemical
engineering) like liquid-liquid extraction equipment or direct contact exchangers. This review
deals with transport at low (creeping flow) and high Reynolds numbers (0 , Re , 400).
