DISSIPATION OF ENERGY DUE TO SOLID PARTICLES SUSPENDED IN A VISCOUS LIQUID

Journal Article · Tue Jul 01 04:00:00 EDT 1958 · Physics of Fluids (U.S.)

DOI:https://doi.org/10.1063/1.1705892· OSTI ID:4289688

Brenner, H

A general method is developed for calculating the additional mechanical energy dissipation incurred by the presence of solid particles suspended in an incompressible viscous fluid in laminar flow. The development is applicable to flow in any apparatus within which the an be described by omitting the inertial terms in the Navier-Stokes equations or in which the motion occurs in concentric circles. The validity of the results obtained is limited to compared to those of the apparatus in which the motion is occurring. The technique, based largely upon a reciprocal theorem for the inertialess flow of viscous fluids, is employed to calculate the permanent pressure drop accp,STAamuomg tje STAassage pf ;oqiod tjrpigj a bed of fluidized solids. When the particles are uniformly distributed throughout the bed, this pressure diminution is equal to to the bed weight (corrected for buoyancy) per unit area of duct-in agreement with experimental data on systems in a state of particulate fluidization. Calculations are also presented for the permanent pressure arising from the passage of fluid past an immobilized spherical particle within a cylindrical duct. Einstein's formula for the apparent viscosity of a dilute suspension of spherical particles is also deduced. By means of a new definition of suspension viscosity the heretofore and Burgers are seen to be consistent with one another. Einstein's result is shown to be independent of the type of viscometer employed provided that the motion of a homogeneous fluid within the device fulfills the previous criteria. In the case of nonspherical particles it is demonstrated that the constant in Einstein's viscosity equation (which has a value of 2.5 for spheres) can never be less than unity, whatever the shape of the rigid particles or their orientation iwht respect to the axes of the apparatus. (auth)

• Research Organization: New York Univ.
• Sponsoring Organization: USDOE
• NSA Number: NSA-12-017102
• OSTI ID: 4289688
• Journal Information: Physics of Fluids (U.S.), Journal Name: Physics of Fluids (U.S.) Vol. Vol: 1; ISSN PFLDA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIELECTRICS
ENERGY
ENGINEERING
EQUATIONS
FLUID FLOW
FLUIDIZATION
FLUIDS
LIQUIDS
MATHEMATICS
NAVIER-STOKES EQUATIONS
PARTICLES
PIPES
PRESSURE
SOLIDS
SPHERES
SUSPENSIONS
VISCOSITY