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General analysis for free drainage of non‐Newtonian films from flat plates when inertial and surface tension forces and normal stresses are negligible
Author(s) -
Pendergrass John
Publication year - 1975
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690210309
Subject(s) - mechanics , dimensionless quantity , surface tension , newtonian fluid , inertial frame of reference , flow (mathematics) , volumetric flow rate , non newtonian fluid , rheology , position (finance) , materials science , plane (geometry) , tension (geology) , inclined plane , classical mechanics , mathematics , thermodynamics , physics , composite material , geometry , engineering , mechanical engineering , ultimate tensile strength , finance , economics
General equations for (1) thickness, (2) specific holdup, and (3) specific flow rate of non‐Newtonian films under conditions of plane free drainage with negligible inertial and interfacial tension forces and normal stresses as functions of position and time are derived. Use of these equations reduces the heretofore tedious process of derivation for a particular rheological model of expressions for film thickness, holdup, and flow rate to a single‐step operation for film thickness and relatively simple processes for holdup and flow rate. The general equations are evaluated for popular non‐Newtonian models, with description of efficient methods for doing so, and the results for thickness, holdup, and flow rate, many new, in compact dimensionless form made available to the interested reader in a supplement.