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Application of the fractional derivatives method to bubble growth/dissolution processes with or without first‐order chemical reaction
Author(s) -
Hong Juan,
Woo H. S.
Publication year - 1985
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.690311012
Subject(s) - dimensionless quantity , bubble , dissolution , ordinary differential equation , partial differential equation , mathematics , fractional calculus , boundary value problem , saturation (graph theory) , differential equation , mathematical analysis , order (exchange) , chemistry , thermodynamics , mechanics , physics , finance , combinatorics , economics
A new application of the fractional derivatives technique is presented to analyze bubble growth/dissolution processes with or without first‐order chemical reaction. The second‐order partial differentail equation with moving boundary conditions is converted to a first‐order ordinary differential equation using the fractional derivatives technique. The first‐order differential equation can be simplified to the quasistationary and the quasisteady‐state equations under appropriate conditions. The predictions of the fractional derivatives solution (FDS) are in excellent agreement with those by numerical methods over a wide range of the dimensionless parameter N a , which describes the extent of gas saturation. The versatility of FDS encompasses various approximate solutions.