เปรียบเทียบวิธี

	ไอโซเทอร์มการดูดซับ (Langmuir-Freundlich)	แบบจำลอง CSTR	แบบจำลอง PFR
สาขาวิชา	ฟิสิกส์ประยุกต์	ฟิสิกส์ประยุกต์	ฟิสิกส์ประยุกต์
ตระกูล	Process / pipeline	Process / pipeline	Process / pipeline
ปีกำเนิด	1918	1962	1962
ผู้ริเริ่ม	Irving Langmuir	Octave Levenspiel	Octave Levenspiel
ประเภท	Empirical and theoretical adsorption equilibrium model	Mathematical model for continuous flow reactor	Mathematical model for plug-flow reactor
แหล่งต้นตำรับ	Langmuir, I. (1918). The adsorption of gases on plane surfaces of glass, mica, and platinum. Journal of the American Chemical Society, 40(9), 1361-1403.	Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). John Wiley & Sons. ISBN: 978-0-471-25424-9	Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). John Wiley & Sons. ISBN: 978-0-471-25424-9
ชื่อเรียกอื่น	Langmuir isotherm, Freundlich isotherm, sorption equilibrium	ideal mixed reactor, back-mix reactor, CSTR	ideal tubular reactor, plug-flow model, PFR
ที่เกี่ยวข้อง	3	3	3
สรุป	Adsorption isotherms describe the equilibrium uptake of a substance on a solid surface as a function of gas or solution phase concentration at constant temperature. The Langmuir isotherm (1918) and Freundlich isotherm (1906) are classical empirical models. The Langmuir model assumes monolayer coverage and is mechanistic; the Freundlich model is empirical and describes multilayer or heterogeneous adsorption. These isotherms are essential for designing separation processes (activated carbon filters, molecular sieves) and understanding pollutant sorption.	The CSTR (Continuous Stirred-Tank Reactor) model describes the behavior of an ideal mixed reactor where fresh feed is continuously added, products are withdrawn, and contents are kept uniform by vigorous stirring. This fundamental model, formalized by Octave Levenspiel in the 1960s, is widely used to design and scale batch and continuous processes. Despite its simplicity, it captures essential dynamics of industrial reactors and is the baseline for process control and optimization.	The PFR (Plug Flow Reactor) model describes the behavior of a tubular reactor in which fluid elements move through as distinct plugs with no axial mixing. Fluid at the inlet is freshly unreacted; as it travels downstream, reactions progress. This idealized model, formalized by Octave Levenspiel alongside CSTR theory, is the opposite extreme: while CSTRs are fully mixed, PFRs have no axial mixing. In practice, PFRs achieve higher conversion than CSTRs for the same residence time and are widely used in the chemical and petroleum industries.