Coffee extraction kinetics in a well mixed system

Kevin M. Moroney, William T. Lee, Stephen B.G. O’Brien, Freek Suijver, Johan Marra

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The extraction of coffee solubles from roasted and ground coffee is a complex operation, the understanding of which is key to the brewing of high quality coffee. This complexity stems from the fact that brewing of coffee is achieved through a wide variety of techniques each of which depends on a large number of process variables. In this paper, we consider a recent, experimentally validated model of coffee extraction, which describes extraction from a coffee bed using a double porosity model. The model incorporates dissolution and transport of coffee in the coffee bed. The model was shown to accurately describe extraction of coffee solubles from grains in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. The full model equations can only be solved numerically. In this work we consider asymptotic solutions, based on the dominant mechanisms, in the case of coffee extraction from a dilute suspension of coffee grains. Extraction in this well mixed system, can be described by a set of ordinary differential equations. This allows analysis of the extraction kinetics from the coffee grains independent of transport processes associated with flow through packed coffee beds. Coffee extraction for an individual grain is controlled by two processes: a rapid dissolution of coffee from the grain surfaces in conjunction with a much slower diffusion of coffee through the tortuous intragranular pore network to the grain surfaces. Utilising a small parameter resulting from the ratio of these two timescales, we construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared with numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters, so the solutions facilitate quick investigation of the influence of various process parameters on the coffee extraction curves.

Original languageEnglish
Article number3
Number of pages19
JournalJournal of Mathematics in Industry
Volume7
DOIs
Publication statusPublished - 30 Jun 2016
Externally publishedYes

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Coffee
Kinetics
Asymptotic Solution
Packed Bed
Dissolution
Brewing
Matched Asymptotic Expansions
Model
Transport Processes
Process Parameters
Porosity
Dimensionless
Small Parameter
Ordinary differential equation
Time Scales

Cite this

Moroney, Kevin M. ; Lee, William T. ; O’Brien, Stephen B.G. ; Suijver, Freek ; Marra, Johan. / Coffee extraction kinetics in a well mixed system. In: Journal of Mathematics in Industry. 2016 ; Vol. 7.
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Coffee extraction kinetics in a well mixed system. / Moroney, Kevin M.; Lee, William T.; O’Brien, Stephen B.G.; Suijver, Freek; Marra, Johan.

In: Journal of Mathematics in Industry, Vol. 7, 3, 30.06.2016.

Research output: Contribution to journalArticle

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