Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process

K. M. Moroney, W. T. Lee, S. B.G. O'Brien, F. Suijver, J. Marra

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Extraction of coffee solubles from roast and ground coffee is a highly complex process, depending on a large number of brewing parameters. We consider a recent, experimentally validated, model of coffee extraction, describing extraction from a coffee bed using a double porosity model, which includes dissolution and transport of coffee. It was shown that this model can accurately describe coffee extraction in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. Despite being based on some simplifying assumptions, this model can only be solved numerically. In this paper we consider asymptotic solutions of the model describing extraction from a packed coffee bed. Such solutions can explicitly relate coffee concentration to the process parameters. For an individual coffee grain, extraction is controlled by a rapid dissolution of coffee from the surface of the grain, in conjunction with a slower diffusion of coffee through the intragranular pore network to the grain surface. Extraction of coffee from the bed also depends on the speed of advection of coffee from the bed. We utilize the small parameter resulting from the ratio of the advection timescale to the grain diffusion timescale to construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared to numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters and so are useful to quickly fit extraction curves and investigate the influence of various process parameters on the extraction.

Original languageEnglish
Pages (from-to)2196-2217
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume76
Issue number6
DOIs
Publication statusPublished - 15 Nov 2016
Externally publishedYes

Fingerprint

Coffee
Asymptotic analysis
Asymptotic Analysis
Asymptotic Solution
Packed Bed
Dissolution
Process Parameters
Advection
Time Scales
Matched Asymptotic Expansions
Model
Asymptotics of Solutions
Brewing
Porosity
Dimensionless
Small Parameter

Cite this

Moroney, K. M. ; Lee, W. T. ; O'Brien, S. B.G. ; Suijver, F. ; Marra, J. / Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process. In: SIAM Journal on Applied Mathematics. 2016 ; Vol. 76, No. 6. pp. 2196-2217.
@article{ff28f0ae2e25449aa344bb6637727c12,
title = "Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process",
abstract = "Extraction of coffee solubles from roast and ground coffee is a highly complex process, depending on a large number of brewing parameters. We consider a recent, experimentally validated, model of coffee extraction, describing extraction from a coffee bed using a double porosity model, which includes dissolution and transport of coffee. It was shown that this model can accurately describe coffee extraction in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. Despite being based on some simplifying assumptions, this model can only be solved numerically. In this paper we consider asymptotic solutions of the model describing extraction from a packed coffee bed. Such solutions can explicitly relate coffee concentration to the process parameters. For an individual coffee grain, extraction is controlled by a rapid dissolution of coffee from the surface of the grain, in conjunction with a slower diffusion of coffee through the intragranular pore network to the grain surface. Extraction of coffee from the bed also depends on the speed of advection of coffee from the bed. We utilize the small parameter resulting from the ratio of the advection timescale to the grain diffusion timescale to construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared to numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters and so are useful to quickly fit extraction curves and investigate the influence of various process parameters on the extraction.",
keywords = "Asymptotic analysis, Coffee brewing process, Coffee extraction kinetics, Double porosity model, Matched asymptotic expansions, Solidliquid extraction",
author = "Moroney, {K. M.} and Lee, {W. T.} and O'Brien, {S. B.G.} and F. Suijver and J. Marra",
year = "2016",
month = "11",
day = "15",
doi = "10.1137/15M1036658",
language = "English",
volume = "76",
pages = "2196--2217",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",

}

Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process. / Moroney, K. M.; Lee, W. T.; O'Brien, S. B.G.; Suijver, F.; Marra, J.

In: SIAM Journal on Applied Mathematics, Vol. 76, No. 6, 15.11.2016, p. 2196-2217.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process

AU - Moroney, K. M.

AU - Lee, W. T.

AU - O'Brien, S. B.G.

AU - Suijver, F.

AU - Marra, J.

PY - 2016/11/15

Y1 - 2016/11/15

N2 - Extraction of coffee solubles from roast and ground coffee is a highly complex process, depending on a large number of brewing parameters. We consider a recent, experimentally validated, model of coffee extraction, describing extraction from a coffee bed using a double porosity model, which includes dissolution and transport of coffee. It was shown that this model can accurately describe coffee extraction in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. Despite being based on some simplifying assumptions, this model can only be solved numerically. In this paper we consider asymptotic solutions of the model describing extraction from a packed coffee bed. Such solutions can explicitly relate coffee concentration to the process parameters. For an individual coffee grain, extraction is controlled by a rapid dissolution of coffee from the surface of the grain, in conjunction with a slower diffusion of coffee through the intragranular pore network to the grain surface. Extraction of coffee from the bed also depends on the speed of advection of coffee from the bed. We utilize the small parameter resulting from the ratio of the advection timescale to the grain diffusion timescale to construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared to numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters and so are useful to quickly fit extraction curves and investigate the influence of various process parameters on the extraction.

AB - Extraction of coffee solubles from roast and ground coffee is a highly complex process, depending on a large number of brewing parameters. We consider a recent, experimentally validated, model of coffee extraction, describing extraction from a coffee bed using a double porosity model, which includes dissolution and transport of coffee. It was shown that this model can accurately describe coffee extraction in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. Despite being based on some simplifying assumptions, this model can only be solved numerically. In this paper we consider asymptotic solutions of the model describing extraction from a packed coffee bed. Such solutions can explicitly relate coffee concentration to the process parameters. For an individual coffee grain, extraction is controlled by a rapid dissolution of coffee from the surface of the grain, in conjunction with a slower diffusion of coffee through the intragranular pore network to the grain surface. Extraction of coffee from the bed also depends on the speed of advection of coffee from the bed. We utilize the small parameter resulting from the ratio of the advection timescale to the grain diffusion timescale to construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared to numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters and so are useful to quickly fit extraction curves and investigate the influence of various process parameters on the extraction.

KW - Asymptotic analysis

KW - Coffee brewing process

KW - Coffee extraction kinetics

KW - Double porosity model

KW - Matched asymptotic expansions

KW - Solidliquid extraction

UR - http://www.scopus.com/inward/record.url?scp=85007048846&partnerID=8YFLogxK

U2 - 10.1137/15M1036658

DO - 10.1137/15M1036658

M3 - Article

VL - 76

SP - 2196

EP - 2217

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -