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.
N1 - Publisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.
PY - 2016
Y1 - 2016
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
AN - SCOPUS:85007048846
SN - 0036-1399
VL - 76
SP - 2196
EP - 2217
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 6
ER -