It is commonly assumed that coffee particles swell during filtration, but it has not been clarified how different degrees of swelling affect the extraction. In this article, we propose a grain swelling model to investigate the influences of swelling on both intra-grain and inter-grain transport. The swelling is modeled through a diffusion process of excess water into the grains. The geometric expansion of the grains is connected to the local concentration of excess water through a specified deformation gradient tensor. Diffusion of soluble compounds inside the grains is coupled with the swelling dynamics through a modified diffusion equation. Inter-grain transport is modeled by solving the Navier–Stokes equation and diffusion equations. This model is solved numerically in the framework of smoothed particle hydrodynamics, and it is used to simulate the extraction of a minimal coffee bed setup and to investigate the effect of a small degree of particle swelling ( in size) on the extraction kinetics. It is found that under the normal operating parameter regime of espresso filtration, swelling affects the extraction mainly through the change of inter-grain transport. Swelling also alters the diffusion inside the grains, but this process has a secondary effect on the extraction. In general, swelling slightly impedes the extraction rate, but enhances the strength considerably at both fixed brewing time and fixed brewing volume. Our results justify the endeavor in the literatures to clarify the effect of possible swelling on brewing and preparation variables during coffee extraction.
References
1.
M.
Povey
, E.
Simone
, M.
Holmes
, M.
Rappolt
, S.
Rafiq
, and M.
Francis
, Physics in Food Manufacturing
(IOP Publishing
, Bristol
, 2020
).2.
J. M.
Bell
and F. K.
Cameron
, “The flow of liquids through capillary spaces
,” J. Phys. Chem.
10
(8
), 658
–674
(1906
).3.
E.
Washburn
, “The dynamics of capillary flow
,” Phys. Rev.
17
, 273
–283
(1921
).4.
M.
Kvick
, M.
Martinez
, D.
Hewitt
, and N.
Balmforth
, “Imbibition with swelling: Capillary rise in thin deformable porous media
,” Phys. Rev. Fluids
2
(7
), 074001
(2017
).5.
D.
Chiang
, C. Y.
Lin
, C. T.
Hu
, and S.
Lee
, “Caffeine extraction from raw and roasted coffee beans
,” J. Food Sci.
83
(4
), 975
–983
(2018
).6.
V. B.
Hargarten
, M.
Kuhn
, and H.
Briesen
, “Swelling properties of roasted coffee particles
,” J. Sci. Food Agric.
100
(10
), 3960
–3970
(2020
).7.
A.
Bradbury
and D.
Halliday
, “Chemical structures of green coffee bean polysaccharides
,” J. Agric. Food Chem.
38
(2
), 389
–392
(1990
).8.
L.
Navarini
, R.
Gilli
, V.
Gombac
, A.
Abatangelo
, M.
Bosco
, and R.
Toffanin
, “Polysaccharides from hot water extracts of roasted Coffea arabica beans: Isolation and characterization
,” Carbohydr. Polym.
40
(1
), 71
–81
(1999
).9.
M.
Arya
and J. M.
Rao
, “An impression of coffee carbohydrates
,” Crit. Rev. Food Sci. Nutr.
47
(1
), 51
–67
(2007
).10.
C.
Cuissinat
and P.
Navard
, “Swelling and dissolution of cellulose, part III: Plant fibres in aqueous systems
,” Cellulose
15
(1
), 67
–74
(2008
).11.
N.
Le Moigne
, “Swelling and dissolution mechanisms of cellulose fibres
,” Ph.D. thesis (École Nationale Supérieure des Mines de Paris
, 2009
)12.
D.
Rivetti
, L.
Navarini
, R.
Cappuccio
, A.
Abatangelo
, M.
Petracco
, and F.
Suggi-Liverani
, “Effects of water composition and water treatment on espresso coffee percolation
,” in 19th International Scientific Colloquium on Coffee
, Trieste, Italy, 2001
.13.
R.-C.
Borja
, “Advancing the engineering understanding of coffee extraction
,” Ph.D.
thesis (University of Birmingham
, 2015
).14.
M.
Maille
, K.
Sala
, D.
Scott
, and H.
Zukswert
, “Critical examination of particle swelling during wetting of ground coffee
,” J. Food Eng.
295
, 110420
(2020
).15.
M.
Mateus
, M.
Rouvet
, J.
Gumy
, and R.
Liardon
, “Interactions of water with roasted and ground coffee in the wetting process investigated by a combination of physical determinations
,” J. Agric. Food Chem.
55
(8
), 2979
–2984
(2007
).16.
M.
Spiro
, R.
Toumi
, and M.
Kandiah
, “The kinetics and mechanism of caffeine infusion from coffee: The hindrance factor in intra–bean diffusion
,” J. Sci. Food Agric.
46
(3
), 349
–356
(1989
).17.
N.
Schorghofer
, B.
Jensen
, A.
Kudrolli
, and D.
Rothman
, “Spontaneous channelization in permeable ground: Theory, experiment, and observation
,” J. Fluid Mech.
503
(503
), 357
–374
(2004
).18.
M.
Malin
and K.
Edgett
, “Evidence for recent groundwater seepage and surface runoff on mars
,” Science
288
(5475
), 2330
–2335
(2000
).19.
C.
Duprat
, “Moisture in textiles
,” Annu. Rev. Fluid Mech.
54
, 443
–467
(2022
).20.
S.
Chang
and W.
Kim
, “Dynamics of water imbibition through paper with swelling
,” J. Fluid Mech.
892
, A39
(2020
).21.
S. H.
Chiu
, M. N. J.
Moore
, and B.
Quaife
, “Viscous transport in eroding porous media
,” J. Fluid Mech.
893
, A3
(2020
).22.
N.
Derr
, D.
Fronk
, C.
Weber
, A.
Mahadevan
, C.
Rycroft
, and L.
Mahadevan
, “Flow-driven branching in a frangible porous medium
,” Phys. Rev. Lett.
125
(15
), 158002
(2020
).23.
K. M.
Pillai
, “Single-phase flows in swelling, liquid-absorbing porous media: A derivation of flow governing equations using the volume averaging method with a nondeterministic, heuristic approach to assessing the effect of solid-phase changes
,” J. Porous Media
17
(10
), 915
–935
(2014
).24.
T.
Sweijen
, B.
Chareyre
, S. M.
Hassanizadeh
, and N. K.
Karadimitriou
, “Grain-scale modelling of swelling granular materials; application to super absorbent polymers
,” Powder Technol.
318
, 411
–422
(2017
).25.
T.
Sweijen
, C. J.
van Duijn
, and S. M.
Hassanizadeh
, “A model for diffusion of water into a swelling particle with a free boundary: Application to a super absorbent polymer particle
,” Chem. Eng. Sci.
172
, 407
–413
(2017
).26.
L. P.
Esteves
, “Superabsorbent polymers: On their interaction with water and pore fluid
,” Cem. Concr. Compos.
33
(7
), 717
–724
(2011
).27.
A.
Krüger
, C.
Ferrero
, and N. E.
Zaritzky
, “Modelling corn starch swelling in batch systems: Effect of sucrose and hydrocolloids
,” J. Food Eng.
58
(2
), 125
–133
(2003
).28.
J. J.
Monaghan
, “Smoothed particle hydrodynamics
,” Annu. Rev. Astron. Astrophys.
30
, 543
–574
(1992
).29.
M.
Ellero
, M.
Serrano
, and P.
Español
, “Incompressible smoothed particle hydrodynamics
,” J. Comput. Phys.
226
(2
), 1731
–1752
(2007
).30.
K.
Müller
, D. A.
Fedosov
, and G.
Gompper
, “Smoothed dissipative particle dynamics with angular momentum conservation
,” J. Comp. Phys.
281
, 301
–315
(2015
).31.
X. Y.
Hu
and N. A.
Adams
, “Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows
,” Phys. Fluids
18
, 101702
(2006
).32.
I. O.
Götze
, H.
Noguchi
, and G.
Gompper
, “Relevance of angular momentum conservation in mesoscale hydrodynamics simulations
,” Phys. Rev. E
76
, 046705
(2007
).33.
A.
Vázquez-Quesada
and M.
Ellero
, “Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics
,” J. Non-Newtonian Fluid Mech.
233
, 37
–47
(2016
).34.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Clarendon Press
, New York
, 1991
).35.
M.
Ellero
and R. I.
Tanner
, “Sph simulations of transient viscoelastic flows at low Reynolds number
,” J. Non-Newtonian Fluid Mech.
132
(1
), 61
–72
(2005
).36.
G.
Zhu
, L.
Zhang
, and J.
Yao
, “Energy capillary number reveals regime transition of imbibition in porous media
,” Phys. Fluids
33
(12
), 123111
(2021
).37.
O.
Fond
, “Effect of water and coffee acidity on extraction. Dynamics of coffee bed compaction in espresso type extraction
,” in Proceedings of the 16th International Scientific Colloquium on Coffee, ASIC (Kyoto)
(ASIC
, Paris
, 1995
), Vol. 413420
.38.
M.
Petracco
and S.
Liverani
, “Espresso coffee brewing dynamics: Development of mathematical and computational models
,” in Colloque Scientifique Int. sur le Cafe
(ASIC Association Scientifique Internationale
, 1993
), Vol. 15
, pp. 702
–702
.39.
J.
Melrose
, “Part I: Internal coffee particle phases and coffee brewing release profiles
,” in Physics in Food Manufacturing
(IOP Publishing
, 2020
), pp. 5-1
–5-18
.40.
E.
Cussler
, Diffusion Mass Transfer in Fluid Systems
(Cambridge University Press
, 2009
).41.
Y. I.
Zhu
, P.
Fox
, and J.
Morris
, “A pore-scale numerical model for flow through porous media
,” Int. J. Numer. Anal. Methods Geomech.
23
(9
), 881
–904
(1999
).42.
M.
Ellero
and L.
Navarini
, “Mesoscopic modelling and simulation of espresso coffee extraction
,” J. Food Eng.
263
, 181
–194
(2019
).43.
A. P.
Thompson
, H. M.
Aktulga
, R.
Berger
, D. S.
Bolintineanu
, W. M.
Brown
, P. S.
Crozier
, P. J.
in't Veld
, A.
Kohlmeyer
, S. G.
Moore
, T. D.
Nguyen
, R.
Shan
, M. J.
Stevens
, J.
Tranchida
, C.
Trott
, and S. J.
Plimpton
, “LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
,” Comput. Phys. Commun.
271
, 108171
(2022
).44.
C.
Mo
, R.
Johnston
, L.
Navarini
, and M.
Ellero
, “Modeling the effect of flow-induced mechanical erosion during coffee filtration
,” Phys. Fluids
33
(9
), 093101
(2021
).45.
46.
B. R.
Corrochano
, J. R.
Melrose
, A. C.
Bentley
, P. J.
Fryer
, and S.
Bakalis
, “A new methodology to estimate the steady-state permeability of roast and ground coffee in packed beds
,” J. Food Eng.
150
, 106
–116
(2015
).47.
© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
