Coffee extraction kinetics in a well mixed system

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.

Potential Mechanisms Underlying the Role of Coffee in Liver Health

“…This is important to take into account, as the preparation method is highly responsible for the final composition of the coffee brew. 24,25 The roasting process, for example, incorporates the activation of the so-called Maillard reaction that causes an increase in antioxidant activity and degradation of polyphenols. The degradation of polyphenols itself causes a decrease in antioxidant activity, and it has therefore been postulated that the intensity of roasting (along with the intensity of the thermal process) are more important for the antioxidant activity of the brew than type of coffee bean alone.…”

Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process

“…The model equations are simplified and nondimensionalized to describe extraction from a packed coffee bed. Approximate solutions for extraction from a dilute suspension of coffee grains are considered in [15]. The nondimensional equations depend on a small number of parameters and represent a vast simplification of the original equations.…”

An Equilibrium Desorption Model for the Strength and Extraction Yield of Full Immersion Brewed Coffee

“…It is straightforward to verify that substitution of equation (10) into equation (16) yields = , i.e., expressions (14) and (16) are self-consistent. Because the TDS is readily measured experimentally, equation (16) provides an easy means to assess the extraction yield of a fullimmersion brewed coffee.…”

“…Fasano and Talamucci presented mathematical models primarily focused on describing the mass transport phenomena taking place in an espresso machine 12 . Moroney and colleagues used multiscale methods to characterize the spatial-temporal dynamics of coffee extraction by hot water from a fixed coffee bed 13 , and subsequently developed a model reduction of this work to describe coffee extraction kinetics in a well-mixed system 14 . They further compared one-dimensional flow models to computational fluid dynamics modelling for packed bed coffee extraction 15 .…”