Johan Marra

Coffee extraction kinetics in a well mixed system

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.

Mathematical Modelling of the Coffee Brewing Process

The drip filter coffee market is a multi-billion euro industry. Despite this, although the chemistry of coffee brewing has been investigated in great detail, the physics of the process has received relatively little attention. In order to explain in scientific terms correlations between the coffee quality and the process variables, a physical model is required. In this study, flow through a static, saturated coffee bed, under the influence of a pressure gradient, is described using a double porosity model. The model is parametrised using experimentally obtained data from a cylindrical flow-through cell containing a coffee bed. Mass transfer from the coffee grains to the interstitial water is modelled using two mechanisms; mass transfer from the surface of the grains and mass transfer from the interior (bulk) of the grains. Mass transfer resistances are estimated by fitting experimental data. Initially coffee extraction is dominated by mass transfer from the grain surface, while transfer from the kernel of the grain is the rate limiting mechanism once the surface coffee has been exhausted.