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.
ABSTRACT
BACKGROUND: Assessment of lesion size and transmurality is currently via indirect measures. Real-time image assessment may allow ablation parameters to be titrated to achieve transmurality and reduce recurrences due to incomplete lesions. OBJECTIVE: The purpose of this study was to visualize lesion formation in real time using a novel combined ultrasound and externally irrigated ablation catheter. METHODS: In an in vivo open-chest sheep model, 144 lesions were delivered in 11 sheep to both the atria and the ventricles, while lesion development was monitored in real time. Energy was delivered for a minimum of 15 seconds and a maximum of 60 seconds, with a range of powers, to achieve different lesion depths. Twenty-two lesions were also delivered endocardially. The ultrasound appearance was assessed and compared with the pathological appearance by four independent blinded observers. RESULTS: For the ventricular lesions (n = 126), the mean power delivered was 6.1 ± 2.0 W, with a mean impedance of 394.7 ± 152.4 Ω and with an impedance drop of 136.4 ± 100.1 Ω. Lesion depths varied from 0 to 10 mm, with a median depth of 3.5 mm. At tissue depths up to 5 mm, changes in ultrasound contrast correlated well (r = 0.79, R(2) = 0.62) with tissue necrosis. The depth of ultrasound contrast correlated poorly with the depth of the zone of hemorrhage (r = 0.33, R(2) = 0.11), and impedance change correlated poorly with lesion depth (r = 0.29, R(2) = 0.08). CONCLUSION: Real-time lesion assessment using high-frequency ultrasound integrated into an ablation catheter is feasible and allows differentiation between true necrosis and hemorrhage. This may lead to safer and more efficient power delivery, allowing more effective lesion formation.