Mathematical Models on Milk, Coffee and Beer

The simple differential equation y' = ky is an important mathematical model. It is well known in Population Dynamics as the Malthusian Equation and it is familiar to food technologists as Bigelow’s First Law, which describes the microbial mortality at constant lethal temperatures. In the paper we focus on the process of thermal sterilization of milk. The Malthusian Equation is also a mathematical model for Newton’s law of cooling or heating. The rate of heat loss of a cooling body is proportional to the difference in temperatures between the body and its surroundings. In the paper we analyze the data of an experimental study on the cooling of coffee conduced by "Mathematics & Real Life" Project. The measurements of the temperature were taken using a centesimal temperature sensor connected to a computer for automatic data capture. Another simple differential equation is Darcy’s equation, a fundamental mathematical model in the filtration theory. In the paper we are interested in mathematical models derived from Darcy’s law, which are applied to the cross flow microfiltration at constant pressure of beer. These models are then tested using experimental data provided by the Italian Brewing Research Centre of the University of Perugia.