We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by fluids behavior, namely, on how binary fluids phase separate. Thus, parameters and hyperparameters have physical meaning, whose effects are studied in several different scenarios. PSBC's equations can be seen as a dynamical system whose coefficients are trainable weights, with a similar architecture to that of a Recurrent Neural Network. As such, forward propagation amounts to an initial value problem. Boundary conditions are also present, bearing similarity with figure padding techniques in Computer Vision. Model compression is exploited in several ways, with weight sharing taking place both across and within layers. The model is tested on pairs of digits of the classical MNIST database. An associated multiclass classifier is also constructed using a combination of Ensemble Learning and one versus one techniques. It is also shown how the PSBC can be combined with other methods - like aggregation and PCA - in order to construct better binary classifiers. The role of boundary conditions and viscosity is thoroughly studied in the case of digits ``0'' and ``1''.