In this paper we are interested in modeling the production of mucus by diatoms under the constraint of a nutrient limitation. The initial questioning comes from the observation of the so-called "liga" on the Aquitaine coast. The biological origin of the phenomenon is presented and discussed based on the existing litterature. A mathematical model is proposed and its theoretical properties are analized: well-posedness and differentiability with respect to the model parameters. Finally, numerical experiments are provided, investigating the possibility of parameter identification for the model using chemostat-type experiments.