Tsallis Entropy applied to microfluidic channels analysis

Abstract

This work investigated the possibility to describe the fluid flow in a microchannel from a thermodynamic point of view, exploring the possibility to evaluate the presence of obstacles (or, more in general, geometry imperfection) and their influence on the fluid. Tsallis entropy concept was employed. This form of entropy was introduced in 1988 by Costantino Tsallis as a basis for generalizing the standard statistical mechanics and as a generalization of the standard Boltzmann-Gibbs entropy. Inspired by nature, where storing information is an intrinsic ability of natural systems, here we investigate the capability of interacting systems to transport/store the information generated/exchanged in the interaction process in the form of energy or matter, preserving it over time. In detail, here we test the possibility to consider a fluid as a carrier of information, speculating about how to use such information. The final goal is to demonstrate that information theory can be used to illuminate physical observations, even in those cases where the equations describing the phenomenon under investigation are intractable, are affected by a budget of uncertainty that makes their solution not affordable or may not even be known. In this exploratory work, an information theory-based approach is applied to microfluidic data. In detail, the classical study of the fluid flow in a microchannel with an obstacle of a specific geometry is faced by integrating fluid mechanics theory with Tsallis entropy. Technically, computational fluid dynamics simulations at Reynolds’ numbers (Re) equal to 1 were carried out in fluidic channels presenting a rectangular obstacle and on the simulated flow fields.