Fluid flow-based description of the geometrical features in fluidic channels using the Shannon’s information theory: an exploratory study

Abstract

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 aim of this work is to propose that information theory can be used to enlighten 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 obstacles of different geometry is faced by integrating fluid mechanics theory with Shannon’s theory of information, interpreted in terms of thermodynamics. Technically, computational fluid dynamics simulations at Reynolds’ numbers (Re) equal to 1 and 50 were carried out in fluidic channels presenting obstacles with rectangular and semicircular shape, and on the simulated flow fields, the Shannon’s information theory was applied evaluating the fluid dynamics information entropy content. It emerged that the Shannon Entropy (SE) evaluated at the outflow section of the flow channel depends upon the geometric features (i.e., position, shape, aspect ratio) of the obstacles. This suggests an interpretation of the fluid dynamics establishing in a flow channel presenting obstacles in terms of information theory, that can be used to identify a posteriori the geometric features of the obstacles the fluid interacts with. The proposed approach can be applied to flow data at the boundaries of fluid domains of interest to extract information on the process occurring inside a system, without making any appeal to the governing equations of the phenomenon under observation or intrusive measurements.