Introduction

Most of us experience physical transport of mass and heat in fluids several times in a day. Mass transport is indeed one of the first processes we deal with every day, when we sit in front of our cup of coffee or tea. Our first action is to stir the fluid in the cup, to mix or blend the sugar uniformly in the fluid. We succeed by generating a highly turbulent flow field where mass is displaced very rapidly within the fluid domain. We continually perform countless actions, including breathing, which aim at enhancing or reducing the physical transport of mass in a fluid.

Physical transport of mass and heat in fluids not only occurs in human behavior, but it is also an inherent part of life in all forms, and plays a fundamental role in the fate of organic as well as inorganic matter. In ecological systems, the fate of substances such as nutrients and toxic matter is of fundamental importance and has received increasing attention in the last decades. The aim of these studies is to explain and model how substances move within and across media, typically water or air, and to estimate what concentration the substance may attain in the domain of interest at any given time. The need to understand the complex physical, chemical, and biological interactions in the environment leads to a wide increase of interdisciplinary studies involving physicists, ecolo-gists, biologists, and engineers, to the development of new branches of science, such as biogeochemistry and environmental engineering, and even to the identification of new physical domains of interests, typically at the interface between the elements (water-soil, soil-air, water-air).

The starting point of the discussion on the physical transport of mass is the evidence that, unless temperature vanishes in absolute terms (0K = — 273 °C), matter moves. Electrons move within atoms, atoms move within molecules, and molecules move within cells and bodies. Even the condition we normally refer to as stillness involves movement, although only at scales that are invisible or imperceptible to our senses. Some examples are trivial: a drop of ink in water is expected to spread in all directions even if the water is motionless! We call this process molecular diffusion - it is the result of small displacements of molecules about their position, a process known as Brownian motion. The displacement of molecules increases with the rise in temperature. While molecules agitate about their local position, we perceive a natural tendency of matter to transfer from regions of high concentration to regions of low concentration. This transfer only stops when the substance is uniformly distributed in the physical domain. However, if Brownian motion is the only cause of mixing, the process is extremely slow and may become negligible when other transport processes are present.

Since ecology is interested in the description of processes at a scale much bigger than the molecular size, a model which describes mass flux as proportional to the gradient of the concentration is sufficient to describe diffusion in still fluids. Such a model, called Fick's law, will be discussed in the section devoted to diffusion. At this point, it is worth noticing that (1) molecular diffusion is active even in the absence of perceivable motion in the fluid, that is, it is the basic process of mass transfer; and (2) diffusion is to be considered an upscaling model rather than a true physical process, as it is a model description of the combined effect of a multitude of individual displacements.

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