Transport phenomena

Transport phenomena is the study of how mass, energy, charge, and momentum move between systems. This field is essential to physics, chemistry, and engineering. It explores the exchange of these properties throughout the physical universe. Scientists view these movements as fundamental building blocks of the universe. They are also responsible for the success of all life on Earth. In engineering, the subject is as fundamental as thermodynamics or electromagnetism. It provides the tools needed to analyze how fluids, heat, and matter interact.

At its core, transport is driven by the search for balance. This state of balance is known as thermodynamic equilibrium. Systems naturally move toward their lowest energy state to reach this equilibrium. When a system reaches equilibrium, all driving forces disappear and transport ceases. Different types of transport lead to different kinds of equilibrium. Heat transfer occurs as a system seeks thermal equilibrium with its surroundings. Mass transfer moves a system toward chemical equilibrium. Momentum transfer moves a system toward mechanical equilibrium.

To understand these movements, scientists rely on two primary concepts. The first is the conservation law, often formulated as continuity equations. These laws state that the total amount of the quantity being studied must be conserved. The second concept involves constitutive equations. These equations describe how a quantity responds to various stimuli. For example, Fourier's law describes how heat flux responds to temperature gradients. The Navier-Stokes equations describe the relationship between fluid flux and applied forces. These mathematical tools allow researchers to predict how systems will behave.

There are three main branches of transport: mass, energy, and momentum. Mass transfer involves the movement of matter, such as molecular diffusion. This can be driven by pressure gradients or temperature gradients, known as thermal diffusion. Energy transfer, or heat transfer, includes conduction and convection. Heat conduction in solids follows Fourier's law. Momentum transfer, or fluid mechanics, involves the movement of motion. Fluid mechanics is divided into fluid statics for fluids at rest and fluid dynamics for fluids in motion.

Remarkably, these three branches share a deep mathematical connection. The equations for momentum, energy, and mass transfer are very similar. For instance, Newton's law of viscosity governs momentum, Fourier's law governs heat, and Fick's law governs mass. Because of these similarities, scientists use analogies to study them. The Reynolds analogy suggests that turbulent diffusivities are equal. However, this does not always work when liquids or drag are present. The most successful version is the Chilton and Colburn J-factor analogy, which uses experimental data to predict mass transfer.

Another profound discovery involves the Onsager reciprocal relations. Lars Onsager used statistical mechanics to show a unique equality in fluid systems. He found that if both pressure and temperature vary, they can influence each other. A temperature difference at constant pressure can cause matter to flow. Similarly, a pressure difference at constant temperature can cause heat to flow. Onsager proved that the heat flow per unit of pressure difference equals the matter flow per unit of temperature difference. This theory is very general and can treat many thermodynamic forces at once.

Transport phenomena are used across many different scientific fields. In chemical engineering, they are vital for reactor design and metallurgy. Biomedical engineers use these principles to study perfusion and thermoregulation in the body. Solid state physicists study the transport of electrons, holes, and phonons. In mechanical engineering, these rules help determine the velocity profile of a fluid in a rigid volume. Even in everyday life, we see these processes. An odor dissipating in a room is a clear example of mass diffusion. A raindrop slowing down due to air resistance shows momentum diffusion through viscous stresses.