diffusion

diffusion, process resulting from random motion of molecules by which there is a net flow of matter from a region of high concentration to a region of low concentration. A familiar example is the perfume of a flower that quickly permeates the still air of a room. Because of the higher kinetic energy of gas molecules and the large spaces between them, diffusion occurs faster in gases than in liquids and solids.

Quantifying diffusion

In 1855 German physiologist Adolf Fick formulated laws that provide the mathematical framework for describing molecular diffusion in solids, liquids, and gases. Fick’s first law of diffusion applies under steady-state conditions, when the concentration profile does not change with time. The law states that the rate of flow of a diffusing substance (its diffusive flux density) is proportional to the concentration gradient. It can be mathematically expressed as $J = -D\left(\frac{dc}{dx}\right)$, where J is the diffusive flux (the amount of substance passing through a reference surface of unit area per unit time), x is the coordinate perpendicular to this reference surface, c is the concentration of the substance, and D is the diffusion coefficient (diffusivity), whose magnitude determines how rapidly diffusion occurs. Diffusivity (D) depends on the nature of the diffusing substance, the medium, and temperature. The term $\frac{dc}{dx}$ represents the rate of change of concentration in the direction x, and the minus sign indicates that the flow is from higher to lower concentration.

Fick’s second law of diffusion is applicable to nonsteady-state systems where the concentration varies with time or the solution is not uniform throughout. It is given by $\frac{dc}{dt } = D\frac{d^{2}c}{d{x}^2}$, where $\frac{dc}{dt}$ represents the rate of change of concentration over time at a specific location and $\frac{d^{2}c}{d{x}^2}$ represents how the concentration gradient changes with distance.

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principles of physical science: Diffusion

Diffusion around us

Heat conduction in fluids involves thermal energy being transported by diffusion from higher to lower temperature regions. Operation of a nuclear reactor involves the diffusion of neutrons through a medium that causes frequent scattering but only rare absorption of neutrons. The movement of oxygen during respiration is an example of diffusion. Oxygen diffuses from the air in the lungs’ alveoli (tiny air sacs), where its concentration is higher, into the pulmonary capillary blood, where its concentration is lower. The oxygen-rich blood then transports oxygen to the body’s cells and tissues, where it diffuses from the blood into the cells down its concentration gradient. Conversely, carbon dioxide, produced by cellular metabolism, diffuses from the cells, where its concentration is higher, into the blood, where its concentration is lower. The carbon dioxide is then transported to the lungs, where it diffuses into the alveoli and is expelled during exhalation.