How a 26-Year-Old Physician Revolutionized Science
Celebrating 150 years of the fundamental principles that predict how our world mixes and moves on a molecular scale
Explore the LegacyImagine a world where oxygen cannot reach our bloodstream, the aroma of coffee never drifts across a room, and life-saving medications cannot disperse within our bodies. This would be reality without the fundamental process of diffusion—the silent, omnipresent force that causes molecules to move from regions of high concentration to low concentration.
For 150 years, our understanding of this crucial process has been guided by Fick's Laws of Diffusion, formulated by a young physiologist, Adolf Fick. His insights, born from simple experiments with salt and water, have become a cornerstone of fields as diverse as medicine, environmental science, and material engineering 8 . This article explores the enduring legacy of Fick's work on its sesquicentennial, uncovering the story behind the laws that predict how our world mixes and moves on a molecular scale.
In 1855, Adolf Eugen Fick, a 26-year-old physician working with his mentor Carl Ludwig at the University of Zürich, published a paper that would bridge the gap between physiology and physics 1 8 . At a time when diffusion in solids was not even considered possible, Fick sought a mathematical description for the movement of dissolved particles in fluids 1 .
Inspired by Joseph Fourier's work on heat conduction and building upon the experimental findings of Thomas Graham, Fick proposed that the diffusion of mass could be described with the same mathematical rigor as the flow of heat 2 8 . Despite apparent discrepancies in his own experimental results, he pressed forward, demonstrating remarkable scientific intuition 8 . This cross-disciplinary approach was pioneering for its time, and the laws he formulated have since become a fundamental part of curricula from secondary schools to postgraduate programs 8 .
Formulated his laws at just 26 years old while working at the University of Zürich.
Applied Fourier's heat conduction principles to molecular diffusion.
Grounded his theoretical work in careful experiments with salt and water.
Fick's Laws are two simple yet powerful statements that quantify the process of diffusion.
Fick's First Law describes diffusion under steady-state conditions, where concentrations might differ between points but do not change over time. It states that the diffusive flux (J)—the amount of substance flowing through a unit area per unit time—is proportional to the negative of the concentration gradient 1 7 .
The negative sign indicates that diffusion occurs down the concentration gradient, from high to low concentration 1 6 . The constant of proportionality, D, is the diffusion coefficient, a material-specific property that measures how easily a particle can move through a particular medium 1 5 .
While the first law is powerful, most real-world scenarios involve concentrations that change with time. Fick's Second Law accounts for these non-steady-state conditions, predicting how the concentration profile evolves 2 7 . In one dimension, it is expressed as a partial differential equation:
This law states that the rate of change of concentration at a specific point is proportional to the second derivative of the concentration with respect to space—essentially, the "curvature" of the concentration profile 1 3 . It is this law that allows scientists to model how a pollutant spreads through a lake or how a drug permeates a tissue over time.
Fick was not only a theoretician; he grounded his laws in careful experiment. His setup was elegant in its simplicity, designed to measure the diffusion of salt in water 1 5 .
Fick used two reservoirs of water connected by a tube. One reservoir contained a solution of salt, while the other contained pure water 1 .
This setup established a well-defined concentration gradient between the two reservoirs—the driving force for diffusion 1 .
He carefully measured the concentrations of salt in the two reservoirs over time, allowing him to determine the concentration gradient. Simultaneously, he tracked the flux (J) of salt—the amount passing through the connecting tube per unit area per unit time 1 .
By analyzing the relationship between the measured flux and the concentration gradient, Fick confirmed it was linearly proportional. The constant of proportionality he determined was the diffusion coefficient (D) for salt in water 1 .
Fick's experiments confirmed that the rate of diffusion was directly proportional to the concentration gradient. This was a revolutionary quantitative confirmation that diffusion could be described by a precise mathematical law, analogous to Fourier's law for heat or Ohm's law for electricity 1 2 .
Despite his own noted "apparent discrepancies," the core relationship held true and provided the experimental bedrock for his first law. The second law was then derived mathematically from the first, combined with the principle of mass conservation 1 . This pair of laws formed a complete framework for predicting the transport of mass by diffusion.
Simplified representation of Fick's experimental apparatus with salt solution and pure water reservoirs connected by a diffusion pathway.
The power of Fick's laws lies in their ability to make quantitative predictions. The following tables showcase the key variables and real-world data that bring these equations to life.
| Term | Symbol | Meaning | SI Units | Dimensional Formula |
|---|---|---|---|---|
| Diffusion Flux | J | The amount of substance passing through a unit area per second | mol/m²·s | mol·L⁻²·T⁻¹ |
| Diffusion Coefficient | D | Measures how fast particles spread through a specific medium | m²/s | L²·T⁻¹ |
| Concentration Gradient | ∂φ/∂x | The rate of change of concentration with distance | mol/m⁴ | mol·L⁻⁴ |
| Substance Pair | Diffusion Coefficient (m²/s) |
|---|---|
| NaCl in Water | 1.24 × 10⁻⁹ |
| N₂ in Water | 2.00 × 10⁻⁹ |
| CO₂ in Water | 1.80 × 10⁻⁹ |
| CO₂ in Air | 1.37 × 10⁻⁵ |
| Water Vapor in Air | 2.20 × 10⁻⁵ |
Higher temperature increases particle kinetic energy, speeding up diffusion.
A steeper gradient (larger concentration difference) results in a faster rate.
Smaller particles diffuse more rapidly than larger ones.
Diffusion is faster in gases than liquids, and slowest in solids.
The experimental and applied study of diffusion relies on several key components, many of which were present in Fick's original work.
The substance of interest whose movement is being tracked (e.g., salt, oxygen, a dye, a drug molecule). Its properties, particularly size, largely determine its diffusion coefficient 1 .
The fluid (e.g., water, air) or solid through which diffusion occurs. The medium's viscosity and temperature dramatically affect the diffusion rate 1 5 .
A permeable layer that separates two regions, creating a concentration gradient. Its thickness and permeability are critical parameters, especially in biological and industrial applications 4 6 .
Essential for quantifying the gradient and flux. Modern tools might include spectrophotometers, chemical sensors, or chromatographs, while Fick used more direct analytical methods of his time 1 .
The principles established by Fick 150 years ago continue to find new applications across diverse scientific and engineering fields.
Fick's Laws explain the fundamental life-sustaining process of gas exchange in our lungs 4 , where oxygen diffuses from alveoli into blood and carbon dioxide diffuses out.
Pharmaceutical scientists use Fick's Laws to design controlled-release medications that deliver drugs at optimal rates through various barriers in the body 6 .
In microelectronics, Fick's Laws guide the doping processes that create p-n junctions in semiconductors, enabling the design of devices that power the modern world 6 .
Fick's Laws are essential in modeling environmental pollution dispersion in air and water, helping predict how contaminants spread through ecosystems 2 .
One hundred and fifty years after their formulation, Fick's Laws of Diffusion remain as relevant as ever.
The story of Fick's Laws is a testament to the power of cross-disciplinary thinking. A young physiologist, drawing inspiration from physics, laid down a mathematical framework that would become a universal language for describing mass transport.
As we commemorate this sesquicentennial, we celebrate not just the laws themselves, but the enduring spirit of inquiry and synthesis they represent—a reminder that the most profound insights often come from connecting the dots between different fields of human knowledge.
Years of Scientific Impact
Age When Laws Were Formulated
Simple Yet Powerful Equations