Fick's Law

  • Gases dissolved in liquids (See: Gases in Liquids) move randomly throughout the liquid in a thermodynamic process described as diffusion. While the diffusion rates of a gas within a continuous body of liquid is constant, the presence of a barrier within the liquid can substantially affect the diffusion rate of the gas. The rate at which gases can diffuse across membranes is an important aspect of respiratory physiology as oxygen and carbon dioxide must cross the alveolar membrane during the gas exchange process. Consequently, it is important to appreciate the physical laws which govern diffusion of dissolved gas across membranes as they heavily inform our understanding of the gas exchange process at the alveolar membrane. Fick's Law describes the rate at which a dissolved gas diffuses across a membrane given certain proporties of the membrane and gas.
Fick's Law
  • Overview
    • Fick's Law essentially states that the rate of diffusion of a gas across a permeable membrane is determined by the chemical nature of the membrane itself, the surface area of the membrane, the partial pressure gradient of the gas across the membrane, and the thickness of the membrane.
  • Fick's Law
    • V'gas = D * A * ΔP/T
    • V'gas = Rate of gas diffusion across permeable membrane
    • D = Diffusion coefficient of that particular gas for that membrane
    • A = Surface Area of the membrane
    • ΔP = Difference in partial pressure of the gas across the membrane
    • T = Thickness of the membrane
  • Qualitative Relationships
    • Fick's Law takes into account that the diffusion of a gas across a membrane depends on the unique chemical properties of the membrane and the gas and how they interact. For example, the chemical hydrophobicity of the gas and membrane are important variables in determining how permeable the membrane will be to the gas. These considerations are generically packaged into the "D" variable which is typically determined empirically. Whatever the particular chemical nature of the gas and membrane, Fick's law states the intuitively intelligible notion that the rate of gasvdiffusion is proportional to the available surface area (A) while inversely proportional to the thickness of the membrane (T). The actual physical factor that actuates unidirectional diffusion of gas across a membrane is the difference in partial pressure of the gas across the membrane and this is captured in the ΔP variable; consequently, the diffusion rate is proportional to the size of the partial pressure gradient. Although the variables of D, A, and T may be easily determined in controlled experimental settings, they are virtually impossible to mathematically determine for any individual's lung. Consequently, the physiological variable of Diffusing Capacity has been developed to combine these immeasurable factors.

Qualitative Relationships in Fick’s Law
The top box shows a pressure gradient across a membrane (purple). The rate of diffusion of gas across this membrane can be increased either by increasing the area (A), reducing the thickness (T), increasing the molecular similarity of the gas to the membrane (D), or increasing the pressure gradient across the gradient (ΔP).