Keith Mack
Fick's First Law of Diffusion, formulated by German physiologist Adolf Fick in the 19th century, describes the rate at which particles (such as molecules, atoms, or ions) diffuse through a medium. The law states that substances will diffuse from areas of high concentration to lower concentration, and the rate of diffusion is directly proportional to the concentration gradient. In other words, Fick's First Law relates the diffusive flux to the gradient of the concentration. The diffusion coefficient, also known as D, is a proportionality constant that depends on the particular substance being measured. This law can only be applied when the conditions within the system are constant, with the flux going in equal to the flux going out.
| Characteristics | Values |
|---|---|
| Fick's First Law | The rate of diffusion of a substance through a medium is directly proportional to the concentration gradient. |
| Flux | Represented by 'y' on the vertical axis of a graph. |
| Gradient | Represented by 'x' on the horizontal axis of a graph. |
| Proportionality Constant | The diffusion coefficient, 'D'. |
| Diffusion Coefficient | Can be calculated if the flux and the change in concentration over time are known. |
| Diffusion Process | If it obeys Fick's First Law, it is called normal or Fickian diffusion; if not, it is called anomalous or non-Fickian diffusion. |
| Application | Can only be accurately applied when the conditions within the system are constant, i.e., the flux going in is the same as the flux going out. |
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What You'll Learn
Flux and the change in concentration over time
Fick's First Law of Diffusion, formulated by Adolf Fick in 1855, describes the phenomenon of diffusion, or the intermingling of substances through the movement of their particles. Fick's First Law states that flux is directly proportional to the concentration gradient. In other words, substances will diffuse from areas of high concentration to lower concentration.
The diffusion process can be represented by the following equation:
> J =-D(dφ/dt) = (-D * A * ΔC)/Δx
Where:
- J is the diffusion flux, or the amount of substance per unit area per unit time.
- D is the diffusion coefficient or diffusivity, which represents the squared velocity of the diffusing particles and depends on factors such as temperature, viscosity, and particle size.
- A is the cross-sectional area being considered.
- Δx is the length of the section being considered.
- ΔC is the change in concentration.
The number of particles in a certain volume is the concentration C, so the flux equation can be expressed in terms of the change in concentration over time. The units of dC/dt are mol cm-3 s-1.
Fick's First Law applies in one, two, or three dimensions. In three dimensions, the flux in each direction is proportional to the rate of concentration change in that direction. The overall molecule motion follows the shortest path to a less crowded region.
Fick's First Law can only be applied when the conditions within the system are constant, meaning the flux going in must be equal to the flux going out.
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Diffusion coefficient
Fick's First Law of Diffusion, formulated by Adolf Fick in 1855, states that substances will diffuse from areas of high concentration to areas of low concentration. The law relates the diffusive flux to the gradient of the concentration. Flux is directly proportional to the concentration gradient, and the proportionality constant is the diffusion coefficient, represented as 'D'.
The diffusion coefficient is defined as a measure of the net collective motion of diffusing species in the presence of a concentration gradient. It is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit. It is usually expressed in the units cm2 s−1. The diffusion coefficient is a physical constant that depends on molecule size, temperature, pressure, and other properties of the diffusing substance. It is a property of a solute in a specific medium or matrix at a constant temperature and pressure.
The diffusion coefficient can be calculated in a homogeneous polymer membrane from the steady-state flux data. It can also be determined from steady-state fluxes or lag times from a membrane permeation study, or from release data of other well-defined systems at a constant temperature. In multicomponent systems, the Maxwell-Stefan equation can be used to derive the diffusion coefficient. The diffusion coefficient in liquids can be determined using the Stokes-Einstein equation, which is based on the model of motion of a spherical particle of the diffusing substance in a viscous liquid.
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Diffusion flux and the gradient of concentration
Fick's First Law of Diffusion, formulated by Adolf Fick in 1855, describes the movement of particles from high to low concentration. It states that flux is directly proportional to the concentration gradient, and the proportionality constant D is the diffusion coefficient.
The concentration gradient is a fundamental concept in diffusion, representing the change in concentration over distance. It is calculated as the difference in concentration between two points, divided by the distance between them. In Fick's First Law, the concentration gradient is a driving force that causes substances to spread out and move from regions of high concentration to regions of low concentration. This movement of substances is known as diffusion.
Diffusion is the intermingling of substances by the natural movement of their particles. It is a stochastic process due to the inherent randomness of the diffusing entity. The central idea of diffusion is that a substance undergoing diffusion spreads out from a point of higher concentration. Fick's First Law can be applied to understand and predict the behaviour of substances in various states of matter, including solids, liquids, and gases.
The diffusion coefficient, denoted as "D", is a crucial constant in Fick's First Law. It represents the proportionality between flux and the concentration gradient. The value of "D" depends on the specific substance being measured and the conditions under which diffusion occurs. By calculating and knowing the value of "D", scientists can determine the rate at which substances will diffuse under given conditions.
Fick's First Law can be represented graphically, with flux plotted on the vertical axis (y-axis) and the concentration gradient plotted on the horizontal axis (x-axis). The flux depends on two factors: the steepness of the concentration gradient and the diffusion coefficient "D". When the conditions within the system are constant, Fick's First Law can be applied to accurately describe the diffusion process.
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Diffusion in cooking
Fick's First Law of Diffusion, discovered by physiologist Adolf Fick in 1855, states that substances will diffuse from areas of high concentration to areas of low concentration. This law is central to many everyday phenomena, including cooking.
Diffusion is the intermingling of substances by the natural movement of their particles. In cooking, this process is essential for developing flavour. For example, when making soup stock, cooks will often simmer meat and vegetables for several hours to extract their flavour. Chopping the vegetables into smaller pieces increases the area of the vegetable-water interface, allowing more molecules to diffuse into the stock per unit of time. This process can be understood through Fick's First Law, which states that flux is directly proportional to the concentration gradient. In this case, the flux is the number of molecules diffusing into the stock, and the concentration gradient is the difference in concentration between the vegetables and the stock.
Fick's First Law can also be applied to other cooking techniques, such as brining and marinating. These techniques involve the diffusion of salt and sugar molecules into meat. Additionally, Fick's First Law can be used to predict the changing moisture profiles across a spaghetti noodle as it hydrates during cooking. The temperature of the water affects how quickly the molecules move, with hotter water causing the molecules to move faster and the dye to diffuse more rapidly.
It's important to note that Fick's First Law assumes constant conditions within the system. Factors such as convection or air currents, which are common in cooking, can facilitate diffusion but are not accounted for in the law. Nonetheless, Fick's First Law provides valuable insights into the diffusion processes that occur during cooking.
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Optical diffusion
Fick's First Law of Diffusion, formulated by physiologist Adolf Fick in 1855, describes the phenomenon of diffusion, which is how gases and fluids spread and mix. The law states that substances will diffuse from areas of high concentration to lower concentration. In other words, flux is directly proportional to the concentration gradient.
Fick's First Law can be represented on a graph, with flux plotted on the vertical axis and the gradient on the horizontal axis. The flux depends on two quantities: the steepness of the gradient and a proportionality coefficient, or the diffusion coefficient "D", based on the particular substance being measured. The diffusion coefficient is a constant that relates the diffusive flux to the gradient of the concentration.
Fick's First Law can only be accurately applied when the conditions within the system are constant, and the flux going in is equal to the flux going out. It is important to note that diffusion can be facilitated by factors that Fick's Law does not take into account, such as convection or air currents, which assist in spreading particles.
Now, let's shift our focus to optical diffusion. In optics, a diffuser, or optical diffuser, is any material that diffuses or scatters light to transmit soft light. Diffused light can be achieved by reflecting light off a white surface or using translucent materials such as ground glass, Teflon, opal glass, or greyed glass. Optical diffusers are used to evenly spread light across a surface, reducing or eliminating bright spots. They are commonly employed in LED illumination systems, photography, film lighting, and stage lighting to create a hazy or softened lighting effect.
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Frequently asked questions
Fick's First Law of Diffusion states that substances will diffuse from areas of high concentration to lower concentrations. This law describes the rate at which particles (such as molecules, atoms, or ions) diffuse through a medium.
The proportionality constant 'D' is the diffusion coefficient. The diffusion coefficient can be solved for with Fick's laws of diffusion, which are broken up into two laws. For light, the diffusivity is proportional to the diffusion length 'D' in cm and the speed of light 'c'.
Fick's First Law can be expressed as the energy flux J [W cm-2] proportional to the diffusion constant D [cm] and the negative fluence gradient dF/dx.
