Which state of gas highest thermal diffusion coefficient?
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Diffusion Coefficient and Laws: Fick’s Laws | Metallurgy
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Fick proposed laws governing the diffusion of atoms and molecules, which can be applied to the diffusion processes in metals and alloys. He proposed two laws, the first for steady-state condition and unidirectional flow of atoms and the second law which deals with time dependence of concentration gradient; and the flow of atoms in all directions.
Fick’s First Law:
Pick’s first law describes the rate at which diffusion occurs under steady-state conditions.
This states that-
Where, dm = The amount of diffusing element that migrates in time dt across a surface of cross-section A lying between two points and being normal to the axis of the bars,
D = Diffusion coefficient,
(The diffusion coefficient; D, may be defined as the amount of substance diffusing in unit time across a unit area through a unit concentration gradient and is generally expressed in cm2/s or m2/s)
A = Area of plane across which diffusion tables place,
dC / dx = The concentration gradient in the X-direction, and
dt = Duration of diffusion.
The negative sign indicates that the flow of matter occurs down the concentration gradient.
The first law entails the following assumptions:
(i) The flux of diffusing atoms is constant throughout in the given direction and is independent of time.
(ii) The jump length is constant, equal to the Burger’s vector of the structure.
(iii) There is only one jump per atom at a time which means that jump frequency is constant.
By definition, the flux J is flow per unit cross-sectional area per unit time so that, Pick’s first law can also be written as-
Under steady-state flow, the flux is independent of time and remains the same at any cross- sectional plane along the diffusion direction.
Fig. 4.6 shows that the concentration gradient varies with x. A large negative slope corresponds to a high diffusion rate. The B atoms will diffuse from the left side in accordance with Pick’s first law. The net migration of B atoms to the right side means the concentration will decrease on the left side of the solid and increase on the right side as diffusion progresses.
Fick’s law is identical in form to Fourier’s law for heat flow under a constant temperature gradient and Ohm’s law for current flow under a constant electric field gradient.
Diffusion Profiles under Steady-State of Flow:
Under steady-state of flow, the flux of atoms flowing is independent of time and remains constant at all cross-sections along the diffusion direction. The profiles are illustrated in Fig. 4.7.
If D = f (C), the profiles will be such that the product D. dC/ dx remains constant. In both the cases the profile does not change with time.
In both the cases the profile does not change with time.
Practical Example of Steady-State Diffusion:
One practical example of steady-state diffusion is found in purification of hydrogen gas. One side of a thin sheet of palladium metal is exposed to the impure gas composed of hydrogen and other gaseous species such as nitrogen, oxygen, and water vapour. The hydrogen selectively diffuses through the sheet to the opposite side, which is maintained at a constant and lower hydrogen pressure.
Fick’s Second Law-Time Dependence:
Fick’s first law permits the calculation of instantaneous mass flow rate (flux) past any plane in a solid but gives no information about the time dependence of the concentration. The time dependence is contained in Fick’s second law, which can be derived using Fick’s first law and second law of conservation of mass.
Fick’s second law states that:
For non-steady state processes, at the same cross- section, the flux is not the same at different times. Hence the concentration-distance profile (Fig. 4.8) changes with time (t).
The differential form of Fick’s second law is the basic equation for the study of isothermal diffusion.
Derivation of Fick’s Second Law:
Consider an elemental slab of thickness Ax along the diffusion distance x. Let the slab X- section be perpendicular to x and its area be unity. The volume of the slab is then ∆x x 1 = ∆x.
Explanation: