Molecular diffusion occurs by any of what four driving forces or potentials? Which one is the most common? What is the bulk-flow effect in mass transfer? How does Fick’s law of diffusion compare to Fourier’s law of heat conduction? What is the difference between equimolar counterdiffusion (EMD) and unimolecular diffusion (UMD)?
The correct answer and explanation is :
Molecular Diffusion and Driving Forces
Molecular diffusion occurs due to four main driving forces or potentials:
- Concentration Gradient: The difference in concentration of a substance across space.
- Temperature Gradient: The difference in temperature that affects molecular motion.
- Pressure Gradient: The difference in pressure which influences the movement of gases or liquids.
- Electric Potential Gradient: The difference in electric potential which drives the movement of charged species (ions).
The most common driving force for molecular diffusion is the concentration gradient because it is present in most natural and industrial systems, where particles move from areas of higher concentration to areas of lower concentration.
Bulk-Flow Effect in Mass Transfer
The bulk-flow effect in mass transfer refers to the macroscopic movement of fluid or gas due to a driving force, like pressure or concentration gradient, which leads to the movement of molecules over large distances. This contrasts with molecular diffusion, where individual molecules move randomly from high to low concentration. Bulk flow typically dominates in situations with large gradients (like pressure differences), and it impacts the overall transport of mass in processes like fluid flow in pipes or air movement in the atmosphere.
Fick’s Law vs. Fourier’s Law
Fick’s Law of Diffusion and Fourier’s Law of Heat Conduction are analogous in their forms:
- Fick’s Law describes the diffusion of particles and is given by:
( J = -D \frac{dC}{dx} )
where ( J ) is the flux, ( D ) is the diffusion coefficient, and ( \frac{dC}{dx} ) is the concentration gradient. - Fourier’s Law describes heat conduction and is given by:
( q = -k \frac{dT}{dx} )
where ( q ) is the heat flux, ( k ) is the thermal conductivity, and ( \frac{dT}{dx} ) is the temperature gradient.
Both laws follow a similar principle: the flux (whether mass or heat) is proportional to the gradient (concentration or temperature) and inversely proportional to a property (diffusivity or thermal conductivity).
Equimolar Counterdiffusion (EMD) vs. Unimolecular Diffusion (UMD)
- Equimolar Counterdiffusion (EMD) refers to the diffusion of two species in opposite directions with the total molar flux being zero. It is typical when two different gases diffuse in a closed system such that the net flow of material is balanced.
- Unimolecular Diffusion (UMD), on the other hand, refers to the diffusion of a single species, often in a medium, where the species moves from high to low concentration without any opposing species.
In summary, while both are forms of diffusion, EMD involves multiple species moving in opposite directions, while UMD focuses on the movement of one species alone.