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[ \frac\partial C\partial t = D_\texteff \left( \frac\partial^2 C\partial r^2 + \frac2r \frac\partial C\partial r \right) ] Where (D_\texteff) = effective diffusivity (depends on temperature and solid structure).
Fick's law of diffusion often applies. The rate is controlled by:
| Parameter | Effect | Optimization Rule | | :--- | :--- | :--- | | | Smaller particles = larger surface area, faster extraction. | Crush or grind – but avoid excessive fines that cause clogging. | | Temperature | Higher temp = higher solubility & faster diffusion. | Maximum possible without degrading heat-sensitive solutes. | | Solvent Choice | Must dissolve solute but not solid. | "Like dissolves like" – polarity matching is key. | | Agitation | Reduces boundary layer resistance. | Moderate stirring – too vigorous may cause emulsification. | | Contact Time | Longer time increases yield (but diminishing returns). | Determine equilibrium time via pilot tests. | | Solvent-to-Solid Ratio | More solvent = higher driving force. | Balance yield vs. downstream concentration costs. |
Smaller particles have a higher surface-area-to-volume ratio, which shortens the distance the solvent must travel to reach the solute.
To maximize the yield of the desired compound, chemical engineers focus on several variables:
The "leaching" of gold, silver, and copper from ore using specific chemical solvents.
The solid and solvent are mixed in a vessel, allowed to reach equilibrium, and then separated. This is common in small-scale herbal extractions.
[ \frac\partial C\partial t = D_\texteff \left( \frac\partial^2 C\partial r^2 + \frac2r \frac\partial C\partial r \right) ] Where (D_\texteff) = effective diffusivity (depends on temperature and solid structure).
Fick's law of diffusion often applies. The rate is controlled by: solid liquid solvent extraction
| Parameter | Effect | Optimization Rule | | :--- | :--- | :--- | | | Smaller particles = larger surface area, faster extraction. | Crush or grind – but avoid excessive fines that cause clogging. | | Temperature | Higher temp = higher solubility & faster diffusion. | Maximum possible without degrading heat-sensitive solutes. | | Solvent Choice | Must dissolve solute but not solid. | "Like dissolves like" – polarity matching is key. | | Agitation | Reduces boundary layer resistance. | Moderate stirring – too vigorous may cause emulsification. | | Contact Time | Longer time increases yield (but diminishing returns). | Determine equilibrium time via pilot tests. | | Solvent-to-Solid Ratio | More solvent = higher driving force. | Balance yield vs. downstream concentration costs. | | Crush or grind – but avoid excessive
Smaller particles have a higher surface-area-to-volume ratio, which shortens the distance the solvent must travel to reach the solute. | | Solvent Choice | Must dissolve solute but not solid
To maximize the yield of the desired compound, chemical engineers focus on several variables:
The "leaching" of gold, silver, and copper from ore using specific chemical solvents.
The solid and solvent are mixed in a vessel, allowed to reach equilibrium, and then separated. This is common in small-scale herbal extractions.