Extraction

Liquid–liquid extraction transfers a solute from one liquid to an immiscible solvent. Learn distribution coefficients, extraction factor, single-stage, cross-current and counter-current extraction, solvent selection, ternary diagrams and equipment (mixer–settlers, columns, centrifugal extractors).

When distillation is impossible or too costly (heat-sensitive compounds, close boiling points, azeotropes), extraction uses a second liquid that dissolves the target selectively. Pharmaceuticals, metals (hydrometallurgy), aromatics and food flavours are recovered this way.

The solvent must then be separated from the solute, often by distillation.

An analogy

Making tea: hot water extracts flavour from leaves. Two short brews with fresh water extract more than one long brew with the same total water.

Principle

Feed (raffinate phase) and solvent (extract phase) are mixed then separated. Solute distributes between phases according to K_D; high K_D means the solvent strongly prefers the solute.

Stage arrangements

Single stage is simple but limited; cross-current uses fresh solvent in each stage; counter-current flows solvent and feed in opposite directions and gives the best use of solvent — standard in industry.

Solvent selection

High selectivity and capacity, immiscibility with the feed, density difference for settling, low viscosity, easy recovery, safety and cost. Ternary (triangular) diagrams show phase regions and tie lines for partially miscible systems.

Equipment and special extractions

Mixer–settlers, agitated columns (Scheibel, Kühni), pulsed columns and centrifugal extractors (Podbielniak). Supercritical CO₂ extraction (decaffeination, essential oils), reactive extraction and ionic liquids broaden applications.

Formulas

• Single stage (fraction remaining): x₁/x₀ = 1/(1 + E)
• Cross-current, n stages (S/n each): x_n/x₀ = 1/(1 + E/n)ⁿ
• Counter-current (Kremser): x_N/x₀ = (E − 1)/(E^(N+1) − 1)

Worked example: Single vs cross-current

Given: K_D = 4, S/F = 1 (E = 4)

Find: Solute remaining.

• One stage: 1/5 = 20 %
• Two stages with half solvent each (E = 2): (1/3)² = 11.1 %
• Three stages (E = 1.33 each): 7.9 %

Answer: 20 % → 11.1 % → 7.9 %

Worked example: Counter-current

Given: E = 4, N = 2

Find: Remaining fraction.

• x_N/x₀ = (4 − 1)/(4³ − 1) = 3/63 = 4.8 %

Answer: ≈ 4.8 % (vs 11.1 % cross-current)

Common mistakes

• Wrong: Using all solvent in a single stage. — Right: Staging (especially counter-current) greatly improves recovery.
• Wrong: Ignoring solvent recovery cost. — Right: Solvent must be separated and recycled — include that step.

Applications

• Pharmaceuticals: Antibiotic and API recovery from fermentation broths.
• Hydrometallurgy: Copper, uranium and rare-earth solvent extraction.
• Petrochemicals & food: Aromatics extraction (sulfolane), decaffeination with supercritical CO₂.

Key takeaways

• K_D sets partitioning; E = K_D S/F.
• Single: 1/(1 + E); counter-current: (E − 1)/(E^(N+1) − 1).
• Counter-current staging uses solvent best.
• Plan solvent recovery.

Going further

• Ternary diagrams: Hunter–Nash stage construction for partially miscible systems.
• pH-swing extraction: Ionisable solutes switch phases with pH (common in pharma).
• Centrifugal contactors: Short residence time for unstable compounds.