Complex coacervation is the food-industry method used to wrap omega-3 fish-oil or vitamin oil droplets in a nanoscale wall of two oppositely charged biopolymers — typically a globular protein (whey/pea, net-positive below its isoelectric point pI≈4.5–5.0) and an anionic polysaccharide (gum arabic, pectin). The two chains associate electrostatically and deposit onto the oil–water interface as a coacervate shell.
Charge-density mismatch (Gaussian pH-optimum model):
ξ(pH) = exp( -(pH - pH_opt)² / (2σ²) ) pH_opt ≈ 4.3, σ ≈ 1.1
Debye screening of the electrostatic driving force:
κ⁻¹ ∝ 1/√I (I = ionic strength, mM NaCl)
ξ_eff = ξ(pH) · Screen(I), Screen(I) = 1 / (1 + I/I₀), I₀ ≈ 60 mM
Wall growth (deposition-limited, saturating):
thickness(t) = t_max · ξ_eff · (1 - e^(-t/τ))
Oxygen-barrier / shelf-life proxy (thicker, denser wall ⇒ lower O₂ flux):
Perm ∝ 1 / thickness² (Fickian barrier scaling)
shelf life ∝ thickness² · ξ_eff
- pH sets how strongly the protein's net charge (positive below its isoelectric point) mismatches the polysaccharide's fixed negative charge — complexation peaks in a narrow window around pH≈4.3, exactly as in real whey-protein / gum-arabic systems.
- Protein : polysaccharide ratio shifts which species dominates the wall; a very lopsided ratio starves the shell of the minority polymer and thins it.
- Ionic strength screens electrostatic attraction (Debye screening) — added salt competes for charged sites and suppresses coacervation, just as it does on the bench.
- Core / oil load is the oil-to-wall-material mass fraction; a higher load means less wall polymer available per droplet, which lowers encapsulation efficiency even at optimal pH.
- The oxygen-permeability and shelf-life readouts are a simplified Fickian barrier-scaling estimate (permeability falls as the square of wall thickness) — this is the physical reason nanoencapsulation protects omega-3 and other oxidation-sensitive nutrients far better than leaving the oil unprotected.
Drag the main view left/right to rotate the cross-section and watch chains dock onto the shell from every side. Charged polymer chains (small dots, colored by species) drift toward the oil core and lock onto its surface once ξ_eff is high enough — at a poor pH or high salt they wander loosely instead, and the shell stays thin and porous.