A hydrophobic drug molecule dissolved in water can partition into the nonpolar core of a surfactant micelle. At equilibrium the ratio of drug concentration inside the cores to drug concentration in water defines the (dimensionless) micelle/water partition coefficient:
P = C_core / C_water, log P shown by the slider
Because each micelle core has a finite volume, it can only hold a limited number of drug molecules — this simulation caps that at the "core loading capacity" slider. With a finite number of binding sites, the equilibrium fraction of drug solubilized follows a Langmuir-type binding isotherm rather than a simple constant ratio:
θ = P·[D_free] / (1 + P·[D_free])
S = N_micelles × capacity (total core sites)
Solve for free drug f: P·f² + (1 + P·S − N·P)·f − N = 0
Each frame, every free drug molecule performs a clamped random walk (Brownian motion, reflecting off the container walls). When it drifts within capture range of a micelle whose core is not full, it binds with probability 1 − e−k_on·dt, where k_on scales with 10log P; a bound molecule can also escape back into the water with probability 1 − e−k_off·dt. Raising log P favors binding over escape, exactly like a more hydrophobic drug (e.g. paclitaxel, log P ≈ 3) loading far more readily than a borderline one.
- Partition coefficient (log P) — how strongly the drug prefers the hydrophobic core over water.
- Micelle concentration — number of micelles in the compartment (above the critical micelle concentration, more micelles means more available core sites).
- Core loading capacity — how many drug molecules a single micelle core can physically hold before it saturates.
- Diffusion rate — how fast drug molecules random-walk through the aqueous phase (a proxy for temperature).
Real-world relevance: this is the mechanism used to formulate poorly water-soluble drugs (paclitaxel, cyclosporine, many oncology payloads) inside amphiphilic block-copolymer or surfactant micelles for intravenous delivery.