Left: plate with a grease patch shrinking as G(t) falls. Right: live grease-remaining curve for the current cycle.
This simulation models how dish soap lifts a grease film off a plate. Rather than a single "cleaning speed" knob, the removal rate constant k is built from a Langmuir adsorption isotherm for how much surfactant reaches the grease-water interface at a given soap concentration, an Arrhenius temperature term, and a scrubbing multiplier — the same building blocks used in the laundry stain-removal kinetics model, applied to a different surface chemistry problem.
A plate with a grease patch that shrinks and fades as coverage G(t) falls, alongside a live G(t) vs time chart and a suds-bubble count that scales with soap concentration.
Drag Soap Concentration, Water Temperature, Scrubbing Intensity and Cycle Duration to watch the rate constant k, time to 50% removal, and remaining grease update live.
The Langmuir isotherm θ = C/(C+K_L) is the same equation chemists use for gas adsorption onto a solid catalyst — surfactant molecules occupying interfacial binding sites behave the same way, which is why extra dish soap past a point barely speeds things up.
The Langmuir isotherm models a finite number of binding sites at the grease-water interface that surfactant molecules can occupy. At low concentration, coverage rises almost linearly with soap added; as sites fill up, coverage saturates near 1 — matching how real dishwashing shows diminishing returns from adding more soap.
Warmer water lowers the melting/softening point effect on many grease and fat films and speeds the molecular processes that let surfactant emulsify them into the wash water — modelled here with the same Arrhenius-style exponential factor used for reaction rates generally.
Scrubbing is a simple multiplier on the rate constant, reflecting how mechanical action helps break up the grease layer and carry it into the surrounding water faster than chemistry alone would.
It uses the same first-order decay structure (dG/dt = −k·G) but swaps the detergent-dose term for a Langmuir adsorption isotherm, which is the more standard way surface chemists describe surfactant coverage of an interface at a given bulk concentration.