Silver Nanoparticle Antibacterial Kinetics

Nanoparticle Dose

Particle diameter 30 nm

Nanoparticle dose 10 mg/L

Time scale 4 h/s

Live Readouts

Dissolved Ag⁺

0.00 µM

Viability

100 %

Elapsed exposure time

0.0 h

How it works

Silver nanoparticles kill bacteria mainly by dissolving into Ag⁺ ions, not through direct particle contact. Dissolution rate is a surface reaction, so it scales with the particle's surface-to-volume ratio, which for a sphere of radius r is:

S/V = 3/r

Halving the diameter triples the ion-release rate per unit mass. This simulator integrates a Noyes–Whitney-style dissolution ODE for the dissolved Ag⁺ concentration C:

dC/dt = k0 · (3/r) · N · (Csat − C)

where N is the nanoparticle number density (set by the dose slider) and Csat is the saturation ion concentration. The released Ag⁺ then kills bacteria following pseudo-first-order Chick–Watson disinfection kinetics, the same CT (concentration × time) law used to size water-treatment disinfectant doses:

dNbact/dt = −kkill · C · Nbact
Viability(t) = Nbact(t) / Nbact(0) × 100%

Each rod in the colony carries its own randomised susceptibility threshold on the integrated Ag⁺ dose (∫C dt), so cells die in a staggered wave rather than all at once — smaller nanoparticles reach lethal cumulative dose far sooner because of their higher S/V ratio.

Particle diameter — sets r in S/V = 3/r; smaller particles dissolve faster per gram.
Nanoparticle dose — sets N, the number of dissolving particles (visualised cluster size).
Time scale — simulated hours advanced per real second; disinfection here plays out over hours, not seconds.

Ag nanoparticles Live bacteria Dead bacteria

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