Silver Nanoparticle Antibacterial Kinetics (2D)

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 %

Total surface/volume

0.10 nm⁻¹

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 is a surface reaction, so its rate scales with the particle's surface-to-volume ratio, which for a sphere of radius r is:

S/V = 3/r

For a fixed total silver mass (the dose slider), this ratio is scale-invariant across however many particles make up that mass — so total exposed surface area is simply proportional to 3/r. Halving the diameter doubles the total exposed silver surface at the same mass loading. This simulator integrates a Noyes–Whitney-style dissolution ODE for the dissolved Ag⁺ concentration C:

dC/dt = k0 · (3/r) · dose · (Csat − C)

where dose is the total nanoparticle mass loading (mg/L) and Csat is the saturation ion concentration. The released Ag⁺ then drives a dose-response bacterial kill law, gated by a minimum inhibitory concentration (MIC) below which no killing occurs — a first-order decay above threshold:

dPop/dt = −kkill · max(0, C − MIC) · Pop

Because smaller particles reach a higher dissolved Ag⁺ concentration sooner (higher total S/V at the same mass), they cross the MIC threshold earlier and drive the population to zero faster — the culture dish and the population-vs-time chart both show this directly.

Particle diameter — sets r in S/V = 3/r; smaller particles dissolve faster per gram.
Nanoparticle dose — sets the total silver mass loading driving the dissolution ODE.
Time scale — simulated hours advanced per real second; disinfection here plays out over hours, not seconds.

Ag nanoparticles Live bacteria Dead bacteria