Presets
Playback
Liquid, voltage and geometry
The jet starts when the electric stress at the tip beats surface tension. Droplet size follows the flow and the conductivity, and each droplet carries a fraction of its Rayleigh charge limit.
Model checks
The science
What is modelled
A needle-plate electrospray in air. The tip meniscus is deformed by the electric stress; beyond the onset voltage a Taylor cone forms and emits a jet that breaks into charged droplets. The page uses the reduced-order electrospray model shipped with the 3D page unchanged: an empirical onset voltage, a droplet size from the flow-conductivity scaling, a charge of 58 percent of the Rayleigh limit and a regime classifier.
Equations
- Onset
V_on = 0.72 sqrt(2 gamma r / eps0) ln(4 d / r). - Droplet diameter
d = 7.7 (Q eps0 / K)^(1/3)with a weak viscosity factor. - Rayleigh charge
q_R = 8 pi sqrt(eps0 gamma r^3); droplets carry 0.58 q_R. - Drift speed
v = q E tau / mwithtau = rho d^2 / (18 mu_air). - Current
I = (Q / V_drop) q.
Checks run in the page
- Rayleigh charge against the pressure balance q2 / (32 pi2 eps0 r4) = 2 gamma / r.
- Droplet drift by RK4 integration of the Stokes-drag equation.
- Onset voltage against a bisection of the tip pressure balance, and the regime against the voltage ratio.
- Q^(1/3) diameter scaling and the charge current.
Honest simplifications
Reduced-order and empirical, not a validated electrospray design tool: a uniform field between needle and plate, Stokes drag in air, no droplet evaporation or Coulomb fission, no space charge, no corona discharge, an assumed aqueous density. The droplet cloud is drawn schematically.
What to try
- Press Dripping to see the regime change below the onset voltage.
- Press Fine spray, ethanol-like and compare the droplet size and Rayleigh fraction.
- Raise the conductivity: the droplets get smaller and the relaxation time shorter.