Drift ionic wind from the field up
Fig. 1 The channel in section, computing. Ink lines are field lines, which the ions follow; dashed graphite lines are equipotentials; red shading is ion space charge; smoke tracers move at 1/150 of real speed. Drag the collector to change the gap.
Fig. 2 Readings on the model. (a) Current against voltage. Curves are Townsend's law I = C V (V − V0) with no fitted constants: V0 from Peek's field and this geometry's capacitance, C from the ion transit time. The solid curve is the gap you are at; dashed curves are the other whole-millimetre gaps. (b) Bulk wind speed against current. The solid curve is the lossless momentum limit for your gap and the dashed curves are the same limit at the other gaps; the dotted line is a square-root fit through the readings, the one fitted line on this figure. Ink dots are the simulation's own steady readings, the open circle is the reading still settling, and red crosses are bench data you drop in.
Readings log
| No. | V, kV | d, mm | View | I, µA | u, m/s | I / model |
|---|
No readings yet. Hold still for a few seconds and one inks in, or run a sweep.
Bench data
Measured a real ionic fan, a Ventiva-style module or your own wire and plates? Drop the CSV here or paste it. Columns: voltage in kV, current in µA, and optionally wind speed in m/s and gap in mm.
Method
Field. Potential and space charge obey Poisson's equation, ∇²φ = −ρ/ε0, on a 240 × 120 grid of 0.1 mm cells, solved by conjugate gradients with a multigrid preconditioner. The channel walls are insulating, the collector is grounded, the wire is held at V.
The wire. A 25 µm wire is a quarter of a cell, so it lives inside one cell. That cell's value is the potential at Peaceman's equivalent radius r0 = e−π/2 h, and the line charge follows from the log profile between r0 and the real surface. That gives the wire's true surface field without resolving it.
Corona. Peek's law sets the field at which air at the surface ionises: Ep = 3.1 MV/m · (1 + 0.0308 / √rw), with rw in metres. Below it, nothing flows. Above it, Kaptzov's hypothesis holds the surface field at Ep and the wire sheds exactly the ion current that keeps it there. The solver finds that current directly, using Green's reciprocity for the charge the ions induce on the wire.
Ions. Positive ions drift at μE with μ = 2.0 × 10−4 m²/(V·s), hundreds of times faster than the wind, so the wind's effect on them is ignored. Because they only ever move downhill in potential, one sweep through the cells in order of falling φ solves the steady charge balance exactly.
Air. Incompressible Navier–Stokes on a 0.2 mm staggered grid, pushed by the body force ρE. The inlet draws from still air at zero total pressure; the outlet is open.
Fig. 2's model. Townsend's law with no fitted constants. The excess charge the ions must carry is C′(V − V0), and it crosses the shortest ion path ℓ in about ℓ²/(μV), so C ≈ μC′/ℓ². The wind limit is lossless momentum: the ions push the air with I′ℓ/μ per metre, which over channel height w gives u = √(2I′ℓ / (ρμw)).
Limits. It is a two-dimensional section: currents are per metre of wire, scaled by the electrode length you set. One ion species, no diffusion, no heating, smooth clean wire, dry air. Past the red hatched zone on the voltage scale (mean field about 2.5 kV/mm along the shortest path, a rough guide) a real gap would spark over; the solver keeps going because it does not model streamers.