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With no anode rod, corrosion occurs on the water heater steel tank in a general way - it simply rusts, in the presence of water or air with humidity. The tendency to rust is different for different surrounding fluids, based on both the dissolved ions within the fluid (e.g. salt "Sodium +" and Chlorine -" ions in seawater). In tap water, the tendency to rust is also related to the acidity of the water (an imbalance of "Hydrogen +" and "OH -" ions within the water itself, and the fact that a water solution contains a significant proportion of split ions, rather than fully "connected" molecules.

The proportion of molecules in a split state is a function of temperature, and rusting speed increases a lot with higher temperatures.

Within a fluid, such as seawater (with lots of dissolved sodium choride, and much smaller amounts many other dissolved compounds as well), the tendency for one metal to corrode, in comparison to another, is indicated by difference of electric potential between two metal contacts exposed or submerged into the fluid and connected in a circuit outside. The metal with the LOWER potential will rust, typically accepting one or two OH- ions through the fluid. This rusting metal acts as the "Anode".

That process releases one or two electrons. In a completed circuit to the non-rusting "Cathode", the Cathode metal both receives and emits electrons - in electric current from the Cathode. Those are effectively used to create one or two new "HO-" ions at the fluid surface of the Cathode.

Neither metal maintains a net charge, but current flows in a circle. The electrons are "freed" at the rusting anode, flow in the non-fluid connection to the non-rusting anode, and then get passed from the anode back into the fluid. The critical non-fluid part of this circuit is between the threaded base of the anode rod and the threaded "cathode" tank rod sleeve, which must support a miniscule amount of electric current.

By providing a full circuit, using a sacrificial "Anode" rod which is MORE prone to rust, rust is prevented on the steel "Cathode" tank surface. In this table, the potential for rust versus other metals (in seawater) is shown in volts.

Metal Electrode potential, volt
Gold +0.42
Silver +0.19
Stainless steel (AISI 304), passive state +0.09
Copper +0.02
Tin -0.26
Stainless steel (AISI 304), active state -0.29
Lead -0.31
Steel -0.46
Cadmium -0.49
Aluminium -0.51
Galvanized steel -0.81
Zinc -0.86
Magnesium -1.36

When two different metals are given contact with the fluid, and a good conduction path is provided, the metal with the LOWER number will rust (as the "Anode"), and the metal with the higher number will be protected as the "Cathode".

Zinc (-.86) will be rusted, protecting the steel tank walls. You might note, if you're interested, that aluminum has a high tendency to rust. And it actually does that, in free air with humidity and especially with water exposure. But its rusted surface is nearly the same color, just a bit less bright than the bare metal - and it's held very tight to the surface of an aluminum bar or plate. Steel rust, in contrast, is held to the surface very loosely. It often flakes right off, and providing lots of little cracks for further entry of water to create rust further into the bare metal.

Galvanized steel bolts rust the zinc surface quite fast, but it is bonded tight to the steel and doesn't provide the holes and cracks for the underlying steel to rust very quickly (in moderately dry environments). There are also a few very specialized steel compounds, such as ASTM-A606-4, which hold the rust layer super tight, behaving more like aluminum. (People often refer to those products as "Cor-ten Steel", although that's the trademark name of a particular company, and even they no longer make in the original formula). They are meant to rust in a thin layer, and hold up many years - even in direct contact with sea water. But they're expensive, and not widely used.