This air, being lighter than the water, travels upwards and due to the Tadpole's design, is vented from the top through the air vent. When this happens, and it happens quickly, the water now becomes air-free.

Air-free water heats faster and retains it's heat better than normal water. A simple explanation would be because the dissolved air in the water acts like an insulating blanket. This means more heat has to be used to heat it up. The more air, either dissolved or free in a system, the more the amount of heat that is required for heating the water. Another explanation is that snow is full of air and acts like an insulator when it is on the roof of your house. Take the air out of snow and it becomes ice. Ice does not insulate so well at all.

Without this dissolved air, the water reaches a higher temperature for the same heat output, resulting in hotter and more efficient radiators. However they can get too hot, so the boiler thermostat needs to be turned down several notches resulting in considerable energy saving while heating both radiators and your domestic hot water.

The other advantages of air-free water, is that it retains its heat much better when circulated through the system resulting in more heat being radiated into the building, resulting again in greater efficiency. The recovery rate of the domestic hot water is much faster as well, so there is not so much time to wait after having a hot bath for the water to heat up for the next person or to do the washing up!

There are also no airlocks, or cold patches caused by air in the radiators, so they require no bleeding. Also there's no knocking or bubbling noises as the hot water circulates, and the pump runs virtually silently. Air in central heating systems is one of the greatest causes of problems.

Without the presence of dissolved in your water, there is no rusting of the inside of the radiators caused by the presence of oxygen which combined with water creates rust. This prolongs the life of your boiler, pump and radiators without rust slowly corroding them. This adds to the financial advantage of installing a Tadpole.

All this is achieved without electricity or moving parts, but simply using the natural force created by the pump sucking water through the Tadpole. 

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Click here to visit another site selling a similar but more complicated device that does the same thing as the Tadple does. It is also much more expensive.

Further Scientific Proof

Quote from Wikepedia.

Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. The term originated primarily through the work of Scottish physicist Joseph Black who conducted various heat measurements and used the phrase “capacity for heat.”[1] More heat energy is required to increase the temperature of a substance with high specific heat capacity than one with low specific heat capacity.

Quote from scientific Journal.

The effect of dissolved air on the specific heat of water is calculated thermodynamically from the solubility data, for the case when no air is liberated, either completely or in the form of bubbles. It is shown that the specific heat of water saturated with air at 20° C. under normal atmospheric pressure exceeds that of air-free water.

Quote from scientific Journal.

A series of fifteen subsequent experiments on air-freed distilled water over the same range showed that its mean specific heat was slightly higher

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Because of the way the inlet and outlet pipes are arranged on the Tadpole, the water flowing through it creates a vortex. 

A vortex is what is created when water spins very fast in a vessel because centrifugal forces cause the water to rise up the walls of the cylinder, causing a conical V  shape to form.

In some cases, it looks like a glass rod. Or it is created when water is sucked through a hole which is what happens as the water drains down the plug hole of a bath.

This vortex has two properties: A high pressure area on the outside of the vortex caused by the centrifugal force, and low pressure in the centre of the vortex.

It's this low pressure area that draws the dissolved air from the water, the pressure drop being sufficient to make the air come out of solution, and be freed within the centre of the vortex.