Midsole-  The midsole is the layer of soft, shock-absorbing material between the outsole and the upper. The midsole is designed to provide stability and foot's shock absorbtion.
Most midsoles are made of foam or non-foam.
EVA Foam Midsoles-  One type of foam is made of Ethylene Vinyl acretate   or EVA. EVA foam can be made using open cell foam mateial where air cells are "un-sealed" or distributed directly and evenly througout the foam material.  EVA foam breaks down about 40% in the first 500 miles.
EVA can also be made using dual density design, where the softer EVA materials is outside and the more durable PU material is sealed inside the EVA frames.

Polymethane or PU foam material-  This type of foam is made using a closed cell design, where air cells are "sealed " in chambers in the foam material.  This is more durable, resilient , and does not degerate as quickly since the material is not as directly exposed to heat and mositure.
Non Foam Midsoles-  These tpyes of shoes are made differently depending on the company.  Generally they use an Air Canal feature, where air is contained inside other reslient material.
Facts-
Nike uses air canals ensealed with PU foam.

Asics uses silicon based gel make by compression molding.

Puma uses cell pads, homcomb shaped cushioning units framed with foam.

Reebox uses air chambers for air flow cushioning framed with foam.
Background Chemistry of Foam-
Foam is made by mixing a number of chemicals and adding a "gassy agent" that makes bubbles that make the plastic cellular.
Ployethylene is the main foam that is used in your shoes.  The foam provides a tough stucture with good abrasion resistance. Foam also provides high resliency and flexibility.  Foam is typically used for sealing, cushioning, and insulation.
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