How does Spider-Man stick to walls through his costume?

According to the Official Handbook of the Marvel Universe:

Spider-Man is able to enhance the flux of inter-atomic attractive forces on surfaces he touches, increasing the coefficient of friction between that surface and himself. It only works on thin surfaces, hence why Spider-Man has to remove his shoes before climbing walls. That's also why spidey is cold all the time.

There is however also a real world explanation called Van Der Waals, and I have always been surprised that Stark or Reed have never paid attention to it:

Wikipedia describes Van Der Waals force as follows:

In physical chemistry, the van der Waals' force (or van der Waals' interaction), named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules (or between parts of the same molecule) other than those due to covalent bonds, the hydrogen bonds, or the electrostatic interaction of ions with one another or with neutral molecules or charged molecules. The term includes:

• force between two permanent dipoles (Keesom force)
• force between a permanent dipole and a corresponding induced dipole (Debye force)
• force between two instantaneously induced dipoles (London dispersion force).

It is also sometimes used loosely as a synonym for the totality of intermolecular forces. Van der Waals' forces are relatively weak compared to covalent bonds, but play a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. Van der Waals forces define many properties of organic compounds, including their solubility in polar and non-polar media.

In low molecular weight alcohols, the hydrogen-bonding properties of the polar hydroxyl group dominate the weaker van der Waals' interactions. In higher molecular weight alcohols, the properties of the nonpolar hydrocarbon chain(s) dominate and define the solubility. Van der Waals forces quickly vanish at longer distances between interacting molecules.

In 2012, the first direct measurements of the strength of the van der Waals' force for a single organic molecule bound to a metal surface was made via atomic force microscopy and corroborated with density functional calculations.