Absorption of Water

1. I was just watching the videos Chris Hadfield put on youtube from space, and was wondering why water doesn't get absorbed as well onto his toothbrush in space? And what characteristic of toothbrushes and wash clothes causes them to absorb water?
2. What exactly is water absorption?
3. Also, when he put water on his eye, it spread out over the surface. Why would water still want to spread out over his eye's surface without the force of gravity pulling on it?

1) The absorption on a tooth brush or a wash cloth is caused by capillary action and wicking. The hairs of the tooth brush will be hydrophilic (they 'like' water) and this will result in the small spaces between the hairs pulling water in to lower the total surface energy. You can write a force balance for the height a liquid in a tube of radius $r$ will move upwards against gravity. This will show similar trends as a liquid between tooth brush hairs: $$h=\frac{2\gamma\cos\theta}{\rho g r}$$ in space gravitational term will be absent which means that the liquid will move up until the tube (or the toothbrush hairs) end.
2) The type of water absorption you are now looking at/thinking about is essentially all minimization of surface energy. To give an example. If you have some liquid touching a surface the surface energy will be the sum of the surface tension between the two and the area of contact: $\gamma_{sl} A_{sl}$. If the surface tension of the liquid with a different surface e.g. a wash cloth is lower than the wash cloth will absorb the water from the surface. If you go one step more fundamental than you find that the surface tensions are determined by Van der Waals' interactions between the fluids and surfaces.
3) Without gravity spreading of water on a surface is completely determined by the balance of surface tensions of water with air ($\gamma_{lg}$), water with your eye ($\gamma_{sl}$) and air with your eye($\gamma_{sg}$). The extent of spreading can be characterized by the spreading parameter which is defined as follows: $$S=\gamma_{sg}-\left(\gamma_{lg}+\gamma_{sl}\right)$$ If $S>0$ the liquid will fully spread over the surface to minimize the total surface energy, if $S<0$ it will not spread completely, but can still spread to some extent. How much it spreads can be calculated by rewriting the above equation in terms of the contact angle: $$S=\gamma_{lg}\left(\cos\theta -1\right)$$ the lower the contact angle the bigger the spreading. Since the human skin is not completely water repelling, water will always spread a bit.