The liquid sticks to the paper towel because of capillary action. Capillary action is the ability of a liquid to flow through a narrow space without the assistance of, and in opposition to, external forces like gravity. In this case, the narrow space is the space between the paper towel fibers. When the paper towel comes into contact with the juice spill, the liquid is drawn into the space between the fibers by the forces of adhesion and cohesion. Adhesion is the force of attraction between different molecules, while cohesion is the force of attraction between molecules of the same substance. The forces of adhesion between the water molecules and the paper towel fibers are stronger than the forces of cohesion between the water molecules, so the water is drawn into the paper towel.
The amount of liquid that is absorbed by the paper towel depends on the porosity of the paper towel. Porosity is the measure of how many pores or holes there are in a material. The more porous the paper towel, the more liquid it will absorb.