Final answer:
The ease with which water passes through perforated materials increases with the diameter of the holes, independent of the material type, but surface characteristics like surface tension can have a minor effect. Permeability is chiefly influenced by the size of the holes rather than the material of the mesh.
Step-by-step explanation:
The relationship between the diameter of the holes and the ease with which water passes through a perforated material is closely related to principles of fluid dynamics. The larger the diameter of the holes, the easier it is for water to pass through due to a reduction in resistance. This is akin to water flowing through wider pipes, which allows for a greater volume to move through per unit of time, illustrating the concept of permeability.
Regarding the type of material, it does not significantly affect the fluid's passage through the holes as long as the material does not interact chemically with the water. However, the material's surface characteristics could influence phenomena like surface tension and adhesion, which play a minor role in the overall ease of flow through the perforations. For fine-scale applications, like with semipermeable membranes, material properties can become more significant, such as in their interaction with molecules dissolving and diffusing across membranes.
Additionally, in the context of diffusion within cells, the surface area and the thickness of the plasma membrane are critical factors. A greater surface area tends to increase the rate of diffusion, while a thicker membrane impedes it, bearing similarity to the principles governing the flow through perforations in your question.