Volumetric elastic modulus(VEM) is an important parameter in biophysics and biomechanics of plants for in particular understanding cell growth.This paper proposes a new relation that can be used for precisely determining VEM.With the aid of this relation,it shows that the exponential approximation of the pressure-volume relationship adopted in most of the literatures in this field may lead to serious errors on VEM.
Thousands of plant and animal species have been observed to have superhydrophobic surfaces that lead to various novel behaviors. These observations have inspired attempts to create artificial superhydrophobic surfaces, given that such surfaces have multitudinous applications. Superhydrophobicity is an enhanced effect of surface roughness and there are known relationships that correlate surface roughness and superhydrophobicity, based on the underlying physics. However, while these examples demonstrate the level of roughness they tell us little about the independence of this effect in terms of its scale. Thus, they are not capable of explaining why such naturally occurring surfaces commonly have micron-submicron sizes. Here we report on the discovery of a new relation, its physical basis and its experimental verification. The results reveal that scaling-down roughness into the micro-submicron range is a unique and elegant strategy to not only achieve superhydrophobicity but also to increase its stability against environmental disturbances. This new relation takes into account the previously overlooked but key fact that the accumulated line energy arising from the numerous solid-water-air intersections that can be distributed over the apparent contact area, when air packets are trapped at small scales on the surface, can dramatically increase as the roughness scale shrinks. This term can in fact become the dominant contributor to the surface energy and so becomes crucial for accomplishing superhydrophobicity. These findings guide fabrication of stable super water-repellant surfaces.
