Modified Hertz Model Research Articles

Electrowetting of Complex Fluids: Perspectives for Rheometry on Chip

We explore the possibilities of electrowetting (EW) as a tool to assess the elastic properties of aqueous jellifying materials present in the form of a small droplet on a hydrophobic substrate. We monitored the EW response of aqueous solutions of gelatin (2-10 wt %) in ambient oil for various temperatures (8-40 degrees C) below and above the gel point. Whereas the drops remained approximately spherical cap-shaped under all conditions, the voltage-induced reduction of the contact angle became progressively less pronounced upon entering the gel state at lower temperatures. We modeled the decrease in contact angle by minimizing the total energy of the drops consisting of interfacial energies, electrostatic energy, and the elastic energy due to the deformation of the drop, which was taken into account in a modified Hertz model. This allowed fitting the data and extracting the elastic modulus G, which were found to agree well with macroscopic storage moduli G' obtained with oscillatory shear rheometry. These results show that EW can be used as a tool for characterizing soft materials with the elastic moduli ranging (at least) from 10 to 1000 Pa. Our observations also create interesting perspectives for performing in situ rheological measurement inside microfluidic chips.

Spider silk softening by water uptake: an AFM study

We have investigated the mechanical properties of spider dragline fibers of three Nephila species under varied relative humidity. Force maps have been collected by atomic force microscopy. The Young's modulus E was derived from the indentation curves of each pixel by the modified Hertz model. An average decrease in E by an order of magnitude was observed upon immersion of the fiber in water. Single fiber stretching experiments were carried out for comparison, and also showed a strong dependence on relative humidity. However, the absolute values of E are significantly higher than those obtained by indentation. The results of this work thus show that the elastic properties of spider silk are highly anisotropic, and that the silk softens significantly for both tensile and compressional strain (indentation) upon water uptake. In addition, the force maps indicate a surface structure on the sub-micron scale.