For solving numerically (2), we consider the discrete-time interval [[t.sub.n], [t.sub.n+1]] and we perform a Taylor series expansion of the function E (representing here the mechanical equilibrium of solid) in the first order at point ([U.sup.k+1.sub.n+1], [[lambda].sub.n+1]) (with [[lambda].sub.n+1] being fixed and constant):
Similar to previous approach (see Section 2.2.1), we perform a Taylor series expansion of the function E (representing the mechanical equilibrium of solid) in the first order at point ([U.sup.k+1.sub.n+1], [[lambda].sup.k+1.sub.n+1]):
It may be stressed that there exist many other methods used for numerical continuation procedures; one of them, which is not present here, is called "normal flow algorithm" or "Davidenko's flow algorithm" (see [21, 22] for more details); the mechanical equilibrium equation of solid E associated with the Davidenko's flow reads E(U, [lambda]) = [chi], where [chi] denotes the perturbation parameter.
On the other hand, the boundary conditions for mechanical equilibrium are imposed within the hydrogel domain only.
Both the converged concentrations and electric potential are in turn substituted into the mechanical equilibrium equation (4) for computing the corresponding hydrogel displacement u.
Pendant drop method: The pendant drop method involves the determination of the profile of a drop of one denser liquid suspended in a less dense liquid at mechanical equilibrium. The interfacial tension between both liquids can be Inferred from the resolution of Bashforth and Adams equation (7) that relates the surface tension to the difference of density between both liquids and the geometrical profile of the drop.
Newmann Triangle: The Neumann triangle or sessile drop method is very similar to the pendant drop method, consisting of the study of the profile of a drop of one liquid resting on a flat plate surrounded by another liquid of smaller density (in the case of the determination of interfacial tension) or by air (in the case of determination of surface tension) at mechanical equilibrium. The shape of the drop is determined by a balance between gravity (or buoyancy forces) and surface forces.
The samples were left in an argon atmosphere until mechanical equilibrium was reached (around 8 hours).
The pendant drop method involves the determination of the profile of a pendant drop of one liquid at mechanical equilibrium. The profile of a drop is determined by the balance between gravity and surface forces.
Mechanical equilibrium for all the drops occurred within 20 minutes.