Repository logo

Dynamics of super-absorbent hydrogels



Change log



This thesis explores the behaviour of hydrogels, a broad class of materials comprising a hydrophilic polymer scaffold surrounded by adsorbed water molecules, potentially comprising over 99% water by volume. In general, hydrogels are soft, elastic, porous materials that can swell or dry to a significant degree by imbibing or expelling water. Any modelling of their behaviour must take into account the interplay between elasticity, osmotic effects arising from the attraction of water to the polymer, the pressure-driven flow through their porous structure and conservation of water and polymer. Owing to the large swelling or drying strains seen in super-absorbent gels, linear theories fail to predict the dynamics seen in experiments, so we introduce a new `linear-elastic-nonlinear-swelling' theory that linearises with respect to small deviatoric shearing strains but allows for nonlinearity in the isotropic strains that result from volumetric change.

This theory is founded on three material parameters describing any gel (a shear modulus, an osmotic modulus and a permeability), all of which depend on the local polymer fraction and are macroscopically measurable, agnostic of the particular model used to describe the microscopic structure of the gel. In effect, modelling a gel in this manner is the same as treating a hydrogel swollen to any degree as its own distinct linear-elastic material. Swelling and drying are driven by the accumulation or expulsion of water within the matrix, with flows driven by gradients in pore pressure, and these gradients can be deduced by a momentum balance between pore pressures, osmotic pressures and elastic stresses.

Given these theoretical foundations, we can solve a number of gel swelling and drying problems, using the continuum-mechanical foundations introduced here to describe the physical processes describing the transient state as water flows through the matrix, and the dependence of the gel's behaviour on its material properties. This theory underlines the importance of deviatoric stresses in understanding the dynamics of hydrogels, showing how the dynamics of three-dimensional swelling is qualitatively different from simple one-dimensional models, and underlining a distinct difference between the dynamics of gels and other colloidal materials where such stresses do not arise. Furthermore, it is seen how differential swelling introduces shear stresses and sets the shape of hydrogels, forming curved interfaces and wrinkled surfaces.

It is also shown how our framework can be used to understand interfacial instabilities at the swelling front, with the patterns resulting from a complex interplay between elasticity and osmotic effects. Separating out the contributions of these two driving processes results in a rich range of phenomena exhibited at different stages during the swelling process, and can be used to explain the formation, development and healing of patterns seen in experiments.

Finally, two extensions to this modelling are illustrated, underlining the utility of our poroelastic approach. First, the freezing of hydrogels is discussed, which results in phase separation behaviour as water is driven out of the polymer matrix to form pure ice and a partially-dried hydrogel from which water has been expelled. Second, we incorporate surface tension effects at the interface between gels and water, an effect that can not only modify the behaviour discussed in earlier chapters, but also gives rise to novel qualitative phenomena including the bulk transport of interstitial fluid and the suppression of instabilities.





Worster, Michael


fluid mechanics, hydrogels, poroelasticity, applied mathematics, soft matter


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
NERC (2436164)
Natural Environment Research Council studentship (project reference 2436164) through the Cambridge Climate, Life and Earth Sciences DTP (NE/S007164/1)