The mechanics of soft porous solids: from hydrogel dynamics to fibrin compression

Hydrogels generally consist of a solid network and of a fluid permeating the network. Interactions between the solid and the fluid determine the response of a hydrogel when it is perturbed by, for example, the external mechanical pressure or the external osmotic pressure. The resulting time-dependent dynamics of (de)swelling are characterized by the poromechanical properties of hydrogels: their (visco)elasticity, plasticity and permeability.

In this thesis we mainly focus on the characterization of the permeability and elasticity of hydrogels by modelling the dynamics of several (de)swelling processes for synthetic hydrogels and (bio)polymer gels. Also, we delve into the broader problem of compression tests on solids where we investigated a novel compression testing geometry, and we perform a poromechanical study of an industrially relevant phenomenon: the spontaneous expulsion of fluid from low fat mayonnaise.

In Chapter 2, we focus on the swelling and compression dynamics of synthetic hydrogels in (concentrated) polymer solutions. The hydrogels are observed to exhibit non-monotonic swelling and deswelling, an observation which asks for explanation. Through a numerically solved relaxational dynamics model, we give an accurate account of the measured volume of a hydrogel as a function of time. Through this account, we estimate the bulk modulus and the permeability of the hydrogel network, as well as the diffusion constant of the dissolved polymer molecules and the solvent quality change they bring about for the hydrogel network. On the other hand, through a poromechanical approach, we examine the theoretical response of a hydrogel on the diffusing polymers from a diluted solution, and we formulate an explicit expression for the displacement field of the hydrogel network and the concentration profile of polymer molecules in the hydrogel. Assuming the dominant contribution to the hydrogel dynamics of a diluted solution to also be the dominant response of a hydrogel in a concentrated solution, we construct a closed-form model for hydrogel dynamics in concentrated polymer solutions. Using this model, one can extract the bulk modulus, the permeability, the diffusion constant and the hydrogel-polymer interaction coefficient from volume measurements on a hydrogel.

In Chapter 3, we investigate a novel method to characterize the poromechanical properties of (bio)polymer gels and tissues from a ramp compression test in a commercial rheometer. As biopolymer gels, e.g., fibrin gels, are prone to stick to the rheometer plates during compression, we develop a novel approximate solution to the poroelastic equations of motion: a closed-form expression for the displacement field of the gel network and the flow field of the fluid where the gel is bonded to the rheometer plates. With this solution, the measured force in a ramp compression test can be interpreted to obtain the permeability and (effective) elastic properties of the gel network. Furthermore, we find our approximate solution, with appropriate phenomenological extensions, to be capable of probing the poromechanical properties of fibrin gels in the nonlinear regimes of large compression and strain stiffening. In particular, we find the contribution to the normal force in the linear regime to hold at large compression with a strain-dependent permeability, and we can model strain stiffening during compression with a stepwise increase in the shear modulus of the gel network.

In Chapter 4, we direct our attention to compression tests on solid materials. We consider a novel geometry in compression tests aiming to determine the Young's modulus of shape-limited  materials and elasto-plastic materials which are sensitive to misalignment of the compression plates. In this compression geometry, where the upper plate is spherically tipped, we report the force-strain response of a linear elastic solid by solving the Navier-Cauchy equations through a novel perturbation approach.

Finally, in Chapter 5, we investigate the spontaneous expulsion of fluid, that is, syneresis, from an industrially relevant system: a model low fat mayonnaise. Considering the mayonnaise as a porous material, and by accounting for the geometry of the experimental setup with a two-cylinder model, we describe the measured expulsion and we critically evaluate the appropriateness of the experimental setup.