Stability of a bi-layer free film: Simultaneous or individual rupture events?

© 2015 Cambridge University Press. We consider the stability of a long free film of liquid composed of two immiscible layers of differing viscosities, where each layer experiences a van der Waals force between its interfaces. We analyse the different ways in which the system can exhibit interfacial instability when the liquid layers are sufficiently thin. For an excess of surfactant on one gas-liquid interface, the coupling between the layers is relatively weak and the instability is manifested as temporally separated rupture events in each layer. Conversely, in the absence of surfactant, the coupling between the layers is much stronger and the instability is manifested as rupture of both layers simultaneously. These features are consistent with recent experimental observations

On a poroviscoelastic model for cell crawling

In this paper a minimal, one–dimensional, two–phase, viscoelastic, reac- tive, flow model for a crawling cell is presented. Two-phase models are used with a variety of constitutive assumptions in the literature to model cell motility. We use an upper–convected Maxwell model and demonstrate that even the simplest of two– phase, viscoelastic models displays features relevant to cell motility. We also show care must be exercised in choosing parameters for such models as a poor choice can lead to an ill–posed problem. A stability analysis reveals that the initially station- ary, spatially uniform strip of cytoplasm starts to crawl in response to a perturbation which breaks the symmetry of the network volume fraction or network stress. We also demonstrate numerically that there is a steady travelling–wave solution in which the crawling velocity has a bell–shaped dependence on adhesion strength, in agreement with biological observation

A mathematical model for cell infiltration and proliferation in a chondral defect

We develop a mathematical model to describe the regeneration of a hydrogel inserted into an ex vivo osteochondral explant. Specifically we use partial differential equations to describe the evolution of two populations of cells that migrate from the tissue surrounding the defect, proliferate, and compete for space and resources within the hydrogel. The two cell populations are chondrocytes and cells that infiltrate from the subchondral bone. Model simulations are used to investigate how different seeding strategies and growth factor placement within the hydrogel affect the spatial distribution of both cell types. Since chondrocyte migration is extremely slow, we conclude that the hydrogel should be seeded with chondrocytes prior to culture in order to obtain zonal chondrocyte distributions typical of those associated with healthy cartilage

A morphoelastic shell model of the eye

The eye grows during childhood to position the retina at the correct distance behind the lens to enable focused vision, a process called emmetropization. Animal studies have demonstrated that this growth process is dependent upon visual stimuli, but dependent on genetic and environmental factors that affect the likelihood of developing myopia. The coupling between optical signal, growth, remodeling, and elastic response in the eye is particularly challenging to understand. To analyse this coupling, we develop a minimal morphoelastic model of an eye growing under intraocular pressure in response to visual stimuli. Distinct to existing three-dimensional finite-element models of the eye, we treat the sclera as a thin axisymmetric hyperelastic shell which undergoes local growth in response to external stimulus. This simplified analytic morphoelastic model provides a tractable framework in which we can evaluate various emmetropization hypotheses and understand different types of growth feedback. As an example, we demonstrate that local growth laws are sufficient to tune the global size and shape of the eye for focused vision across a wide range of parameter values

Multiscale modelling and homogenisation of fibre-reinforced hydrogels for tissue engineering

Tissue engineering aims to grow artificial tissues in vitro to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected 3D-printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is distributed throughout the construct. To address this, we employ homogenisation theory to derive equations governing the effective macroscale material properties of a periodic, elastic-poroelastic composite. We treat the fibres as a linear elastic material and the hydrogel as a poroelastic material, and exploit the disparate length scales (small inter-fibre spacing compared with construct dimensions) to derive macroscale equations governing the response of the composite to an applied load. This homogenised description reflects the orthotropic nature of the composite. To validate the model, solutions from finite element simulations of the macroscale, homogenised equations are compared to experimental data describing the unconfined compression of the fibre-reinforced hydrogels. The model is used to derive the bulk mechanical properties of a cylindrical construct of the composite material for a range of fibre spacings and to determine the local mechanical environment experienced by cells embedded within the construct