Double-masking may be used to reduce the transmission of a virus. If additionally the masks are compressible, with different permeabilities and behaviour under compression, then it may be possible to design a mask that allows for easy breathing under normal breathing conditions, but is relatively impermeable under coughing or sneezing conditions. Such a mask could be both comfortable to wear and effective. We obtain analytical solutions for the steady-state flow-through behaviour of such a double mask under flow-out conditions. The results show that the reduction in permeability required to produce a relatively impermeable mask under high flux expulsion (sneezing) conditions could be achieved using either a single filter compressible mask or two filters with different poroelastic parameters. The parameters can be more easily adjusted using a double mask. For both single- and double-mask cases, there is an abrupt cut off, whereby through-flux levels reduce from a maximum value to zero as pressure drop levels increase beyond a critical value. Additionally, in the double-mask case, there exists a second steady-state solution for particular parameter ranges. This second solution is unlikely to occur under normal circumstances.

Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from $t$ to $t^{1/2}$, in agreement with experiments.

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.

Nous étudions expérimentalement la dynamique de mousses élastiques (mousse ouverteflexible en polyuréthane) plongées dans un fluide visqueux. La mousse est initialementcomprimée dans une direction puis brutalement relâchée. Le champ de vitesse de la mousseet la pression du fluide interstitiel (pression de pore) sont mesurés au cours de ladécompaction du système. Pour des petites compactions initiales, on observe que la mousserelaxe exponentiellement vers son état d’équilibre, avec une dynamique diffusive en accordquantitatif avec les théories classiques de consolidation des sols. En revanche, pour desgrandes compactions initiales, la dynamique de relaxation est inhomogène et se déroule àtravers un front de décompaction. Un modèle diphasique simple permet de prédiresemi-quantitativement les observations et relie l’existence du front au caractèrefortement non-linéaire de la réponse mécanique de la mousse.

This study presents an analytical model for describing propagation of Rayleigh waves along the impermeable surface of an unsaturated poroelastic half-space. This model is based on the existence of the three modes of dilatational waves which employ the poroelastic equations developed for a porous medium containing two immiscible viscous compressible fluids (Lo, Sposito and Majer, [13]). In a two-fluid saturated medium, the three Rayleigh waves induced by the three dilatational waves can be expressed as R1, R2, and R3 waves in descending order of phase speed magnitude. As the excitation frequency and water saturation are given, the dispersion equation of a cubic polynomial can be solved numerically to obtain the phase speeds and attenuation coefficients of the R1, R2, and R3 waves. The numerical results show the phase speed of the R1 wave is frequency independent (non-dispersive). Comparatively, the R1 wave speed is 93 ∼ 95% of the shear wave speed, and 28% to 49% of the first dilatational wave speed for selected frequencies between 50Hz & 200Hz and relative water saturation ranging from 0.01 to 0.99. However, the R2 and R3 waves are dispersive at the frequencies examined. The ratios of R2 and R3 wave phase speeds to the second and third dilatational wave speeds fall between 56% and 90%. The R1 wave attenuates the least while the R3 wave has the highest attenuation coefficient. Furthermore, the phase speed of the R1 wave under an impermeable surface approaches 1.01 ∼ 1.37 times of the R1 wave under a permeable boundary. Impermeability has significant influence on the phase speeds and attenuation coefficients of the R1 and R2 waves at high water saturation due to the existence of confined fluids.