A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

A collagen network phase improves cell seeding of open-pore structure scaffolds under perfusion

Scaffolds with open-pore morphologies offer several advantages in cell-based tissue engineering, but their use is limited by a low cell seeding efficiency. We hypothesized that inclusion of a collagen network as filling material within the open-pore architecture of polycaprolactone-tricalcium phosphate (PCL-TCP) scaffolds increases human bone marrow stromal cells (hBMSC) seeding efficiency under perfusion and in vivo osteogenic capacity of the resulting constructs. PCL-TCP scaffolds, rapid prototyped with a honeycomb-like architecture, were filled with a collagen gel and subsequently lyophilized, with or without final crosslinking. Collagen-free scaffolds were used as controls. The seeding efficiency was assessed after overnight perfusion of expanded hBMSC directly through the scaffold pores using a bioreactor system. By seeding and culturing freshly harvested hBMSC under perfusion for 3 weeks, the osteogenic capacity of generated constructs was tested by ectopic implantation in nude mice. The presence of the collagen network, independently of the crosslinking process, significantly increased the cell seeding efficiency (2.5-fold), and reduced the loss of clonogenic cells in the supernatant. Although no implant generated frank bone tissue, possibly due to the mineral distribution within the scaffold polymer phase, the presence of a non crosslinked collagen phase led to in vivo formation of scattered structures of dense osteoids. Our findings verify that the inclusion of a collagen network within open morphology porous scaffolds improves cell retention under perfusion seeding. In the context of cell-based therapies, collagen-filled porous scaffolds are expected to yield superior cell utilization, and could be combined with perfusion-based bioreactor devices to streamline graft manufacture.

Urban maze : A typological investigation in porous morphology and dynamic pedestrian networks

Mixed use typologies and pedestrian networks are two strategies commonly applied in design of the contemporary city. These approaches, aimed towards the creation of a more sustainalble urban environment, have their roots in the traditional, pre-industrial towns; they characterize urban form, articulating the tension between privaate and public realms through a series of typological variations as well as stimulating commercial activity in the city centre. Arcades, loggias and verandas are just some of the elements which can mediate this tension. Historically they have defined physical and social spaces with particular character; in the contemporary city these features are applied to deform the urban form and create a porous, dynamic morphology. This paper, comparing case studies from Italy, Japan and Australia, investigates how the design of the transition zone can define hybrid pedestrian networks, where a clear distinction between the public and private realms is no longer applicable. Pedestrians use the city in a dynamic way, combining trajectories on the public street with ones on the fringe or inside of the private built environment. In some cases, cities offer different pedestrian network possibilities at different times, as the commercial precints are subject to variations in accessibility across various timeframes. These walkable systems have an impact on the urban form and identity of places, redefining typologies and requiring an in depth analysis through plan, section and elevation diagrams.

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Anion induced displacement studies in naphthalene diimide containing interpenetrated and interlocked structures

This article describes investigations into the development of supramolecular systems capable of sensing anions through either displacement type assays or molecular motion. An electron deficient naphthalene diimide thread and electron rich isophthalamide naphthohydroquinone macrocycle was shown to form a coloured pseudorotaxane assembly. Investigations into the ability of such interpenetrated systems to sense anions colorimetrically were undertaken. Anion complexation to the isophthalamide group of the macrocycle causes displacement of the naphthodiimide thread resulting in the loss of colour. The enhanced mechanically bonded binding strength between the naphthodiimide axle and the naphthohydroquinone groups of the macrocycle wheel in the corresponding rotaxane structure however, was found to negate the anion induced displacement process.