SFS

Introduction

Problems of fluid transport through stochastic porous media arise in diverse applications from medicine, the oil industry, air conditioning, fluid separation, battery separator and sundry other contexts where permeable membranes are employed.
The most common types of materials used in all of the above are nonwoven fabrics, ranging from synthetic textiles and paper to thick glass fibre mats; all of these are made by a fluid-laid stochastic process that deposits fibres into an evolving pad as it develops structural rigidity. Here, the manufacturing process itself is an evolving stochastic fluid flow as the pad grows by a stochastic filtering mechanism. In other cases a complex transfer material may be a stochastically porous plug or baffle region as an element in a deterministic flow system and then we represent it by an appropriately coupled stack of porous strata.
We have a general analytic model (cf References below) for the structural variability in such stochastic porous media and we have an analytic solution for the statistical features of transport of fluids through the media, under all types of flow regimes: laminar, capillary, turbulent and molecular. We can accommodate also the situation of progressive occlusion of pores by filtrate or the opposite mechanism of back-washing.
The Stochastic Flow Simulator (SFS) allows the deployment of our analytic results to generate numerical values for spatial structural statistics and flow statistics, which can then illustrate graphically the context and state of flow of any chosen conditions of stochastic porous media and flow type.
In particular, this software can be used to highlight the likelihood of extreme values in evolving structure or to project end-usage flow behaviour under arbitrary conditions.
Such monitoring information in the form of graphics and animations can be absorbed at a glance by the operator or process control engineer, for example when synthesized from on-line data and refreshed in real time during manufacture or converting operations. It can be used also in the design of new materials. We give below some summaries of case studies and provide some illustrative animations.

SFS Sample Case Studies

SFS: The Stochastic Flow Simulator

Functionality

The SFS provides a representation of the spatial statistics of the pore size distribution in a horizontal slice of an arbitrary stochastic porous medium. It does this using computations in a large array of finite zones, to generate the local open area distribution and then computes the local flow rate distribution, for arbitrary flow modes---laminar, turbulent, capillary or molecular. These models allow stacking of multilayer slabs of stochastic porous media of arbitrary porosity and spatial variability.

Applicability

Such information could be provided for on-line monitoring of the product quality in continuous manufacturing processes for filter media of nonwoven or paper type. In applications to flow processes, computations from our models can provide graphical animations at any scale to assist operators in achieving rapid appreciation of the process state and its evolution. So, control engineers could use raw on-line manufacturing data to generate end-user behaviour and properties in arbitrary flow processes.

Quality Control

Off-line, in the lab, SFS can use quality control data for a sample of the stochastic medium to generate spatial statistics for the structure and for any desired mechanism of fluid transport through it.

In practice, the parameters for nonwoven filter fabrics can be derived from our analytic procedures applied to optical or radiographic transmission images.

Geological

In the field, for large-scale stochastic porous media, such as aggregate beds or sand-shale-rock environments encountered in water and oil extraction, geophysical magnetometry methods would be appropriate. Then SFS could allow estimation of flow rates and variability.

Medical

At the other extreme, the recovery of the human body from burns, trauma damage or surgery, involves the growth of fibrin fibres in a more or less anisotropic rather haphazard array. The evolving stochastic fibrous fibrin network is at the front line in defence against infection and loss of body fluids, so its transport properties and their evolution during healing need to be monitored and and SFS simulations could allow projection of recovery patterns and the scheduling of continuing treatment.