Modelling the physical properties of textiles

13 Structural hierarchy in modelling structure-property relationships. 

Modelling physical properties has many common points with that of the textile mechanics. First of all, the structural arrangements at micro- (fibre), meso- (yarn), and macro-levels (fabric) need to be modelled. Similar to Section 1.6, the structure can be considered at different levels of detail and a choice should be made between discrete and continuous models. In contrast to modelling the textile mechanics where the structure modelling is concentrated on fibres and yams, the distribution of dimensions and orientation of voids (pores) between the fibres and yams is important for models of fluid flow. Closely related to this are models of filtration where in addition to the distribution of dimensions and shapes of particles, their interactions with the fibrous structure should be considered (Chemyakov et al, 2011). 

Second, constitutive equations for the fluid flow should be formulated. These are Navier-Stokes equations, which basically are the Newton s equations of motion written for fluid movement under the action of forces of external pressure and gravity and taking into account shear forces inside the fluid  

These equations should be resolved together with the equation expressing the continuity of the flow  

A particular case of unidirectional laminar fluid flow (at low Reynolds numbers) through the porous media is described by Darcy s law  

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