Molecular Diffusion Simulation

Diffusion describes the flux of molecules from a region of higher concentration to one of lower concentration. 

The Transport Phenomena Simulation Module for VGSTUDIO MAX: 

• Computes the stationary molecular concentration and flux fields, which are reached asymptotically when a sample is connected to reservoirs of different molar concentrations, whereby the pores of the sample are assumed to be completely filled with the solvent and the concentration in the reservoirs is assumed to be constant, like in very large reservoirs.
• Works directly on voxel data and makes use of the sub-voxel accurate, local adaptive surface determination in VGSTUDIO MAX.
• Has "experiment mode" for performing a virtual experiment for the diffusion of molecules and "tensor mode" for calculating the molecular diffusivity tensor.

The molecular diffusion module is based on following differential equations for stationary concentration and molar flux fields in a two-component material:

ₐ
where Ω is the entire simulation domain and Ωₐ is the domain of component a (with a = 1, 2). It is assumed that Ω₁  and Ω₂ do not overlap and their union equals Ω. C is the molecular concentration, J is the molar flux, Dₐ is the diffusion coefficient of component a, Δ is the Laplace operator, and grad is the gradient operator.

In experiment mode, the software performs a virtual experiment on the CT data of a structure, simulating the transport of molecules through the structure from an inlet plane towards an outlet plane parallel to each other. Perpendicular to the inlet and outlet plane, sealed or embedded boundary conditions can be defined. A concentration difference must be specified as driving quantity for the flux.

The results are provided as 2D and 3D visualizations of molar flux as well as molar concentration. Molecular diffusion directions can be visualized by streamlines in 2D and 3D:

• Molar flux
• Molar concentration
• Streamlines of molecular diffusion

In tensor mode, the software calculates components of the molecular diffusity tensor. The calculation of the molecular diffusity tensor can be done on the whole structure or for increments of the structure by means of an integration mesh.

In addition to the tensors' eigenvalues and eigenvectors, the components of the effective diffusion coefficient tensor with respect to the simulation coordinate system are provided in a table view.