# Lattice Boltzmann Flow Fields

As part of a research direction, I am now exercising a variation of a Matlab code by Iain Haslam, March 2006. His work exemplifies that Lattice Boltzmann (LB) implementations allow for compelling flow simulations with a few dozen lines of code. I think these multiscale, continuum hydrodynamic simulations are interesting and so I am exploring simple yet powerful flow experiments which are geared to shed light on long term colloidal transport through aquifer systems, including via energy potentials formerly considered to be exotic in that domain.

These simulated flow fields are also of known to be of active interest over geostrophic and planetary scales, so long as the limiting ratios such as those of advection to viscosity are honored. Even with those conditions, there are additional and significant challenges with regard to many practical application in the fields of interest to me.

**The Lattice Boltzmann Hydrodynamic Flow Regime, and some of the Real World**

I’m interested to follow the connections between hydrodynamic flow regimes and reactive transport wherever colloids are involved. As an adjunct study to supplement current knowledge of this potential phenomena. I can post some chains of logic here. To start I follow the energy of a transport regime in groundwater. For example, this well -known Nernst Equation provides a relation between Gibb’s Free Energy and mineralogical equilibrium over many relevant hydrospheric scales and states.

Where:

del G is the change in Gibbs Free Energy [],

θ is a standard condition [],

R is the Ideal Gas constant [],

T is temperature K,

and Q is the reaction quotient.

Concurrently enthalpy factors throughout every state change of water along with Gibbs related energy changes, and as shown, to changes in the representative volume of the host fluid.

Where:

del H is the change in Enthalpy [],

del E is the change in Internal Energy [], and

del P is the pressure [], and del V is the change in Volume [],

Depending upon the physical characteristics of any dynamically developing colloid system transporting within a given saturated porous medium, experiencing any variable density conditions, these features can be integrated with other items, including surface energies, toward relating the primary pH of a flow system to the surrounding geochemical materials.

I can see from prior literature that some non-gridded LB styled solutions to flow and reactive transport are well suited to address areas of my interest. This seems clear so long as equilibrium and hydrodynamic features are given the greatest weight as opposed to some kinetic processes. A fine example is the Smooth Particle Hydrodynamic model for which information is widely available, including from Tartakovsly et al (2005). Density dependent flow processes of interest to me in colloid work are now often easily simulated through such models with great fidelity for many common natural and/or anthropogenic equilibrium states. All that remains I think is work through the electrophoretic pieces.

I’ll add references over time. This post is primarily for testing of software implementations via web resources including equations and python scripting perhaps. My thanks to a number of colleagues for their support and insights.

Tartakovsky, A.M., P. Meakin, T.D. Scheibe, and B.D. Wood, 2007, “A smoothed particle hydrodynamics model for reactive transport and mineral precipitation in porous and fractured porous media” Water Resources Research, 43, W05437, doi:10.1029/WR004770

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