Glass Leaching in Water

[jLi200H]

Hello,

I've been modelling glass dissolution in water, aiming to determine the concentration of leached species in solution as a function of time. Water diffuses into the initially pristine glass (with zero flow), kinetically driven glass dissolution occurs, and consequently, leached species diffuse out into the solution. Currently, my results indicate too fast dissolution. I have some questions about my approach, please can someone help?

1) In my model, the kinetic equations are independent of spatial position within the glass. I've used an infilling solution (Solution 0 with 0.3 kg of water). The glass is considered to be 1 cell, Solution 1, initially containing a specific number of moles of glass and 1e-3 kg of water i.e. made extremely dilute. The TRANSPORT data-block considers one cell with boundary conditions of "constant" and "closed" at either end. Does this all seem reasonable? I'm particularly unsure about the number of cells.

2) For TRANSPORT, I've used a cell length to be 75e-6 m (the size of the glass). Is this OK, or should I be using a larger length-scale, considering that there is surrounding water?

3) Is the use of a single diffusion coefficient OK in this case for TRANSPORT?

4) I understand how to choose the TRANSPORT numerical time-step. However, I'm unsure how I should choose the KINETICS time-step? Should it be made very small and singular e.g. 1e-6 s or should it for example, follow a longer time-scale e.g, "259200000 second in 3000 steps"?

5) I'm plotting the concentration of leached species as a function of time for Cell 1. Is this OK, to determine the concentration of species dissolved into the surrounding solution vs time?

Many thanks in advance for your help.

[dlparkhurst]

Tell me something about the physical setup of your experiment. Is it a bit of glass dropped into a beaker? Conceptually a pore in the glass? Is the diffusion radial or linear? or something else?

You may consider the reaction to be a batch reaction, in which case a SOLUTION reacts with KINETICS. In that case, the time step is controlled by the steps defined in the KINETICS definition. If you use TRANSPORT, then the time step defined in TRANSPORT applies to both the diffusive transport and the kinetic reaction.

[jLi200H]

Thanks very much for your quick response.

The physical setup is a piece of glass dropped into a beaker. Diffusion is linear. There is movement of water/dissolved species only on the left boundary (not the right). Glass dissolution kinetics follow a Monod-type law, in which the gradual formation of a particular precipitate progressively slows down the rate of release of dissolved glass species. Other precipitates form via equilibrium phase reactions.

I hope this is more clear.

[dlparkhurst]

So, you have a surface of glass exposed to a solution. It sounds like the solution volume is large relative to the changes in concentration from glass dissolution to be using the constant boundary condition.

Seems like you could model the reaction as occurring at the surface that is exposed to the solution, simply with SOLUTION and KINETICS, plus EQUILIBRIUM_PHASES for secondary minerals. The 1e-3 L of solution looks pretty arbitrary, and I assume you do not know the porosity or micro-structure of the glass, so setting up a multi-cell diffusion problem has a lot of unknowns. The simplest is simply to assume the reactive surface area is the surface that is exposed to the solution and work on your rates on that basis. If that is not sufficient, then you can think about how to modify the conceptual model.

[jLi200H]

OK, I'll see how I get on with the model just using kinetics/equilibrium phases then.

Thanks again.