Latest Computer Model of Sieving Looks Terrific

ByKarl Smith
After a great deal of debugging and thought, I’ve made a small breakthrough in the modeling of sieving behavior using MATLAB, Bill Deen’s electrostatic model of pore-particle interactions, and a boltzman distribution to model concentration polarization (previous blog posts: Part 1 Part 2 Part 3). I had made a small conceptual error while generating the algorithm behind this numerical approximation, and yesterday I figured out my mistake, enabling me to acquire these curves today:
Josh graph with model predictions
From Josh W’s nitride fabrication paper (which is where the original, model-curve-free figure is from):

While the membranes cut-offs correlate with the relative pore sizes of the two NPN membranes, neither the average pore sizes (58 nm for 30 s RIE; 79 nm for 40 s RIE), nor the maximum pore sizes (100 nm for 30 s RIE; 120 nm for 40 s RIE) are predictive of the actual cut-off. This is expected for gold filtration in deionized water as the electrostatic and electrokinetic interactions between charged nanoparticles and membranes make the effective pore sizes smaller than their physical dimensions.

Three important caveats: the model as yet uses an array of perfectly monodisperse pores of the same diameter as Josh’s average pore size, the model assumes constant pressure (it does not account for the fact these separations were done in the centrifuge *EDIT: these separations were performed at constant pressure and not in the centrifuge, which is great*) and it doesn’t account for the fact that the concentration buildup at the membrane will contribute to the hydraulic resistance. That said, the overlap is super encouraging, and all three caveats can be accounted for somewhat straightforwardly in the next version of this program.
All values are from a MATLAB program I plan to upload in the next post.
Specifics of the separation I used for the model:

transmembranePressurePSI = 3; % We assume the pressure is 5.5 PSI = 37921.16 pascals

zetaMembrane = -0.020; %in V

zetaParticle = -0.015;

molarSaltConcentration = 0.001; %In moles of KCl.

particleDiameter = 20 – 50 E-9;

particleRadius = particleDiameter/2;

poreDiameter = 58 (or 79) E-9;

poreRadius = poreDiameter/2;

membraneThickness = 50E-9;  %in m

approxNumberOfPoresInSepcon = 400000000; %(number)

porosity = 0.05; %fraction       

activeArea = 1.5E-6; % m^3

fluxthroughpore = DaganFlow(poreRadius, membraneThickness, transmembranePressure); % m^3/s

solventSpeed = (fluxthroughpore/(pi*poreRadius^2));  %m/s

iterations = 300; %number

timeOfSeparation = 2E-7/(fluxthroughpore*approxNumberOfPoresInSepcon); %s

The model was run until 200 uL of the sample had passed through the membrane.

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2 Comments

  1. Those curves are reassuring on many levels. Hooray!

    One less caveat to worry about, the separations for that figure were done by Sarah and I using constant pressure.

    Cheers- Josh

  2. Great! Sometimes it really helps to put these things down for awhile and take a fresh look later.

    Can you thicken the membrane and see the curves flatten out in the simulation?

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