Hello!
I would like to understand in what cases blood or some other biological liquid passes through implant or graft with some porous microstructure according the Darcy law (thanks to the pressure differences).
I have an idea to produce a research about blood permeability through various implants microstructure, but unfortunately it is harder than I thought to found some justification in literature that blood actually could pass through such microstructure due the Darcy law. Thus, I would be grateful for your help in this question - maybe you have some papers about it or some other helpful stuff.
Sincerely, Catherine
Blood in continuous moving case can pass through a porous structure under higher pressure difference than Newtonian fluids. Darcy law is not enough in this case. You must add the effect of Inertia, Forchheimer-Brinlman terms and the effect of Non-Newtonian fluid must appear in the viscosity term. Darcy's law only is not enough.
First of all why you want to study this aspect in particular. What would be its clinical implication? Would the answer (if you discover) will solve any problem that is currently faced in implantology.
Logically, blood may penetrate the implant surface porosity to certain microns but not do through and through and fill the central void. If any implant company designs a thin walled implant with greater porosity and a wider empty space in between then may be blood may travel through and through, but again the implant fracture failure rate will be tremendously high in this implants not only in function but majority will fracture at high placing torque itself.
good luck
The main parameters affecting the blood flow in porous media are:
1- Viscosity of blood (Non-Newtonian Fluid) It must be treated as NonNewtonian
2- Porosity of the medium ( implant )
3- Pressure force that pushes the fluid
4- Inertia force
5- Friction effect and No Slip condition
6- Channeling effect of the porous media ( implant ) if exists
All these parameters must considered with Darcy's equation when solving this flow.
Dear Amit Agrawal,
thank you for your answer!
I am interested in this issue through the field of modeling and additive technologies. We have an idea to model various microstructures with the help of Function Representation approach (it is my supervisor's development) and than to study its permeability.
Due to the fact that our Center is about Additive manufacturing and my background mostly too, I asked this question to understand the opportunities of this project in the aspect of medicine.
My colleague has a research installation to study permeability using Darcy law, therefore I asked this question to understand whether this installation needs to be improved or not.
For the implant destroying, could it probably be useful if we want to make a biodegradable implant, for example?
Sincerely, Catherine
Dear Gamal B. Abdelaziz ,
Thank you for your answer!
As I understand, Forchheimer-Brinlman terms and Darcy law and other criteria must form a system of equations, or be combined and accounted for in one?
I am sorry if this is a stupid question, I just don 't have the proper experience in studying permeability yet.
Sincerely, Catherine
Dear Pascale Royer,
Thank you! But as far as I know, it can be adapted for the Non-Newtonian fluid, isn't it?
Sincerely, Catherine
Gamal B. Abdelaziz ,one more question, whether I understand well, I need to use Brinkman-Forchheimer- Darcy extended equation ?
Yes, You must use Darcy Forchheimer-Brinkman equation considering Non-Newtonian Effect in viscosity Term to study all parameters affecting this flow
Yes, You must use Darcy Forchheimer-Brinkman equation considering Non-Newtonian Effect in viscosity Term to study all parameters affecting this flow
Gamal B. Abdelaziz , at this stage I think yes, thank you. I will discuss with my colleague who has an experimental machine about further details and maybe new questions will appear.
Thank you very much and I hope to recieve any updating about this flow
Well,
https://iopscience.iop.org/book/978-0-7503-1997-3/chapter/bk978-0-7503-1997-3ch3
Regards
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