High Viscous Flow in Silk Spinneret

1. High Viscous Flow in Silk Spinneret 2004.May.4th Tetso Asakura* Ayano Ino* Toshiyuki Suzuki** * Tokyo University of Agriculture and Technology ** CHAMJapan

2. Introduction Silk worm • For create silk artificially, it is important to application of process of silk spinning.

3. Silkworm spinneret 530μm from Spigot Spinneret

4. 3D structure silkworm spinneret 530m 1mm 10m 100m Silk Press part chitin plate Silk Silk tube spigot

5. Process of Silk spinning Shear Stress β α Liquid Protein Fiber • Silk spinning 　　→ “α to β transition” by shear Stress

6. Shear rate of Silk fibroin • Experiment of critical shear rate • Kataoka at.al transition shear rate is 1E+02～1E-3 sec-1 Critical shear rate concentration

7. Molecular Dynamics simulations Tensile stress =0.1GPa Shear stress =0.3,0.5,0.7,1.0GPa Conformational probability

8. Geometry from Biology Electron microscope Reconstruct 3D solid PHOENICS Object

9. PHOENICS OBJECTS ■PHOENICS-VR “Objects” → Don’t need BFC meshing & Easy to Use ■Complex Geometry →facet data converted from STL format ■Wall friction added automatically on Object face

10. STL(Stereo Lithograph) file • STL file • Solid model ⇒ triangle patches It accepts the un-closed and twist surface • Many tools can be used to make it

11. Graphical tools to Object（Make STL file from picture) Electron Microscope Reconstruct 1000piece Picture

12. Repair STL Repair STL file Cimatron Magics • What is required before importing PHOENICS ? ・ No Hole or Gap ・ Surface vector is the same direction(twist) ・ Cut small parts ・ Smoothing

13. Repaired by Magics Electron Microscopic

14. Model (meshing) 820μm (nz=205) 152μm (ny=78) 156μm (nx=78)

15. Properties of Silk fibroin • Density • 75%water 1.075[g/cm3] • Viscosity • Neuton Fluid 6.5E+4[P] • Ref: Water=0.01[P],Glycerin=7.982[P]

16. Boundary Conditions • Inlet Velocity 0.178cm/sec (spinneret velocity=1.0cm/s) • Outlet P=0 • Wall Non-Slip

17. High Viscosity Flows • Transport Equations ∇●u=0 ∇●uu=　ー∇p/ρ ＋　μ∇２u • Finite volume equations ΦP=(aNΦN+aSΦS+etc.)/aP

18. Continuity Equations • Error of continuity R*=cN-cS+etc. c: convective flux • Pressure correction equation aPpP= aNpN+aSpS+etc.+R* by default: a=dc/dp

19. Convergence acceleration • Pressure correction equation at ADDDIF option for High Viscosity flow aPpP=aNpN+aSpS+etc.+R* a=d(c+d)/dp Diffusion Flux

20. Corresponding in MIGAL • MIGAL Solver　⇒ Velocity-Pressure Coupling ApΦp=ΣAnbΦnb+b Matrix A included convection and diffusion fluxes

21. Convergent test • Use cut model near chitin plate No. of cells =94x114x63

22. Flow rate balance=(inlet+outlet)/inlet

23. Monitor value Pressure Z Velocity X Velocity

24. Residual Pressure Z Velocity X Velocity

25. Pressure and Velocity Pressure[kPa] Streamline[msec]

26. Slip velocities(shear rate) • In PHOENICS, the magnitude of the total rate of strain GEN1 is given as, GEN1=2*[(du/dx)2+(dv/dy)2+(dw/dz)2] +(du/dy+dv/dx)2 +(dv/dz+dw/dy)2 +(dw/dx+du/dz)2 Slip velocity is Vs=SQRT(GEN1)

27. Slip Velocities of cross section [1/sec]

29. Summary & Conclusion • About Simulation Result • The maximum shear velocities is 45[1/s] at silk press part. Where is provided the transition from liquid protein to fiber. • Static Pressure loss is Giga Pascal order in spinner. It is as same as the transition stress with the molecular dynamics simulation.

30. Summary & Conclusion 2 • About CFD technique • With some graphical tools, we can calculate easily the case with complex biology geometry by PHOENICS. • A better convergence has been gotten by adding the diffusion velocity into pressure correction equation for High Viscous Flow, If we desire much better performance, we can use MIGAL.

31. Summary & Conclusion 3 • Future and next step • PARSOL (Cut cell) • Pressing at chitin plate (use Moving Grid or MOFER). • Survey for the fibroin properties.