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

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

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Silkworm spinneret Spinneret 530μm from Spigot

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

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Process of Silk spinning Silk spinning α to β transition by shear Stress β Shear Stress FiberLiquid Protein α

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

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

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Geometry from Biology Electron microscope Reconstruct 3D solid PHOENICS Object

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PHOENICS OBJECTS PHOENICS-VR Objects Dont need BFC meshing & Easy to Use Complex Geometry facet data converted from STL format Wall friction added automatically on Object face

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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

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

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

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Electron Microscopic Repaired by Magics

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

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Properties of Silk fibroin Density 75%water1.075[g/cm3] Viscosity Neuton Fluid6.5E+4[P] Ref:Water=0.01[P],Glycerin=7.982[P]

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Boundary Conditions Inlet Velocity0.178cm/sec (spinneret velocity=1.0cm/s) OutletP=0 WallNon-Slip

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

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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

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

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Corresponding in MIGAL MIGAL Solver Velocity-Pressure Coupling ApΦp=ΣA nb Φ nb +b Matrix A included convection and diffusion fluxes

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

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Flow rate balance=(inlet+outlet)/inlet

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Monitor value Pressure Z Velocity X Velocity

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Residual Pressure Z Velocity X Velocity

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Pressure and Velocity Pressure[kPa] Streamline[msec]

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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)

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Slip Velocities of cross section [1/sec]

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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.

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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.

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

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