High Viscous Flow in Silk Spinneret

2004.May.4th

Tetso Asakura*Ayano Ino*Toshiyuki Suzuki**

* Tokyo University of Agriculture and Technology ** CHAM Japan

Introduction

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

Silk worm

Silkworm spinneret

Spinneret

530μm from Spigot

3D structure silkworm spinneret

Silk

chitin plate

Silk Press part

530m

10m100m

1mm

spigot

Silk tube

Process of Silk spinning

Silk spinning → “ α to β transition” by shear

Stress

β

Shear Stress

FiberLiquid Protein

α

Shear rate of Silk fibroin

Experiment of critical shear rate

Kataoka at.al

transition shear rate is

1E+02 ～ 1E-3 sec-1

concentration

Cri

tica

l sh

ear

rate

Molecular Dynamics simulations

Tensile stress= 0.1GPa

Shear stress=0.3,0.5,0.7,1.0GPa

Conformationalprobability

Geometry from Biology

Electron microscope

Reconstruct 3D solid

PHOENICS Object

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

STL(Stereo Lithograph) file

STL file

Solid model ⇒ triangle patchesIt accepts the un-closed and twist

surface Many tools can be used to make it

Graphical tools to Object（ Make STL file from picture)

ElectronMicroscope

1000piecePicture

Reconstruct

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

Electron Microscopic Repaired by Magics

Model (meshing)

820μm(nz=205)

156μm (nx=78)

152μ

m (

ny=

78)

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]

Boundary Conditions

Inlet Velocity 0.178cm/sec(spinneret

velocity=1.0cm/s)

Outlet P=0

Wall Non-Slip

High Viscosity Flows

Transport Equations∇●u=0

∇●uu= ∇ー p/ρ ＋ μ∇ ２ u

Finite volume equations

ΦP=(aNΦN+aSΦS+etc.)/aP

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

Convergence acceleration

Pressure correction equation at ADDDIF option for High Viscosity flow

aPpP=aNpN+aSpS+etc.+R*

a=d(c+d)/dp

Diffusion Flux

Corresponding in MIGAL

MIGAL Solver ⇒ Velocity-Pressure Coupling

ApΦp=ΣAnbΦnb+b

Matrix A included convection and diffusion fluxes

A

x x x

y y y

c c c

u

v

p

b

r

r

r

nb

u

nb

v

nb

p

nb

u

nb

v

nb

p

nb

u

nb

v

nb

p

nb

nb

nb

nb

nb

u

nb

v

nb

p

L

NMMM

O

QPPP

L

NMMM

O

QPPP

L

NMMM

O

QPPP

, ,

Convergent test

Use cut model near chitin plate

No. of cells =94x114x63

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250

Time of sweeps[x1000sec]

Flow

rate

Bal

ance

[/]

Orginal

ADDDIF

MIGAL

Flow rate balance=(inlet+outlet)/inlet

0.E+00

1.E-03

2.E-03

3.E-03

4.E-03

5.E-03

6.E-03

0 50 100 150 200 250

Time of sweeps[x1000sec]

U1

on m

onito

r po

int[

m/s

]

Original

ADDDIF

MIGAL

Monitor value

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

7.E+05

8.E+05

9.E+05

1.E+06

0 50 100 150 200 250

Time of sweeps[x1000sec]

P1

on m

onito

r po

int[

kPa]

Original

ADDDIF

MIGAL

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0 50 100 150 200 250

Time of sweeps[x1000sec]

W1

on m

onito

r po

int[

m/s

]

Original

ADDDIF

MIGAL

Pressure

Z Velocity

X Velocity

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

0 50 100 150 200 250

Time of sweeps[x1000sec]

Res

idua

l of P

1ADDDIF

MIGAL

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

0 50 100 150 200 250

Time of sweeps[x1000sec]R

esid

ual o

f W1

ADDDIF

MIGAL

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

0 50 100 150 200 250

Time of sweeps[x1000sec]

Res

idua

l of U

1

ADDDIF

MIGAL

ResidualPressure

Z Velocity

X Velocity

Pressure and Velocity

Pressure[kPa] Streamline[msec]

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)

Slip Velocities of cross section [1/sec]

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.

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.

Summary & Conclusion 3

Future and next step PARSOL (Cut cell) Pressing at chitin plate (use Moving Grid

or MOFER). Survey for the fibroin properties.