A Numerical Model of Bubbling Thermoplastics
A Numerical Model of Bubbling Thermoplastics
A Numerical Model of Bubbling Thermoplastics
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Bubble Migration<br />
• Driven by gravity, temperature gradients<br />
(surface tension, viscosity dependence on T)<br />
U<br />
=<br />
−<br />
2<br />
2(<br />
ρ p − ρ g ) gR ⎡ ⎛ d ln µ ⎞ R ⎛ d lnσ<br />
⎞⎤<br />
∂T<br />
+ ⎢2RR&<br />
⎜−<br />
⎟ + ⎜−<br />
⎟<br />
9µ<br />
dT<br />
dT<br />
⎥<br />
⎣ ⎝ ⎠ 3µ<br />
⎝ ⎠⎦<br />
∂z<br />
• Wake effects<br />
• Bubbles slow as approach surface
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