Faxen's 2nd Law: Learn How to Calculate Viscous Torque

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SUMMARY

Faxen's 2nd Law provides a formula for calculating the viscous torque on a rotating sphere, expressed as τr φ = -3 μ Ω sin(θ), where μ represents the dynamic viscosity, Ω is the angular velocity, and θ is the angle of rotation. The torque is derived from the integral of the vector cross product of the position vector and the force vector. Understanding this law is crucial for accurately calculating viscous torque in fluid dynamics applications.

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RobosaurusRex
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Can someone show me how Faxen's 2nd law for the viscous torque on a rotating sphere comes to be?

I know tau_(r phi) = -3 mu Omega sin(theta)

Torque is integral of vec(r) cross vec(f)

But I can't get the right answer so I am doing something very wrong

Help?
 
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This talk may help explain it better:

file://fileportal/redirect/Downloads/2_-_One_Sphere_in_Stokes_Flow.pdf
 

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