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The motion of axis of symmetry of a spheroidal particle is given by the relation, p = p . + k 2 - 1 2

The motion of axis of symmetry of a spheroidal particle is given by the relation,
p=p.+k2-12+1(p.E-ppp:E)
Where p= orientation of the particle, p= angular velocity of the particle, E= symmetric component of the velocity gradient tensor, and = anti-symmetric component of the velocity gradient tensor. For a particle with an aspect ratio of k=100, calculate the ratio of angular velocity of the particle when it is aligned in the flow direction (x-direction) and when it is aligned in the gradient direction (y-direction). The fluid flow is simple shear flow given by,
vx=y
Where the shear rate, =1s-1. Assume the rotary Brownian diffusivity of the particle to be negligible. (Connect this ratio of angular velocity in the two orientations with the shear thinning behaviour of dilute particle suspension)
Consider it a two dinemensional problem

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