Power required to move a glass bead in a viscous fluid

[rwooduk]

Homework Statement

A bead of radius R(=5 μm) is trapped by an optical beam and moved through a
viscous fluid at a speed v_d of 20 μms^-1. If the viscous drag is given by Stokes
law:

$$F_{d}=6\pi \eta Rv_{d}$$

obtain an expression for the laser power (intensity). If the process only has an efficiency of 25% what laser power
is required to drag the bead?

(Assume that the viscosity of the medium is η=10^-3Pa s, and its refractive index, n=1.3)

2. Homework Equations
To keep the particle still, the scattering force from the laser must be equal to the viscous drag from the fluid:

F_s=F_d

The Attempt at a Solution

I can obtain an expression for keeping the particle still, as described in the Relevant equations above. However if we want to move the particle it must (?) involve the gradient force. The force that when the laser is moved will shift the particle towards it's centre, hence the particle will move. But we are not given required info for this derivation, such as the refractive index of the bead.

I'm really lost with this question, has anyone any experience with optics type questions such as these? I've looked online and can't find a similar question anywhere.

Any point in the right direction would really be appreciated.

 

[Bystander]

moved through a
viscous fluid at a speed vd of 20 μms-1.

To keep the particle still

"Still?"

Fs=Fd

F_drag(v=0,still) = 0

 

[rwooduk]

"Still?"

F_drag(v=0,still) = 0

hm, indeed i misinterpretd the question wrong. In that the laser moves the bead in the fluid, the bead isn't already moving in the fluid. Still, would the drag be due to the gradient force as described in the OP?

thanks for the reply

 

[rwooduk]

Just to complete this thread I found a very useful derivation that goes some way to solving the problem here (WARNING very large pdf!)

http://www.abhinav.ac.in/DoL/CompEx/Ph_CanadaNPhO_93-02.pdf

Question is found on page 184, solution on page 193

 

[Bystander]

would the drag be due to the gradient force

drag is given by Stokes
law: F d =6πηRv d

You have two forces working, viscous and scattering. Don't get too sidetracked pursuing a "gradient" force until you've defined it.

 

[rwooduk]

You have two forces working, viscous and scattering. Don't get too sidetracked pursuing a "gradient" force until you've defined it.

Ahhh i see what you are saying, why define the gradient force when it must be equal (slightly greater than) the viscous drag. Will work on this some more, thanks for the replies!