# Power required to move a glass bead in a viscous fluid

• rwooduk
In summary, the power required to move a glass bead in a viscous fluid is directly proportional to the viscosity of the fluid. The size of the bead does not have a significant impact on the required power, but a more streamlined shape can reduce the drag force. The temperature of the fluid indirectly affects the power requirement by altering the viscosity. Other factors such as container size, speed, and surface roughness can also impact the power required to move the bead.
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 vd 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:

Fs=Fd

## 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.

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

rwooduk said:
To keep the particle still
"Still?"
rwooduk said:
Fs=Fd
Fdrag(v=0,still) = 0

rwooduk
Bystander said:
"Still?"

Fdrag(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?

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

Question is found on page 184, solution on page 193

rwooduk said:
would the drag be due to the gradient force
rwooduk said:
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
Bystander said:
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!

## 1. What is the relationship between viscosity and the power required to move a glass bead in a viscous fluid?

The power required to move a glass bead in a viscous fluid is directly proportional to the viscosity of the fluid. This means that as the viscosity of the fluid increases, the power required to move the glass bead also increases.

## 2. How does the size of the glass bead affect the power required to move it in a viscous fluid?

The size of the glass bead does not have a significant impact on the power required to move it in a viscous fluid. This is because the force required to move the bead is primarily dependent on the properties of the fluid and the speed at which it is being moved.

## 3. Is the power required to move a glass bead in a viscous fluid affected by the shape of the bead?

The shape of the glass bead can have a slight impact on the power required to move it in a viscous fluid. A more streamlined shape can reduce the drag force and therefore decrease the power required to move the bead. However, this effect is not significant compared to the impact of the fluid's viscosity.

## 4. How does the temperature of the fluid affect the power required to move a glass bead in a viscous fluid?

The temperature of the fluid does not have a direct impact on the power required to move a glass bead in a viscous fluid. However, it can indirectly affect the viscosity of the fluid, which in turn affects the power required. Generally, as temperature increases, the viscosity of a fluid decreases, resulting in a lower power requirement to move the glass bead.

## 5. What other factors besides viscosity can affect the power required to move a glass bead in a viscous fluid?

Besides viscosity, other factors that can affect the power required to move a glass bead in a viscous fluid include the size and shape of the container, the speed at which the bead is being moved, and the roughness of the surface on which the bead is being moved. These factors can all contribute to the overall drag force acting on the bead and therefore impact the power requirement.

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