Measurement of viscosity of polymer

[hizen_14]

Homework Statement

if we have only a measuring cylinder (500mm high and 50mm diameter), a stop-watch, a ruler and a 100μL syringe. We assume that the density of the suspension is 1g/cm3, and that the polymers are spherical How can we determine the viscosity and the volume fraction of the polymers in solution?

Homework Equations

Strokes Law and Einstein equation

The Attempt at a Solution

To measure viscosity of liquid I normally think of a falling sphere object known mass and density in a cylinder contain a unknown viscosity sample. So I can use Strokes' Law to find the viscosity and Einstein equation to find a volume fraction.

But No sphere object is provided in this question.
Any idea what to do with syringe.

Thanks

Zen

 

[anathema]

ith,

Thank you for your question. In this situation, we can still use Strokes' Law and Einstein equation to determine the viscosity and volume fraction of the polymers in solution. However, instead of using a falling sphere, we can use the 100μL syringe as our object with known mass and density.

First, we will need to measure the time it takes for the syringe to fall from the top to the bottom of the measuring cylinder using the stop-watch. We will also need to measure the distance it falls using the ruler. From these measurements, we can calculate the velocity of the syringe using the equation v = d/t, where v is the velocity, d is the distance, and t is the time.

Next, we can use Strokes' Law, which states that the drag force on an object moving through a fluid is proportional to its velocity, density, and radius, to calculate the viscosity of the solution. The equation for Strokes' Law is F = 6πηrv, where F is the drag force, η is the viscosity, r is the radius of the object, and v is the velocity. Since we know the density of the solution and the radius of the syringe, we can rearrange this equation to solve for the viscosity (η = F/6πrv).

Finally, we can use Einstein equation, which relates the viscosity of a solution to the volume fraction of the particles in the solution, to calculate the volume fraction of the polymers. The equation is η = η0(1 + 2.5φ), where η0 is the viscosity of the solvent and φ is the volume fraction of the particles. By rearranging this equation, we can solve for the volume fraction (φ = (η/η0 - 1)/2.5).

In summary, by using Strokes' Law and Einstein equation, we can determine the viscosity and volume fraction of the polymers in solution using the 100μL syringe as our object. I hope this helps and let me know if you have any further questions.