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## Homework Statement

I am currently looking for a (simplified) model to see how far/fast a object will sink in a high viscous fluid.

I found alot of information about sinking spheres and the maximum contact angle with the fuild because of the surface tension before it sinks. And a example explanation of a sinking sphere in a fluid (to calculate the speed it sinks), but this one did not start at the surface:

"Let's combine all these things together for a sphere falling in a fluid. Weight goes down, buoyancy goes up, drag goes up. After awhile, the sphere will fall with constant velocity. When it does, all these forces cancel. When a sphere is falling through a fluid it is completely submerged, so there is only one volume to talk about — the volume of a sphere."

Here they calculate the sinking speed when the sphere is fully emerged in the water.

F.buoyance + F.viscousdrag = F.massa ;ρ*g*V + 6πηrv = ρ*g*V

But in my model I need to know how fast a object (in my case a rectangle form with low height, a small flate in the order of 2 mm in length) sinks when put on the surface area of a fluid (glass) with high viscosity. In the beginning not fully emerged into the fluid.

Is it possible to give an esstimate of how fast the object will sink. I need this info because then I can calculate for how long the glass needs to be in that viscous state before the object sinks in too deep into the glass.

the object needs to stay on top of the glass but can sink a little bit (but never be fully emerged in the fluid) before changing the glass viscosity back (by lowering the temperature).

## Homework Equations

Is the surface tension neglectiable when the viscosity is very high?

Because then the object will only sink very slowly, and no high contact angle will be made?

What physics law's do I need to use for my problem (can be simplified)?

## The Attempt at a Solution

Only valid with a sphere fully emerged into the water

F.buoyance + F.viscousdrag = F.massa ;ρ*g*V + 6πηrv = ρ*g*V

V = 2* ∇ρ*g*r^2 / ( 9*viscosity )

The first attempt was with the law of archimedes, but that is only to see if it would sink.

With his law I could calculate how far it would sink because of its Volume and desity. But not how fast it would sink.

- Massa of the object is known

- volume is known

- viscosity at given temperature is known

- desity are known

I hope you can help me to give me the right direction to look into, to solve my problem.

Greetings,

spitskool