Approximating a collection of particles as a liquid

[awygle]

This may be hard to explain, but here goes...

Say you have one of those little plastic BBs. When there's just one, it behaves like a solid sphere (which it is). But if you have a large number of them, the mass sort of acts like a liquid - it pours and flows and similar things.

My questions are, what parameters affect whether this is a reasonable metaphor to adopt? Obviously number of particles, perhaps size and shape? Is this something other people think about, or is it just me?

Any thoughts appreciated, thank you

 

[Drakkith]

I'd venture a guess and say size of the particles, shape, size of the system, and a myriad of other factors.

 

[Andy Resnick]

This may be hard to explain, but here goes...

Say you have one of those little plastic BBs. When there's just one, it behaves like a solid sphere (which it is). But if you have a large number of them, the mass sort of acts like a liquid - it pours and flows and similar things.

My questions are, what parameters affect whether this is a reasonable metaphor to adopt? Obviously number of particles, perhaps size and shape? Is this something other people think about, or is it just me?

Any thoughts appreciated, thank you

google "granular flow". Lots of very good groups study that problem.

 

[Mapes]

Is this something other people think about, or is it just me?

It's something many physicists are thinking about. Because the assembly isn't quite a liquid; you could obviously form piles of spheres that wouldn't spontaneously flatten out. So there's some agitation that's needed to obtain flow. On the other hand, the piles are barely solids, as en masse they're thousands or millions of times more compliant than the material that forms the individual spheres.

As Andy says, the field is called granular flow, and it's a challenging and exciting area of physics.

 

[Curl]

In a real liquid there are many more particles. I.e. a cup of BBs can have no more than 1 million particles, where as a cup of water has 10^25 or so.

Also energy behaves differently when it enters the system, i don't know how to explain.

 

[Andy Resnick]

It's something many physicists are thinking about. Because the assembly isn't quite a liquid; you could obviously form piles of spheres that wouldn't spontaneously flatten out. So there's some agitation that's needed to obtain flow. On the other hand, the piles are barely solids, as en masse they're thousands or millions of times more compliant than the material that forms the individual spheres.

As Andy says, the field is called granular flow, and it's a challenging and exciting area of physics.

One interesting specific problem being studied is the 'glass transition'- how the glassy state forms, and is related to jamming.

Another interesting concept is how to define a temperature- the problem is most clear when discussing a monodisperse colloidal system of spheres. For example, there is a phase transition between fluid and crystal at a certain value of the volume fraction (0.58, IIRC)- how much volume is occupied by spheres. The volume fraction is then a proxy for thermodynamic temperature T, but clearly the volume fraction is unrelated to the temperature you would measure with a thermometer.

 

[Mapes]

Another interesting concept is how to define a temperature- the problem is most clear when discussing a monodisperse colloidal system of spheres. For example, there is a phase transition between fluid and crystal at a certain value of the volume fraction (0.58, IIRC)- how much volume is occupied by spheres. The volume fraction is then a proxy for thermodynamic temperature T, but clearly the volume fraction is unrelated to the temperature you would measure with a thermometer.

Definitely tracking with you there - my recent work has been on the mechanical properties of tissue cells, another type of soft, disorganized "material". The creep compliance of cells scales as $t^a$, where $a$ is typically 0.1-0.3, and one interpretation is that the effective "temperature" in the cells (essentially, the agitation energy you describe) is 10-30% above a glass transition "temperature". Cells, as you likely know, lie in an intriguing intermediate position between elastic solids (whose creep compliance is $\propto t^0$, or constant) and fluids (whose creep compliance is $\propto t^1$). It's exciting to watch these complex states of matter - cells, granular materials, and related states - become better understood.

 

[Andy Resnick]

Definitely tracking with you there - my recent work has been on the mechanical properties of tissue cells, another type of soft, disorganized "material". The creep compliance of cells scales as $t^a$, where $a$ is typically 0.1-0.3, and one interpretation is that the effective "temperature" in the cells (essentially, the agitation energy you describe) is 10-30% above a glass transition "temperature". Cells, as you likely know, lie in an intriguing intermediate position between elastic solids (whose creep compliance is $\propto t^0$, or constant) and fluids (whose creep compliance is $\propto t^1$). It's exciting to watch these complex states of matter - cells, granular materials, and related states - become better understood.

Very cool! Do you work in either Janmey's or Fredberg's groups?

 

[Mapes]

Very cool! Do you work in either Janmey's or Fredberg's groups?

Neither of those, but I do follow the Fredberg group's output closely. Also Ben Fabry's cell rheology papers, which I think are outstanding.