*Week 1*

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## April 04, 2005

### Dilute Granular Collpase

Following discusions the following synthesis was arrived at under which the dilute granular gas collapses without compact clusters, yet with some of the same scaling.## March 31, 2005

### David Pine Seminar 31 March 05

#### Jamming in dense suspensions.

link to full kitp media of this talk

Interest in how thngs STOP flowing. Eta vs phi plot

Universality?

– role of interactions

– peclet number g a^{2/D order 10}8 in Pine’s expts, so diffusion comparatively unimprtant.

System eventually jams

-at what volume fraction? Random close packing or less?

-Dependence on Pe?

Random Loose packing Onoda and Liniger PRL 643 2727 (1990)

=loosest packing that can support external load

density matched expts., extrapolating phi to perfect bouyancy matching, leading to 55%. << rcp

Lootens et al PRL 90 178301 (2003)

Constant shear rate couette -> spiky fluctuations in measured stress. Associated with jamming state, but it is forced to flow in these expts.

DP expts: controlled stress so that the system has the option to jam.

“non-colloidal suspensions” => negligible Brownian motion.

Match refractive index for transparency and match density to cancel gravity.

Particles deliberately polydisperse to discourage crystallisation under shear.

Gap: particle diameter 10 to 1000. Walls rough through glued particles.

Need protocol to produce well-defined initial conditions: use oscillating stress of amplitude decreasing from value giving strain ~3. Gives reproducible loosely packed state.

Weak polydispersity to reduce shear induced ordering. (RCB: target this for simualtions?)

Plot reduced viscosity vs strain, measured in runs at constant shear stress. Normal force measurements avaialable from parallel plate measurements. N1=sigma_xx–sigma_yy (x=flow, y=gradient directions). Negative in concentrated suspension. N1~=|s_xy|

Abrupt switch in behaviour: vf =55% flows (just) wheres 56% jams, at strain ~1%.

Flow reversal (repeated) measurements at low stress seem to converge towards a doubly locked state. (another target for simulations?).

Similar measurements at higher stress lead to increasing range of unjammed strain.

System flows at still higher stresses.

Following Particle Trajectories

Pair distribiution functions measured: little altered up on jamming, because the strains involved are so small.

Flowing systems exhibit string like ordering with clear evidence of some layering.

Summary:

Non-colloidal suspensions jam above a (gap dependent) volume fraction

Suspensions jam both ways (work hardennign)

Flowing dense suspensiosn organise into strings in teh flow direction.

These strings are organised into sheets in teh velocity-vorticity plane

sigma_c jamming occurs only below a critical stress.

### Unsolved Problems, 2005–03–30

### 1 Packing

#### Robin Ball, Thomas Halsey and David Pine

What physically realisable protocols lead to average coordination number d+1 in the limit of perfectly stiff, frictional particles? Is there a critical volume fraction, less than random close pack, above which granular systems will jam after a finite shear, and below which they can shear indefinitely?

### 2 Homogenous cooling in granular gases.

#### Eli Ben-Naim

How can the exponent be derived for the decay of energy in homogenous cooling states? What is the relation to compression shocks in piston type flows.

### 3 Constitutive Laws and Field Variables for Granular Flows

#### Jerry Gollub

What constitutive laws are appropriate in different flows? What additional field variables, such as correlation length or granular temperature, are necessary?

### 4 Boundary Layers

#### Daniel Lhuillier

Are boundary layers important in granular flows?

### 5 Effect of strain history on yield stress.

#### Jean Carlson

### 6 Granular pressure and thermodynamics

#### David Dean

### 7 Interaction of granular flows with the ambient fluid

#### Jim McElwaine

How to granular flows interact with the ambient fluid? When to dense flows become suspension currents? What is the effect of suspended particles on turbulent structure? How does particle sedimentation effect turbulent entrainment of the ambient fluid?

## March 29, 2005

### Opening Discussion 28 March

This was a first day meeting amidst the dazzling views of the "fishbowl" (aka porthole room).

We agreed to hold INFORMAL MEETINGS 10 am on TUESDAYS, now booked into KITP's Small Seminar Room; the first of these will be an opportunity for everyone to introduce themselves and their research interests in the field.

FORMAL SEMINARS we have set for 10 am on THURSDAYS;

David Pine (UCSB) will give the first of these, title: "Jamming in Dense Suspensions".

PROGRAM DINNERS will be THURSDAY evenings. The first of these will be at Beachside Restaurant, Goleta Beach; as we need to reserve this please reply to Thomas Halsey if you want to come, ASAP please.

Robin Ball.

#### Scientific Introductions Tuesday 29 March

See Participants and their Interests category (link in left column)