## Chocolate Rheology

### Quick Start

Chocolate is a highly-filled system during its processing. It's easy to make it flow - just add lots of fat (which is liquid at processing temperatures), but that's not what we want. Instead we want maximum solids with minimal fat. To get this the chocolate is "conched", spending a long time being broken up into smaller particles, which in turn get surrounded by anti-friction agents, or, as more normally called, dispersants or emulsifiers.

Here we see why both effects of conching are necessary. The app is based on a wonderful, open access paper1 led by a team from U Edinburgh

As the paper stresses, and as discussed below, the implications go far beyond the conching of chocolate.

### Chocolate Rheology

N - Agglomeration number
μ friction coefficient

Take the ingredients (cocoa solids, milk solids, sugar and cocoa butter) and "melt" them together and you get a coarse powder looking nothing like nice pourable chocolate. Now let it sit for some hours being sheared by a mixer. This makes it into a finer powder. Now add some suitable dispersants such as lecithin and PGPR (polyglycerol polyricinoleate) and the powder transforms into the classic flowable, pourable chocolate.

The process is called conching because when invented by Rodolphe Lindt in 1879, the machine had an odd bowl shape, reminiscent of a conche shell. The invention transformed chocolate production and is as important now as it was for Lindt Chocolates back in the 19th century.

The paper shows that there are two effects:

1. Large aggregates are broken down closer to individual particles. This has a big effect on φm because clumped particles pack less well.
2. The friction between particles is reduced by the dispersants. This changes the effective φm and also the yield stress.

What is φm? This is the maximum packing fraction at which the particles can no longer flow - as discussed in the other particle rheology apps.

The paper chooses to use the equation for dependence of relative viscosity on volume fraction, φ as:

η_"rel"=(1-φ/φ_m)^-λ

The power λ is 2 for perfect spheres but in the paper it varies from about 1.9 down to 1.5 for agglomerates. The value of φm is 0.64 for pure spheres with very low particle friction, going down to 0.4 for large agglomerates and high friction. The app takes your agglomeration size and friction inputs and approximates the values in the paper. The app is only trying to show plausible trends and in any case different chocolate formulations will show somewhat different curves, even though the trends will be similar.

### Yield Stress

The friction has a very strong effect on the yield stress, as you would expect. This is illustrated, though some of the subtleties of the original (e.g. a rise in viscosity at higher shear stress in the low friction system) are not replicated.

### Beyond chocolate

The principles are general. The effects are as important for making cement as they are for making chocolate. Any process requiring high volume fractions will benefit from dis-aggregation and a reduction in particle friction. In cement, the arrival of superdispersants made it possible to create cement that required less water for a pumpable mix. Even a small % reduction has a big effect when you have to pump 1000s of tons of cement.

Similarly, making high-performance ceramics is all about casting the highest-possible volume fraction of ceramic with the minimum of extra ingredients so that the "green" strength is maximal and shrinkage on sintering is minimal.

1Elena Blancoa, Daniel J. M. Hodgson, Michiel Hermesa, Rut Besseling, Gary L. Hunter, Paul M. Chaikin, Michael E. Catesa, Isabella Van Damme, and Wilson C. K. Poon, Conching chocolate is a prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content, https://doi.org/10.1073/pnas.1901858116