**15. Centre of concentration**

The *centre of concentration (G(r,θ)* or *G(x,y))* of particle suspensions can be as important as the *centre of mass* in the mechanics of solids. Uniform suspension is

#### **Figure 7.**

*Locus of Centre of concentration (LCC) from ERT measurements. (2 mm beads of RD 1.4 and concentrations 7.31%, 5.48%, 3.66% and 1.79% v/v in water).*

#### **Figure 8.**

*Centre of concentration calculations using the two-layer model as an approximation to the actual concentration distribution in the cross section.*

indicated if *G* is near the geometrical centre of the duct. If it is near the periphery of the duct, sluggish or static settlement can be inferred.

**Figure 7** shows the *locus of centre of concentration (LCC)* for a series of concentrations The origin (0,0) is the centre of the pipe*.* The position of *G* for a given pipe velocity changes as concentration increases. This downward trend is a *locus of centre of concentration (LCC),* which can be used to study the state of suspension of the medium.

The current version of the *2LM* model computes the first moment of the two layers and combines these results to obtain the centre of concentration of the whole. All three results are useful in different ways. The position of the centre of concentration for the upper layer for example may be important when a stationary bed is indicated. The estimates are surprisingly close to those obtained from tomography measurements (see **Figure 8**). The *2LM* estimates are above the parity line because the actual interface between layers is a diffuse boundary rather than a precise chord.

**Figure 9.** *2LM example — Coarse particles in water.*
