Phase segregation through transient network formation in a binary particle suspension in simple shear: Application to dough

In this paper we describe a viscoelastic type of phase separation in a simulated binary fluid with a sticky and an inert component, without any external gradients. Phase segregation under simple shear occurs due to transient network formation of the sticky component, expelling the inert particles from the network. When model parameters are adjusted to reduce network formation and rearrangement, the segregation effect is significantly smaller or absent. The behavior is independent of shear rate; segregation increases mainly with shear strain. The model is applied to wheat dough. Recent experiments have shown that prolonged shear flow of wheat dough can even give macroscopic segregation.

Figure 1

A bond between two sticky particles.

Figure 2

Number of gluten particles in the largest cluster in a sample without shear. Cluster-cluster aggregation leads to the formation of a gel structure at about $t$ = 0.6. Other clusters attach to the gel until all gluten particles are bonded into a single cluster.

Figure 3

Pair correlation functions for the gluten particles (gg), starch particles (ss), and between gluten and starch particles (gs). The gg-correlation function shows the clustering into a gel structure, the ss- and gs-correlations only show the soft overlap repulsion exclusion region.

Figure 4

Graphical image of the gelling sample, from the start (a), to just after a gel is formed (b), to the developed gel at the end of the simulation run (c). Gluten particles are colored yellow (light gray), starch particles are red (dark gray). Because of the periodical boundary conditions, the image is actually just a vertical cut across the bulk sample at an arbitrary position in the $z$ direction. Shear is in the horizontal $x$ direction, the shear gradient in the vertical $y$ direction.

Figure 5

Pair correlation function of a sample sheared at a rate of 0.1, at a strain of 2.5. The gg correlation shows a similar series of peaks indicative of the gel structure as formed without shear. The gs correlation shows a shallow depletion region between two and four particle radii.

Figure 6

Snapshot of a sample sheared at a rate of 0.1, at a strain of 2.5. The left image shows both the gluten and starch particles; the middle image shows only the gluten network. Particles further to the back have a darker shade than those to the front, giving an idea of the voids in the three-dimensional structure. The right image shows the starch particles only.

Figure 7

Correlation functions (a) and snapshot (b) of a sample sheared at a rate of 0.1, at a strain of 25. The depletion zone in the gs correlation is substantially more pronounced, as is the clustering of the gluten particles in the sample picture. Both the ss correlation and the snapshot show some minor structure in the starch phase.

Figure 8

Correlation functions (a) and snapshot (b) of a sample sheared at a rate of 1.0, at a strain of 25. The differences with the sample sheared at a rate of 0.1 are minor.

Figure 9

Correlation functions (a) and snapshot (b) of a sample sheared at a rate of 10, at a strain of 25. The snapshot suggests somewhat smaller starch patches.

Figure 10

Gluten-starch correlation function of sample sheared at a rate of 1.0, at a strain of 2.5, for different size ratios. Higher size ratios show a more pronounced depletion zone, so there is more segregation.

Figure 11

Snapshots of samples with starch-gluten size ratio of 0.6, 0.75, 1.0, 1.5, and 2.0 (left to right), at shear rate of 1.0 and strain of 25.

Figure 12

Simulation results of samples where the gluten particles may only form strings. Shear rate is 1.0; strain is 25. There is no network and the structure is layered (a). The gs correlation (b) shows only local segregation, independent of the size ratio.