Stripes instability of an oscillating non-Brownian iso-dense suspension of spheres

Abstract

We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap H. We do observe an instability of the initially homogeneous concentration in form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions φ ≥ 0.25 and a gap large enough compared to the sphere diameter (H/d ≥ 8). Mapping the domain of existence of this instability in the space of the control parameters shows that it occurs only in a limited range of amplitudes of the fluid displacement. The analysis of the concentration distribution across the gap supports a scenario of particle migration towards the wall followed by an instability due to a particle concentration gradient with a larger concentration at the walls. In order to account for the main features of this stripes instability, we use the theory of longitudinal instability due to normal stresses difference and recent observations of a dependence of the first normal stresses difference on the particle concentration.p-1

Instability in suspensions oscillating along narrow channels

“…This is specially relevant for oscillatory flows, where a succession of reversals happen. Oscillatory flows of suspensions in Hele-Shaw cells has been shown to be unstable at low Reynolds numbers, with a modulation of the particle volume fraction along the flow direction visible as stripes [9]. Recently, we studied the motion of the particles during the onset of this instability using experiments with a model system composed of non-Brownian spherical particles and a Newtonian solution [10].…”

Striped Patterns in Radially Driven Suspensions with Open Boundaries

“…Formation of elongated patterns is ubiquitously observed in a wide variety of horizontally driven granular systems. Examples range from ripples in sandy deserts and along many coasts to striped patterns in colloids, suspensions, dry granular media, and nanoparticle composites [1][2][3][4][5][6][7][8][9][10][11][12]. Under horizontal shaking or oscillatory excitation, various types of instabilities may arise in dry granular media and suspensions.…”

“…Under horizontal shaking or oscillatory excitation, various types of instabilities may arise in dry granular media and suspensions. This can lead to, e.g., separation of different species [13], shear-induced segregation [14,15] in environments with a nonuniformly distributed shear strain [16,17], or, more frequently, stripe formation [8][9][10][11][12][18][19][20][21][22][23][24].…”

“…While the origin of stripe formation in granular mixtures is often attributed to the differences between the components [8][9][10][11][18][19][20][21][22], stripes form even between identical particles [4,5,23]. The role of lateral walls in stripe formation [12,23,31] and whether the coarsening of the patterns leads eventually to phase separation [4,10,32,33] have also been under debate.…”

“…w was reported to grow with the amplitude A of the oscillatory drive in suspensions [10]. There is a consensus that the increase of A enhances λ in ripples and stripes (though with various different λ−A dependencies) [7,10,12,18,30,34,35]. However, various contradicting relations (i.e., increase, decrease, or none) between λ and the frequency f of the oscillatory drive have been reported in the literature [7,10,12,18,19,30,[35][36][37].…”