Volume fraction instability in an oscillating non-Brownian iso-dense suspension

ROHT, Y.L.; HULIN, J.P.; GAUTHER, G.; SALIN, D.; CHERTCOFF, R.; AURADOU, H.; IPPOLITO, I.

Montpellier

Congreso; 8th International Conference on Micromechanics of Granular Media; 2017

We study experimentally the instability that appears in a non-Brownian iso-dense suspension of spheres submitted to a periodic flow in a Hele-Shaw cell. The suspension is made of mono-disperse polystyrene beads of radius a = 40 m dispersed in a water glycerol mixture of the same density as that the particles = 1050 kg.m-3) and of viscosity  = 1.7 m2s-1. The suspension is injected in glass Hele-Shaw cells of length 10 cm, aperture b = 0.4 mm and width 8 mm, illuminated from below. A programmable pump produces square wave flow rate variations with a frequency f up to 2.5 Hz and injected volumes during each half cycle up to 16 mm3 (corresponding highest peak to peak fluid displacements up to 10 mm). To minimize the effect of sedimentation due to a small difference of densities between the fluid and the particles the front walls of the Hele Shaw cell are horizontal. The instability is marked by stripe shaped variations of light parallel to the width of the cell and thus perpendicular to the fluid displacement. The wavelength of the pattern does not vary with f and depends weakly on the amplitude of the fluid displacement: its value  is of the order of twice the cell aperture (  0.8 mm). Close-up visualizations of the distribution of particles in the gap of the cell show that the stripes created by the instability correspond to spatial variations of the volume fraction  of particles in the bulk of the supension. The instability occurs only for  > 0.25 and in a limited range of flow rates depending on f. At a high frequency f = 2Hz stripes are observed for an average fluid displacement, A, between 0.4 mm and 1.4 mm corresponding to a strain   [1, 3.5]. At a lower one f = 0.1 Hz, the range of observation of the instability is reduced to A  [0.8, 1.1] mm. In this range of parameter values the Reynolds number Re = 2Af b/  for the global flow remains below 1.3 while the particulate Reynolds number Rep =  a2 f /  is lower than 3 10-2: thus we can consider that this instability corresponds to a non Brownian suspension at low Reynolds number. Finally, it has to be noted that the instability was not observed in cells of aperture less than 10 particles' diameter (no instability occured in a Hele-Shaw cell of aperture b=0.4 mm with a suspension of particles of diameter d = 60 m and for b=0.3 mm with d = 40 m).