We analyze experimentally the behavior of a non-Brownian, iso-densesuspension of spheres submitted to periodic square wave oscillations of theflow in a Hele-Shaw cell of gap $H$. We do observe an instability of theinitially homogeneous concentration in form of concentration variation stripestransverse to the flow. The wavelength of these regular spatial structuresscales roughly as the gap of the cell and is independent of the particleconcentration and of the period of oscillation. This instability requires largeenough particle volume fractions $\phi\geq 0.25$, a gap large enough comparedto the spheres diameter ($H/d \geq 8$) and is observed in a rather broad rangeof periods of the square waves and amplitudes of the fluid displacement. We mapthe domain of existence of this instability in the space of the controlparameters. The analysis of the concentration distribution across the gap showsthat the instability is likely to be associated to the migration of theparticles from the center towards the cell walls. In order to account for themain features of this stripes instability, we use the theory of longitudinalinstability due to normal stresses difference and recent measurements of thefirst normal stresses difference dependence with particles concentration.
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机译：我们在实验上分析了在间隙$ H $的Hele-Shaw单元中，流的周期性周期性波动引起的非布朗球体的等密度悬浮行为。我们确实观察到以浓度变化条纹横穿流的形式出现的初始均一浓度的不稳定性。这些规则空间结构的波长大致按单元的间隙缩放，并且与粒子浓度和振荡周期无关。这种不稳定性需要足够大的粒子体积分数$ \ phi \ geq 0.25 $，与球体直径（$ H / d \ geq 8 $）相比，间隙足够大，并且在方波的较大周期范围内以及在流体排量。我们在控制参数的空间中映射了这种不稳定性的存在域。对间隙中浓度分布的分析表明，不稳定性可能与颗粒从中心向细胞壁的迁移有关。为了解释这种条纹不稳定性的主要特征，我们使用了由于法向应力差引起的纵向不稳定性理论，以及最近对第一法向应力差与颗粒浓度的依赖关系进行了测量。
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