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We present a model describing the rebound of a drop impinging on a rigid plane wall immersed in water. This model is based on the resolution of the drop equation of motion in an unbounded fluid in which an additional pressure force is introduced accounting for the wall effect on the drop motion. This force is computed from a film drainage simulation model during the approach of the deformable particle to the wall. Results of the model have been compared with experimental trajectories of drops impinging vertically at terminal rise velocity against a horizontal wall immersed in water at rest. These trajectories have been obtained with the help of an image processing technique. A wide range of experimental conditions has been studied (drop diameter, interfacial tension, drop viscosity, and density). In most of the cases, the model predicts the experimental trajectories within a very good accuracy (height of bouncing, deformation, number of rebounds) even in the case of a significant deformation. The numerical results show that the rebound of a deformable inclusion against a wall in water is essentially governed by the balance between the added mass force and the film pressure force exerted on the drop during the impact. The model has also been successfully tested in the case of an impinging bubble at high particle Reynolds number, based on experimental data taken from Tsao and Koch [Phys. Fluids 9, 44 (1997)].

The presence of finite-size particles in a channel flow close to the laminar-turbulent transition is simulated with the Force Coupling Method which allows two-way coupling with the flow dynamics. Spherical particles with channel height-to-particle diameter ratio of 16 are initially randomly seeded in a fluctuating flow above the critical Reynolds number corresponding to single phase flow relaminarization. When steady-state is reached, the particle volume fraction is homogeneously distributed in the channel cross-section (φ ∼ = 5%) except in the near-wall region where it is larger due to inertia-driven migration. Turbulence statistics (intensity of velocity fluctuations, small-scale vortical structures, wall shear stress) calculated in the fully coupled two-phase flow simulations are compared to single-phase flow data in the transition regime. It is observed that particles increase the transverse r.m.s. flow velocity fluctuations and they break down the flow coherent structures into smaller, more numerous and sustained eddies, preventing the flow to relaminarize at the single-phase critical Reynolds number. When the Reynolds number is further decreased and the suspension flow becomes laminar, the wall friction coefficient recovers the evolution of the laminar single-phase law provided that the suspension viscosity is used in the Reynolds number definition. The residual velocity fluctuations in the suspension correspond to a regime of particulate shear-induced agitation.

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Gum Arabic is a natural acacia tree exudate containing hyperbranched polysaccharides and proteins. Here, we perform a dual chromatographic separation together with small-angle X-ray and neutron scattering structural characterizations. We show that the different species present in Gum Arabic can not be easily classified in distinct families. They are rather build from various combinations of two building blocks that are evidenced by a mismatch between small-angle X-ray and neutron scattering. One block corresponds to hyperbranched polysaccharides, which we describe as three-dimensional multi-scale porous colloids possessing three length scales of 7, 2 and 0.7 nm. The other block corresponds to protein chains that organize as Gaussian chains in solution and are prone to aggregation. A large array of polysaccharide/protein conjugates was identified, which differs in size, hydrophobicity and amino-acid content. Still, their structure is always the juxtaposition of the two building blocks structures. Additionally, small-angle neutron scattering reveals that large-scale structures are ubiquitous in Gum Arabic solutions and originate from the self-association of both free and conjugated polypeptide chains. Despite its compositional complexity, Gum Arabic solutions thus possess a robust multi-scale structure that is mainly impacted by concentration and ionic repulsions.

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