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The motion and deformation of a neutrally buoyant drop in a rectangular channel experiencing a pressure-driven flow at a low Reynolds number has been investigated both experimentally and numerically. A moving-frame boundary-integral algorithm was used to simulate the drop dynamics, with a focus on steady-state drop velocity and deformation. Results are presented for drops of varying undeformed diameters relative to channel height ($$D/H$$), drop-to-bulk viscosity ratio ($$\lambda$$), capillary number ($$Ca$$, ratio of deforming viscous forces to shape-preserving interfacial tension) and initial position in the channel in a parameter space larger than considered previously. The general trend shows that the drop steady-state velocity decreases with increasing drop diameter and viscosity ratio but increases with increasing$$Ca$$. An opposite trend is seen for drops with small viscosity ratio, however, where the steady-state velocity increases with increasing$$D/H$$and can exceed the maximum background flow velocity. Experimental results verify theoretical predictions. A deformable drop with a size comparable to the channel height when placed off centre migrates towards the centreline and attains a steady state there. In general, a drop with a low viscosity ratio and high capillary number experiences faster cross-stream migration. With increasing aspect ratio, there is a competition between the effect of reduced wall interactions and lower maximum channel centreline velocity at fixed average velocity, with the former helping drops attain higher steady-state velocities at low aspect ratios, but the latter takes over at aspect ratios above approximately 1.5. 

Oblique collisions of three solid spheres coated with thin viscous layers are simulated, both to elucidate the interesting physics of the collision outcomes and to lay the groundwork for a new approach to modeling flows of many wet particles. Included in the analysis are fluid viscous and capillary forces, as well as solid contact and friction forces. A novel approach is developed based on a rotating polar coordinate system for each particle pair in near contact, including the possibility that a given particle is in simultaneous contact with both other particles. As the Stokes number (a dimensionless ratio of particle inertia and viscous forces) is increased, the collision outcome progresses from full agglomeration (all three particles sticking together due to viscous and capillary forces) to partial agglomeration (two particles sticking together while the third one separates) to full separation (all three particles separating post-collision). The results are also sensitive to various physical and geometrical properties, such as the ratio of fluid film thickness to particle diameter, the coefficient of friction, and the collision angles.