The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier–Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalised by the bubble radius) and the angle θ (0° ≤ θ ≤ 90°) formed between the centreline and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0°) by Legendre, Magnaudet & Mougin (J. Fluid Mech., vol. 497, 2003, p. 133) and for two bubbles moving in line (θ = 90°) by Yuan & Prosperetti J. Fluid Mech., vol. 278, 1994, p. 325). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore's correction) and a significant wake effect observed on both the drag and the transverse forces of the second bubble when located in the wake of the first one.

The evolution of the concentration and flow fields resulting from the gravitational mixing of two interpenetrating miscible fluids placed in a tilted tube or channel is studied by using direct numerical simulation. Three-dimensional ͑3D͒ geometries, including a cylindrical tube and a square channel, are considered as well as a purely two-dimensional ͑2D͒ channel. Striking differences between the 2D and 3D geometries are observed during the long-time evolution of the flow. We show that these differences are due to those existing between the 2D and 3D dynamics of the vorticity field. More precisely, in two dimensions, the strong coherence and long persistence of vortices enable them to periodically cut the channels of pure fluid that feed the front. In contrast, in 3D geometries, the weaker coherence of the vortical motions makes the segregational effect due to the transverse component of buoyancy strong enough to preserve a fluid channel near the front of each current. This results in three different regimes for the front velocity ͑depending on the tilt angle͒, which is in agreement with the results of a recent experimental investigation. The evolution of the front topology and the relation between the front velocity and the concentration jump across the front are investigated in planar and cylindrical geometries and highlight the differences between 2D and 3D mixing dynamics.