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Hydrodynamic interactions between two identical elastic dumbbells settlingunder gravity in a viscous fluid at low-Reynolds-number are investigated withinthe point-particle model. Evolution of a benchmark initial configuration isstudied, in which the dumbbells are vertical and their centres are alignedhorizontally. Rigid dumbbells and pairs of separate beads starting from thesame positions tumble periodically while settling down. We find that elasticity(which breaks time-reversal symmetry of the motion) significantly affects thesystem's dynamics. This is remarkable taking into account that elastic forcesare always much smaller than gravity. We observe oscillating motion of theelastic dumbbells, which tumble and change their length non-periodically.Independently of the value of the spring constant, a horizontal hydrodynamicrepulsion appears between the dumbbells - their centres of mass move apart fromeach other horizontally. The shift is fast for moderate values of the springconstant k, and slows down when k tends to zero or to infinity; in theselimiting cases we recover the periodic dynamics reported in the literature. Formoderate values of the spring constant, and different initial configurations,we observe the existence of a universal time-dependent solution to which thesystem converges after an initial relaxation phase. The tumbling time and thewidth of the trajectories in the centre-of-mass frame increase with time. Inaddition to its fundamental significance, the benchmark solution presented hereis important to understand general features of systems with larger number ofelastic particles, at regular and random configurations.

Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion