AbstractBulk flows of galaxies moving with respect to the cosmic microwave background are well established observationally and seen in the most recent ΛCDM simulations. With the aid of an idealised Gadget-2 simulation, we show that void asymmetries in the cosmic web can exacerbate local bulk flows of galaxies. The {\it Cosmicflows-2} survey, which has mapped in detail the 3D structure of the Local Universe, reveals that the Local Group resides in a “local sheet” of galaxies that borders a “local void” with a diameter of about 40 Mpc. The void is emptying out at a rate of 16 km s^-1 Mpc^-1. In a co-moving frame, the Local Sheet is found to be moving away from the Local Void at ∼ 260 km s^-1. Our model shows how asymmetric collapse due to unbalanced voids on either side of a developing sheet or wall can lead to a systematic movement of the sheet. We conjectured that asymmetries could lead to a large-scale separation of dark matter and baryons, thereby driving a dependence of galaxy properties with environment, but we do {\it not} find any evidence for this effect.