Static wall layers in plane channel displacement flows

For pulsating displacement flow rates, Q(t) = 2(1 + Asin  ωt) : A ∈ [0, 1) we study two ranges: ωRe ≪ 2π and ωRe ≫ 2π. For the viscous regime (ωRe ≪ 2π) a pseudo-steady 1D model predicts that the residual layer should remain static for 3(1 + Asin  ωt) < MB. In practice we find that partial mobilisation of the residual layer occurs even when this inequality is satisfied, but not if MB becomes significantly larger than 3(1 + A). For ωRe ≫ 2π we mobilise the layer for significantly larger values of MB and at smaller A, than in the viscous regime. This effect is traced to the occurrence of out-of-phase velocity fluctuations in the displacing fluid within a wall layer close to the interface.