Effects of applied pressure difference (Δp = p1 − p2) on plug propagation and rupture. Time evolution of (a) plug length (Lp), (b) maximum difference in wall pressure (Pmax−Pmin), (c) maximum difference in wall shear stress (τmax − τmin) and (d) the retraction after the rupture for the applied pressure difference in the range 0.75 ⩽ Δp ⩽ 3. (Lpi = 1.0, h2 = 0.05, λ = 100, β = 0.7, χ = 0.01, Sc = 10, Scs = 100, Ka = 104, Kd = 100, C0 = 10−4).