We investigate experimentally the effects of a pipe axial rotation on buoyant miscible displacement flows in an inclined pipe. The displacing Newtonian fluid (salt-water solution) is heavier than the displaced viscoplastic one (Carbopol solution). Via image processing techniques and ultrasound Doppler velocity measurements, we analyze the key flow features such as the flow patterns, the velocity and concentration fields, and the leading front velocity (${\hat{V}}_f$) as well as the trailing front velocity (${\hat{V}}_t$) of the displacement flow. The main flow parameters in our experiments are the pipe inclination angle, the small density difference between the two fluids, the yield stress of the displaced fluid, the imposed mean flow velocity (${\hat{V}}_0$), and most importantly the pipe rotation speed. We find that increasing the pipe rotation speed enhances the transverse mixing between the two fluids and, above a critical transition, leads to a complete removal of the displaced viscoplastic fluid. We classify the flow regimes into efficient and inefficient displacement flows, using appropriate dimensionless groups, i.e. the Rossby number ($Rb$) and the Froude number ($Fr$). We find that the critical transition between the two flow regimes can be roughly described by a critical Rossby number ($R{b}_c$), as a function of $Fr$, independent of the other flow dimensionless numbers. For $Rb\le R{b}_c$, we find that ${\hat{V}}_f\approx 1.6{\hat{V}}_0$ and ${\hat{V}}_t\approx {\hat{V}}_0$, while for $Rb>R{b}_c$ we propose an empirical relation for the leading front velocity versus the Rossby number. These findings can offer new insight to control viscoplastic displacement flows using rotational motion.

我们通过实验研究了管道轴向旋转对倾斜管道中可浮混溶位移流的影响。置换的牛顿流体（盐水溶液）比置换的粘塑性流体（Carbopol溶液）重。通过图像处理技术和超声多普勒速度测量，我们分析了关键的流动特征，例如流动模式，速度和浓度场以及前锋速度（${\hat{V}}_F$）以及尾随速度（${\hat{V}}_{Ť}$）的位移流量。我们实验中的主要流量参数是管道倾斜角，两种流体之间的密度差小，驱替流体的屈服应力，施加的平均流速（${\hat{V}}_0$），最重要的是管道的旋转速度。我们发现，增加管的旋转速度会增强两种流体之间的横向混合，并且在临界过渡以上会导致置换出的粘塑性流体的完全清除。我们分类的流动状态为有效的和低效的位移流动，使用合适的无量纲基团，即，在罗斯贝数（$\mathrm{[R}b$）和弗洛伊德数（$F\mathrm{[R}$）。我们发现两种流动状态之间的临界过渡可以用临界Rossby数（$\mathrm{[R}{b}_C$），作为 $F\mathrm{[R}$，与其他流无量纲数无关。对于$\mathrm{[R}b\le \mathrm{[R}{b}_C$，我们发现 ${\hat{V}}_F\approx \mathrm{1个}。6{\hat{V}}_0$ 和 ${\hat{V}}_{Ť}\approx {\hat{V}}_0$，而 $\mathrm{[R}b>\mathrm{[R}{b}_C$我们提出了领先的前沿速度与Rossby数的经验关系。这些发现可以为使用旋转运动控制粘塑性位移流动提供新的见解。