Axisymmetric gas-liquid displacement flow under a confined elastic slab
Axisymmetric gas-liquid displacement flow under a confined elastic slab
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有限弹性板下轴对称气液驱替流
DOI：
10.1103/physrevfluids.8.094005
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发表时间：
2023
影响因子：
2.7
通讯作者：
Peng G
中科院分区：
文献类型：
--
作者：
Peng G
由体积受限的弹性固体限定的圆形Hele-Shaw单元可以充当流体熔断器：在径向向外的流体流动期间，固体响应于粘性压力场而变形，使得差距在入口附近（在中心处）膨胀并且在出口附近（在边缘周围）收缩。如果流速超过临界值，则出口处的差距可完全关闭，从而中断/阻塞流动。在这里，我们考虑注入气体到这样一个软壁Hele-Shaw细胞充满粘性液体。通过对膨胀气泡驱动的轴对称流场的理论模型和数值模拟，发现气泡通过两种机制提高了阻塞临界流速。首先，当界面接近边缘时，它减少了粘性压力梯度使固体变形的长度，这增加了临界流速，高于该临界流速时发生阻塞。第二，气体的压缩相对于入口流率降低了出口流率。因此，对于大的注入速率，建立了一个近阻塞状态，其中出口流速变得独立于注入速率，而是仅取决于界面的瞬时位置。我们的行波模型的气泡前的进步将使未来的降阶建模的非轴对称问题，如粘性指。
A circular Hele-Shaw cell bounded by a volumetrically confined elastic solid can act as a fluidic fuse: during radially outward fluid flow, the solid deforms in response to the viscous pressure field such that the gap expands near the inlet (at the center) and contracts near the outlet (around the rim). If the flow rate exceeds a critical value, then the gap at the outlet can close completely, interrupting/choking the flow. Here, we consider the injection of gas into such a soft-walled Hele-Shaw cell filled with viscous liquid. Our theoretical model and numerical simulations for axisymmetric flow driven by the injection of an expanding gas bubble show that the bubble increases the critical flow rate of choking via two mechanisms. First, as the interface approaches the rim, it reduces the length over which the viscous pressure gradient deforms the solid, which increases the critical flow rate above which choking occurs. Second, compression of the gas reduces the outlet flow rate relative to the inlet flow rate. As a consequence, for large injection rates, a near-choking regime is established in which the outlet flow rate becomes independent of the injection rate and instead depends only on the instantaneous position of the interface. Our traveling-wave model for the advancement of the bubble front will enable future reduced-order modeling of nonaxisymmetric problems, such as viscous fingering.