流体饱和颗粒层中杆的有效阻力
Effective drag of a rod in fluid-saturated granular beds
摘要：
我们测量阻力所遇到的垂直定向杆移动穿过沉积颗粒床浸没在稳态条件下的流体。在低杆速度下，由于浮力，流体的存在导致较低的阻力，而随着速度的增加观察到显著较高的阻力。观察到阻力作为深度的函数从低速时的二次曲线减小到高速时的线性曲线。通过将阻力与作用在杆上的颗粒的平均重量成比例，我们获得了在六个数量级的速度上遇到的有效摩擦$μ_e$。当颗粒尺寸、杆深和流体粘度在低速下变化时，发现恒定的$μ_e$，而当速度增加时，观察到系统的增加。我们用惯性数$I$和粘性数$J$来分析$μ_e$，以分别理解惯性力和粘性力的相对重要性。对于足够大的流体粘度，我们发现，不同的速度，深度和粘度的影响可以描述的经验函数$μ_e = μ_o + k J^n$，其中$μ_o$是在准静态极限测量的有效摩擦，和$k$和$n$是材料常数。然后根据有效粘度$η_e$分析阻力，发现阻力作为$J$的函数系统性降低。我们进一步表明，$η_e$作为$J$的函数与流体粘度和杆所遇到的$μ_e$成正比。
英文摘要：
We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction $μ_e$ encountered over six orders of magnitude of speeds. While a constant $μ_e$ is found when the grain size, rod depth and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze $μ_e$ in terms of the inertial number $I$ and viscous number $J$ to understand the relative importance of inertia and viscous forces, respectively. For sufficiently large fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function $μ_e = μ_o + k J^n$, where $μ_o$ is the effective friction measured in the quasi-static limit, and $k$ and $n$ are material constants. The drag is then analyzed in terms of the effective viscosity $η_e$ and found to decrease systematically as a function of $J$. We further show that $η_e$ as a function of $J$ is directly proportional to the fluid viscosity and the $μ_e$ encountered by the rod.
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