Gómez González Rubén, Abad Enrique, Bravo Yuste Santos, Garzó Vicente
Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain.
Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06800 Mérida, Spain.
Phys Rev E. 2023 Aug;108(2-1):024903. doi: 10.1103/PhysRevE.108.024903.
The Enskog kinetic theory is applied to compute the mean square displacement of impurities or intruders (modeled as smooth inelastic hard spheres) immersed in a granular gas of smooth inelastic hard spheres (grains). Both species (intruders and grains) are surrounded by an interstitial molecular gas (background) that plays the role of a thermal bath. The influence of the latter on the motion of intruders and grains is modeled via a standard viscous drag force supplemented by a stochastic Langevin-like force proportional to the background temperature. We solve the corresponding Enskog-Lorentz kinetic equation by means of the Chapman-Enskog expansion truncated to first order in the gradient of the intruder number density. The integral equation for the diffusion coefficient is solved by considering the first two Sonine approximations. To test these results, we also compute the diffusion coefficient from the numerical solution of the inelastic Enskog equation by means of the direct simulation Monte Carlo method. We find that the first Sonine approximation generally agrees well with the simulation results, although significant discrepancies arise when the intruders become lighter than the grains. Such discrepancies are largely mitigated by the use of the second Sonine approximation, in excellent agreement with computer simulations even for moderately strong inelasticities and/or dissimilar mass and diameter ratios. We invoke a random walk picture of the intruders' motion to shed light on the physics underlying the intricate dependence of the diffusion coefficient on the main system parameters. This approach, recently employed to study the case of an intruder immersed in a granular gas, also proves useful in the present case of a granular suspension. Finally, we discuss the applicability of our model to real systems in the self-diffusion case. We conclude that collisional effects may strongly impact the diffusion coefficient of the grains.
恩斯科格动力学理论被用于计算浸没在由光滑非弹性硬球（颗粒）组成的颗粒气体中的杂质或侵入体（建模为光滑非弹性硬球）的均方位移。两种粒子（侵入体和颗粒）都被一种间隙分子气体（背景）包围，该气体起到热浴的作用。后者对侵入体和颗粒运动的影响通过标准粘性阻力来建模，并辅以与背景温度成正比的类似朗之万随机力。我们通过在侵入体数密度梯度中截断到一阶的查普曼 - 恩斯科格展开来求解相应的恩斯科格 - 洛伦兹动力学方程。通过考虑前两个索宁近似来求解扩散系数的积分方程。为了检验这些结果，我们还通过直接模拟蒙特卡罗方法从非弹性恩斯科格方程的数值解中计算扩散系数。我们发现，尽管当侵入体比颗粒轻时会出现显著差异，但第一个索宁近似通常与模拟结果吻合良好。通过使用第二个索宁近似，这些差异在很大程度上得到缓解，即使对于中等强度的非弹性和/或不同的质量与直径比，也与计算机模拟结果非常吻合。我们引入侵入体运动的随机游走图像来揭示扩散系数对主要系统参数复杂依赖性背后的物理原理。这种最近用于研究浸没在颗粒气体中的侵入体情况的方法，在当前颗粒悬浮液的情况下也证明是有用的。最后，我们讨论了我们的模型在自扩散情况下对实际系统的适用性。我们得出结论，碰撞效应可能会强烈影响颗粒的扩散系数。
