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Enskog kinetic theory for multicomponent granular suspensions.
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012904 Rubén Gómez González 1 , Nagi Khalil 2 , Vicente Garzó 3
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012904 Rubén Gómez González 1 , Nagi Khalil 2 , Vicente Garzó 3
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The Navier-Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a normal solution to the set of Enskog equations is obtained by means of the Chapman-Enskog expansion around the local version of the homogeneous state. To first order in spatial gradients, the Chapman-Enskog solution allows us to identify the Navier-Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for dilute multicomponent granular suspensions [Khalil and Garzó, Phys. Rev. E 88, 052201 (2013)10.1103/PhysRevE.88.052201] to higher densities.
中文翻译：
多组分颗粒悬浮液的Enskog动力学理论。
在（非弹性）Enskog动力学理论的背景下获得了中等密度下多组分颗粒悬浮液的Navier-Stokes输运系数。悬浮液被建模为固体颗粒的集合体，其中间隙气体对颗粒的影响是通过粘性阻力加上根据背景温度定义的随机朗格文式术语产生的。在没有空间梯度的情况下，首先表明系统达到了均匀的稳态，在该稳态下，由于非弹性碰撞和粘滞摩擦而损失的能量由随机力注入的能量补偿。一旦表征了均质稳态，就可以通过围绕均质态局部形式的Chapman-Enskog展开获得对Enskog方程组的正解。在空间梯度上一阶，Chapman-Enskog解决方案使我们可以识别与质量，动量和热通量相关的Navier-Stokes传输系数。另外，还计算了对局部温度和冷却速率的一阶贡献。通过将前项保留在Sonine多项式展开中，可以在稳态条件下获得扩散系数，剪切粘度和体粘度以及对部分温度和冷却速率的一阶贡献的显式形式。结果表明，输运系数对非弹性的依赖性明显不同于其颗粒状形式（无气相）中的依赖性。本工作扩展了稀多组分颗粒悬浮液的先前理论结果[Khalil andGarzó，Phys。版本号
更新日期：2020-01-17
中文翻译：
多组分颗粒悬浮液的Enskog动力学理论。
在（非弹性）Enskog动力学理论的背景下获得了中等密度下多组分颗粒悬浮液的Navier-Stokes输运系数。悬浮液被建模为固体颗粒的集合体，其中间隙气体对颗粒的影响是通过粘性阻力加上根据背景温度定义的随机朗格文式术语产生的。在没有空间梯度的情况下，首先表明系统达到了均匀的稳态，在该稳态下，由于非弹性碰撞和粘滞摩擦而损失的能量由随机力注入的能量补偿。一旦表征了均质稳态，就可以通过围绕均质态局部形式的Chapman-Enskog展开获得对Enskog方程组的正解。在空间梯度上一阶，Chapman-Enskog解决方案使我们可以识别与质量，动量和热通量相关的Navier-Stokes传输系数。另外，还计算了对局部温度和冷却速率的一阶贡献。通过将前项保留在Sonine多项式展开中，可以在稳态条件下获得扩散系数，剪切粘度和体粘度以及对部分温度和冷却速率的一阶贡献的显式形式。结果表明，输运系数对非弹性的依赖性明显不同于其颗粒状形式（无气相）中的依赖性。本工作扩展了稀多组分颗粒悬浮液的先前理论结果[Khalil andGarzó，Phys。版本号
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