González Rubén Gómez, Khalil Nagi, Garzó Vicente
Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain.
Escuela Superior de Ciencias Experimentales y Tecnología (ESCET), Universidad Rey Juan Carlos, Móstoles 28933, Madrid, Spain.
Phys Rev E. 2020 Jan;101(1-1):012904. doi: 10.1103/PhysRevE.101.012904.
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.
在（非弹性）恩斯科格动力学理论的框架下，获得了中等密度多组分颗粒悬浮液的纳维 - 斯托克斯输运系数。该悬浮液被建模为固体颗粒的集合，其中间隙气体对颗粒的影响通过粘性阻力以及根据背景温度定义的类似随机朗之万项来体现。在不存在空间梯度的情况下，首先表明系统达到均匀稳态，其中非弹性碰撞和粘性摩擦损失的能量由随机力注入的能量补偿。一旦确定了均匀稳态，通过围绕均匀态的局部版本进行查普曼 - 恩斯科格展开，得到了恩斯科格方程组的正规解。对于空间梯度的一阶情况，查普曼 - 恩斯科格解使我们能够确定与质量、动量和热通量相关的纳维 - 斯托克斯输运系数。此外，还计算了对偏温度和冷却速率的一阶贡献。通过保留索宁多项式展开中的主导项，在稳态条件下得到了扩散系数、剪切粘度和体粘度以及对偏温度和冷却速率的一阶贡献的显式形式。结果表明，输运系数对非弹性程度的依赖性与颗粒体系（无气相）中的情况明显不同。本工作将先前关于稀多组分颗粒悬浮液的理论结果[Khalil和Garzó，《物理评论E》88，052201（2013年）10.1103/PhysRevE.88.052201]扩展到了更高密度的情况。
