论文标题
NAVIER-用于限制的准二维粒度二进制混合物的模型的运输系数
Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
论文作者
论文摘要
Navier-速溶系数的传输系数，用于从Boltzmann动力学方程式确定无弹性硬球的粘合二维粒度二元混合物的模型。 Boltzmann方程的正常或流体动力解决方案是通过Chapman-enskog方法获得的，用于近距离时间依赖性状态的局部版本附近的状态。确定质量，动量和热通量在流体动力场的空间梯度中确定第一阶，并确定相关的运输系数。正如预期的那样，它们是根据一组耦合线性积分方程的解决方案给出的。此外，与低密度颗粒混合物获得的先前结果相反，对部分温度的一阶近似值$ t_i^{（1）} $和冷却率$ζ^{（1）} $也有非零的贡献。扩散传输系数，剪切粘度系数以及$ t_i^{（1）} $和$ζ^{（1）} $的显式形式，是通过假设稳态条件和稳态条件获得的。上述运输系数是根据混合物组成部分的恢复，浓度以及质量和直径的系数给出的。该结果原则上适用于任意非弹性程度，并且不限于浓度，质量和/或尺寸比的特定值。作为这些结果的简单应用，根据问题的参数空间来量化对狭窄的颗粒混合物的Onsager倒数关系的侵犯。
The Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman--Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. As expected, they are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures $T_i^{(1)}$ and the cooling rate $ζ^{(1)}$. Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities $T_i^{(1)}$ and $ζ^{(1)}$ are obtained by assuming the steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply in principle for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.
