Extended dynamical density functional theory for colloidal mixtures with temperature gradients.
Extended dynamical density functional theory for colloidal mixtures with temperature gradients.
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具有温度梯度的胶体混合物的扩展动态密度泛函理论。
DOI：
10.1063/1.4769101
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
H. Brand
中科院分区：
文献类型：
--
作者：
R. Wittkowski;H. Löwen;H. Brand
在过去的十年中，经典动力密度泛函理论（DDFT）得到发展并广泛应用于相互作用胶体颗粒的布朗动力学。从微观动力学中导出 DDFT 的可能途径之一是通过具有缓慢变化变量（例如单粒子密度）的 Mori-Zwanzig-Forster 投影算子技术。在这里，我们使用投影算子方法将 DDFT 扩展到各个方向：首先，我们将 DDFT 推广到 n 个不同种类的球形胶体颗粒的混合物。我们表明，浓度场之间通常存在非平凡的交叉耦合项，并为具有成对流体动力学相互作用的胶体混合物明确指定它们。其次，我们将内部能量密度视为一个额外的慢变量，并推导出也包含内部能量密度的扩展 DDFT 的形式表达式。后一种方法原则上可以应用于非零温度梯度下的胶体动力学。对于没有流体动力相互作用的情况，扩散张量是对角线的，而热扩散（内部能量密度和浓度之间的耗散交叉耦合项）在此极限下不为零。对于有限的流体动力学相互作用，交叉扩散系数也呈现有限值。我们证明，作为特殊情况，扩展 DDFT 的结果包含流体力学极限（长波长、低频）中的输运系数。
In the past decade, classical dynamical density functional theory (DDFT) has been developed and widely applied to the Brownian dynamics of interacting colloidal particles. One of the possible derivation routes of DDFT from the microscopic dynamics is via the Mori-Zwanzig-Forster projection operator technique with slowly varying variables such as the one-particle density. Here, we use the projection operator approach to extend DDFT into various directions: first, we generalize DDFT toward mixtures of n different species of spherical colloidal particles. We show that there are in general nontrivial cross-coupling terms between the concentration fields and specify them explicitly for colloidal mixtures with pairwise hydrodynamic interactions. Second, we treat the internal energy density as an additional slow variable and derive formal expressions for an extended DDFT containing also the internal energy density. The latter approach can in principle be applied to colloidal dynamics in a nonzero temperature gradient. For the case without hydrodynamic interactions the diffusion tensor is diagonal, while thermodiffusion--the dissipative cross-coupling term between internal energy density and concentration--is nonzero in this limit. With finite hydrodynamic interactions also cross-diffusion coefficients assume a finite value. We demonstrate that our results for the extended DDFT contain the transport coefficients in the hydrodynamic limit (long wavelengths, low frequencies) as a special case.
影响因子：
8.6
作者：
Giomi, Luca;Marchetti, M. Cristina;Liverpool, Tanniemola B.
通讯作者：
Liverpool, Tanniemola B.