Extended dynamical density functional theory for colloidal mixtures with temperature gradients.

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Colloidal Science

Background:

• Classical dynamical density functional theory (DDFT) is established for Brownian dynamics of interacting colloidal particles.
• The Mori-Zwanzig-Forster projection operator technique is a key method for deriving DDFT from microscopic dynamics.
• Existing DDFT models primarily focus on single-component systems or lack extensions for thermal gradients.

Purpose of the Study:

• To generalize DDFT for mixtures of multiple spherical colloidal particle species.
• To extend DDFT by incorporating internal energy density as a slow variable for systems with temperature gradients.
• To derive formal expressions for these extended DDFT frameworks and analyze cross-coupling terms.

Main Methods:

• Utilizing the Mori-Zwanzig-Forster projection operator technique.
• Generalizing DDFT for n-species colloidal mixtures, explicitly defining cross-coupling terms for pairwise hydrodynamic interactions.
• Treating internal energy density as an additional slow variable to derive extended DDFT expressions.

Main Results:

• Nontrivial cross-coupling terms between concentration fields are identified for colloidal mixtures.
• Formal expressions for extended DDFT including internal energy density are derived, applicable to systems with temperature gradients.
• Thermodiffusion and cross-diffusion coefficients are analyzed, showing nonzero values in the presence of hydrodynamic interactions.

Conclusions:

• The developed extended DDFT frameworks provide a more comprehensive description of colloidal dynamics.
• These extensions are crucial for understanding complex phenomena in multi-component colloidal systems and those under thermal gradients.
• The derived expressions encompass transport coefficients in the hydrodynamic limit as a special case.