[Paper Review] Pattern formation in colloidal mixtures under external driving fields

Joachim Dzubiella, Hartmut Loewen|Aug 6, 2002

Material Dynamics and Properties45 references19 citations

TL;DR

This study investigates pattern formation in binary colloidal mixtures under non-uniform external driving fields using nonequilibrium Brownian dynamics simulations and a simple theoretical model. It reveals that non-parallel forces induce tilted lane structures aligned with the force difference vector, while parallel forces on a crystalline field-free state trigger a reentrant melting-recrystallization transition into sliding, demixed crystalline lanes.

ABSTRACT

The influence of an external field acting differently on the two constituents of a binary colloidal mixture performing Brownian dynamics is investigated by computer simulations and a simple theory. In our model, one half of the particles ($A$-particles) are pulled by an external force ${\vec F}^{(A)}$ while the other half of them ($B$-particles) are pulled by an external force ${\vec F}^{(B)}$. If ${\vec F}^{(A)}$ and ${\vec F}^{(B)}$ are parallel and the field-free state is a mixed fluid, previous simulations (J. Dzubiella et al, Phys. Rev. E {\bf 65} 021402 (2002)) have shown a nonequilibrium pattern formation involving lanes of $A$ or $B$ particles only which are sliding against each other in the direction of the external forces. In this paper, we generalize the situation both to non-parallel external forces and to field-free crystalline states. For non-parallel forces, lane formation is also observed but with an orientation {\it tilted} with respect to the external forces. If the field-free state is crystalline, a continuous increase of the parallel external forces yields a novel {\it reentrant freezing} behavior: the crystal first melts mechanically via the external force and then recrystallizes into demixed crystalline lanes sliding against each other.

Motivation & Objective

• To understand how non-parallel external forces induce pattern formation in binary colloidal mixtures beyond the parallel-force case.
• To investigate the effect of external fields on a field-free crystalline state, particularly the emergence of mechanical melting and recrystallization.
• To generalize previous findings on fluid lane formation to systems with crystalline ground states and non-parallel driving forces.
• To propose experimental realizations in colloidal suspensions and pedestrian dynamics using controlled external fields.
• To explore the role of hydrodynamic interactions and alternative field configurations (e.g., oscillatory fields) in stabilizing lane patterns.

Proposed method

• Simulates a 2D binary colloidal mixture of A and B particles using overdamped Brownian dynamics with identical pair interactions via a Yukawa potential.
• Applies distinct external forces F^(A) and F^(B) to A and B particles respectively, modeling differential response to external fields.
• Uses Langevin equations with additive white noise to describe particle motion, assuming complete overdamping and neglecting hydrodynamic interactions.
• Performs simulations for both fluid and crystalline field-free states under varying force magnitudes and directions.
• Analyzes structural evolution via snapshots and order parameters to identify lane formation, melting, and recrystallization transitions.
• Compares results with phenomenological theories and discusses implications for experimental systems like sedimenting colloids or pedestrian flow.

Experimental results

Research questions

• RQ1 How does non-parallel external forcing affect lane formation in binary colloidal mixtures?
• RQ2 What structural transitions occur when a crystalline field-free state is subjected to increasing parallel external forces?
• RQ3 Can a reentrant phase transition—melting followed by recrystallization—be induced by mechanical work from external fields?
• RQ4 What is the orientation of the resulting lanes relative to the external force vectors in the non-parallel case?
• RQ5 How can the predicted patterns be experimentally realized in colloidal systems or pedestrian dynamics?

Key findings

• For non-parallel external forces, lane formation occurs with lanes oriented along the vector difference F^(B) - F^(A), resulting in tilted lanes relative to the individual force directions.
• In the crystalline field-free state, increasing parallel external forces first induces mechanical melting, followed by a reentrant recrystallization into demixed A- and B-rich crystalline lanes.
• The recrystallized state features completely demixed crystalline lanes that slide against each other, analogous to the fluid lane state but in a solid phase.
• The critical force for lane formation can be estimated by comparing the external force to the typical interaction force from the Yukawa potential.
• Hydrodynamic interactions, though neglected in the model, are expected to lower the critical field strength needed for lane formation due to long-ranged flow fields.
• The model predicts experimentally verifiable phenomena in colloidal suspensions under crossed fields (e.g., gravity and electric fields) and in pedestrian dynamics with directional flow lanes.