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The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
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Growing Protein Crystals with Distinct Dimensions Using Automated Crystallization Coupled with In Situ Dynamic Light Scattering
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Active and driven hydrodynamic crystals.

N Desreumaux1, N Florent, E Lauga

  • 1Laboratoire de Physique et Mécanique des Milieux Hétérogénes, CNRS, ESPCI, Université Paris 6, Université Paris 7, Paris, France. nicolas.desreumaux@espci.fr

The European Physical Journal. E, Soft Matter
|August 7, 2012
PubMed
Summary
This summary is machine-generated.

This study theoretically analyzes the stability of active and driven microfluidic crystals. We found that active crystals exhibit instabilities dependent on lattice symmetry and density, providing a basis for experimental research.

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Area of Science:

  • Soft Matter Physics
  • Fluid Dynamics
  • Crystallography

Background:

  • Microfluidic devices enable precise control over monodisperse particle assembly.
  • Hydrodynamic interactions in confined fluids are crucial for understanding particle dynamics.
  • Active and driven systems offer unique possibilities for material properties.

Purpose of the Study:

  • To theoretically investigate the hydrodynamic stability of driven and active crystals in microfluidic systems.
  • To derive equations of motion for particles and analyze lattice stability.
  • To differentiate stability criteria for driven versus self-propelling (active) crystals.

Main Methods:

  • Derivation of particle equations of motion using hydrodynamic interactions (superposition of potential dipolar singularities).
  • Analysis of stationary solutions for planar Bravais lattices.
  • Investigation of phonon modes and eigenmode structures in driven crystals.
  • Stability analysis of active crystals considering lattice symmetry, perturbation wavelengths, and crystal density.

Main Results:

  • All five planar Bravais lattices are stationary solutions.
  • Driven crystals exhibit marginally stable phonon modes, with eigenmode structures dependent on lattice symmetry and driving force orientation.
  • Active crystal stability depends on symmetry, density, and wavelength, not the specific propulsion mechanism.
  • Square and rectangular lattices become unstable at short wavelengths and high densities; hexagonal, oblique, and face-centered lattices are always unstable.

Conclusions:

  • The theoretical framework provides insights into the stability of microfluidic crystals.
  • Active crystal stability is complex and sensitive to parameters like density and wavelength.
  • Findings lay the groundwork for experimental studies on flowing microfluidic active and driven crystals.