Hybrid lattice Boltzmann model for binary fluid mixtures

Tiribocchi, Adriano; Stella, N.; Gonnella, Giuseppe; Lamura, A.

doi:10.1103/physreve.80.026701

Cited by 73 publications

(60 citation statements)

References 31 publications

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“…Numerical results: To test these ideas we have solved Active Model H numerically on a square lattice of size l x = l y = 256 by using a noise-free (i.e., Λ = 0) hybrid Lattice Boltzmann (LB) scheme [39]. We initialized the system in a mixed state with a small initial uniformly distributed noise with −0.1 < φ(r, 0) < 0.1.…”

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confidence: 99%

Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

et al. 2015

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We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation we introduce a scalar concentration field φ with advective-diffusive dynamics. Activity creates a contribution Σij = −ζ((∂iφ)(∂jφ) − (∇φ) 2 δij/d) to the deviatoric stress, where ζ is odd under time reversal and d is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus the interplay of activity and hydrodynamics is highly nontrivial, even without alignment interactions.PACS numbers: 63.50.Lm, 47.57.E-'Active matter' means the collective dynamics of selfpropelled particles at high density. By converting energy into motion, such particles violate time-reversal symmetry (TRS) at the micro-scale. This violation changes the structure of coarse-grained equations of motion, allowing far-from-equilibrium physics to dominate at large scales [1]. Active matter can be 'wet', i.e., coupled in bulk to a momentum-conserving solvent, or 'dry', i.e., for instance in contact with a momentum-absorbing wall. 1 'Wet' active systems include not only bacterial swarms in a fluid, the cytoskeleton of living cells, and biomimetic cell extracts [1-4], but also synthetic colloidal swimmers in a fully bulk geometry. Such swimmers may in future offer a toolbox for directed assembly of new materials in three dimensions. Many of these artificial colloidal swimmers are spherical objects, with asymmetric coatings that cause them to move through a bath of fuel and/or under illumination with light [5].Of particular importance is the 'active liquid crystal' (ALC) theory [1,6], which starts from a passive fluid of rod-like objects [7] with either a polar order parameter P [8], or a nematic one Q [9]. An active stress is then added; this is −ζP ⊗ P or −ζQ, with ζ odd under time reversal and the dyadic product ⊗, representing the leading-order TRS violation in an orientationally ordered medium. This causes new physics such as giant number fluctuations [10], and spontaneous flow above an activity threshold that vanishes for large systems [8,9]. This instability depends on whether particles are extensile (pulling fluid inwards equatorially and emitting it axially) or contractile (vice versa). Numerical solutions [11][12][13] show spontaneous flows resembling experiments on bacterial swarms [2] and on microtubule-based cell extracts [4].There is one important effect of activity that ALC models do not capture (unless added by hand [14]):1 This wet/dry terminology has become conventional, although many 'dry' systems are immersed in a fluid.motility-induced phase separation (MIPS) [15,16]. If their propulsion speed falls fast enough with density (e.g., due to crowding interactions), even purely repulsive active particles phase-separate into dense and dilute ...

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Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

et al. 2015

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“…(7,8,9,10) are solved numerically by using a hybrid lattice Boltzmann method previously used in similar systems such as binary fluids 26 , liquid crystals 27,28 and active matter [29][30][31] . Unless explicitely stated otherwise, most of the simulations are performed on a two-dimensional rectangular lattice (Lx = 400, Ly = 120) in which an isotropic droplet is initially placed at its centre and surrounded by a nematic liquid crystal.…”

Section: Numerical Aspects and Mapping To Physical Unitsmentioning

confidence: 99%

“…This deviation however is, in terms of the radius of the droplet, < 1% and does not affect in an appreciable way the dynamics of the droplet under shear. Finally at the walls we impose noslip boundary conditions for the velocity field, neutral-wetting (meaning that there are no flows of matter across the walls 26 ) for the concentration field and strong anchoring of the nematic (this is achieved by setting the anchoring strength W = 0.4).…”

Section: Numerical Aspects and Mapping To Physical Unitsmentioning

confidence: 99%

Shear dynamics of an inverted nematic emulsion

Tiribocchi

Marenduzzo

et al. 2016

Soft Matter

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Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic fluid. We find that in this regime the 2D droplet can tilt and move in the flow, or tumble incessantly at the centre of the channel. For sufficiently strong anchoring, finally, one or both of the topological defects which form close to the surface of the isotropic droplet in equilibrium detach from it and get dragged deep into the nematic state by the flow. In 3D, instead, the Saturn ring associated with normal anchoring disclination line can be deformed and shifted downstream by the flow, but remains always localized in proximity of the droplet, at least for the parameter range we explored. Tangential anchoring in 2D leads to a different dynamic response, as the boojum defects characteristic of this situation can unbind from the droplet under a weaker shear with respect to the normal anchoring case. Our results should stimulate further experiments with inverted liquid crystal emulsions under shear, as most of the predictions can be testable in principle by monitoring the evolution of liquid crystalline orientation patterns or by tracking the position and shape of the droplet over time.

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“…Rather than a front of polymerization, we are focusing on situations that involve mass redistribution and momentum cannot be neglected. In [14,15] the momentum is considered and numerical methods are used to study the advancing front and One of the novel aspects of this manuscript is the application of marginal stability analysis that, while an approximation, is more general than purely numerical observations and much simpler than other analytic methods.…”

Section: Introductionmentioning

confidence: 99%

Marginal stability and traveling fronts in two-phase mixtures

Cogan

Donahue²,

Whidden³

2012

Phys. Rev. E

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Mixtures of materials that move relative to each other arise in a variety of applications, especially in biophysical problems where the mixture consists of materials with different material properties. The variety of applications leads to a bewildering array of multiphase models, each with slightly different behaviors and interpretations, depending on the application. Some of the behaviors include phase separation, traveling waves and linear instabilities. Because of the variability of the predicted behaviors, there has been considerable attention payed to minimal models to determine the fundamental solutions, bifurcations and instabilities. In this manuscript, we describe a new solution for the simplest two-phase system where both phases are dominated by viscous forces, one phase response to osmotic forces and the phases interact through a drag term. The system develops a traveling front separating an unstable, uniform solution from a patterned, phase separated solution. We seek the velocity of the traveling front and show that, for large diffusion, marginal stability gives a simple and accurate prediction for the velocity. For smaller diffusion constants, the front is 'pushed', and the linear prediction fails.

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Hybrid lattice Boltzmann model for binary fluid mixtures

Cited by 73 publications

References 31 publications

Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

Shear dynamics of an inverted nematic emulsion

Marginal stability and traveling fronts in two-phase mixtures

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