Frozen states and order-disorder transition in the dynamics of confined membranes

Goff, Thomas Le; Politi, Paolo; Pierre-Louis, Olivier

doi:10.1103/physreve.90.032114

Cited by 10 publications

(40 citation statements)

References 37 publications

(58 reference statements)

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“…∂ λ L λm ≤ 0. This is in contrast with the tensionless limit where the linear instability was producing a stable periodic steady-state [16].…”

Section: B Transient Coarsening and Disordering In Ch4mentioning

confidence: 69%

“…We attribute the absence of perpetual coarsening to the existence of oscillatory interactions between the kinks, as already discussed in Refs. [16,27].…”

Section: B Transient Coarsening and Disordering In Ch4mentioning

confidence: 99%

“…to form blebs [13][14][15]. * olivier.pierre-louis@univ-lyon1.fr For the sake of simplicity, and following our previous work [16], we consider a two-dimensional system. As a consequence, the interface-hereafter denoted as a membrane-is effectively a one-dimensional object.…”

Section: Introductionmentioning

confidence: 99%

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Transition to coarsening for confined one-dimensional interfaces with bending rigidity

Goff

Politi²,

Pierre-Louis³

2015

Phys. Rev. E

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We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimension hydrodynamic model, where membranes are effectively one-dimensional objects. In a previous work [T. Le Goff et al, Phys. Rev. E 90, 032114 (2014)], we have shown that this model predicts frozen states caused by bending rigidity-induced oscillatory interactions between kinks (or domain walls). We here demonstrate that in the presence of tension, potential asymmetry, or thermal noise, there is a finite threshold above which frozen states disappear, and perpetual coarsening is restored. Depending on the driving force, the transition to coarsening exhibits different scenarios. First, for membranes under tension, small tensions can only lead to transient coarsening or partial disordering, while above a finite threshold, membrane oscillations disappear and perpetual coarsening is found. Second, potential asymmetry is relevant in the non-conserved case only, i.e. for permeable walls, where it induces a drift force on the kinks, leading to a fast coarsening process via kink-antikink annihilation. However, below some threshold, the drift force can be balanced by the oscillatory interactions between kinks, and frozen adhesion patches can still be observed. Finally, at long times, noise restores coarsening with standard exponents depending on the permeability of the walls. However, the typical time for the appearance of coarsening exhibits an Arrhenius form. As a consequence, a finite noise amplitude is needed in order to observe coarsening in observable time.

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“…∂ λ L λm ≤ 0. This is in contrast with the tensionless limit where the linear instability was producing a stable periodic steady-state [16].…”

Section: B Transient Coarsening and Disordering In Ch4mentioning

confidence: 69%

“…We attribute the absence of perpetual coarsening to the existence of oscillatory interactions between the kinks, as already discussed in Refs. [16,27].…”

Section: B Transient Coarsening and Disordering In Ch4mentioning

confidence: 99%

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Transition to coarsening for confined one-dimensional interfaces with bending rigidity

Goff

Politi²,

Pierre-Louis³

2015

Phys. Rev. E

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“…This fact, the relevance of bending rigidity with respect to surface tension, is not purely phenomenological. On the contrary, it has been recently derived rigorosuly from an hydrodynamic model [7]. According to this model, the energy cost of inhomogeneities is proportional (in a onedimensional model) to the squared second spatial derivative of h, (h xx ) 2 , rather than to the squared derivative, (h x ) 2 .…”

Section: Introductionmentioning

confidence: 99%

Kink dynamics with oscillating forces

Goff¹,

Pierre-Louis²,

Politi³

2015

J. Stat. Mech.

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It is well known that the dynamics of a one-dimensional dissipative system driven by the Ginzburg-Landau free energy may be described in terms of interacting kinks: two neighbouring kinks at distance ℓ feel an attractive force F (ℓ) ≈ exp(−ℓ). This result is typical of a bistable system whose inhomogeneities have an energy cost due to surface tension, but for some physical systems bending rigidity rather than surface tension plays a leading role. We show that a kink dynamics is still applicable, but the force F (ℓ) is now oscillating, therefore producing configurations which are locally stable. We also propose a new derivation of kink dynamics, which applies to a generalized Ginzburg-Landau free energy with an arbitrary combination of surface tension, bending energy, and higher-order terms. Our derivation is not based on a specific multikink approximation and the resulting kink dynamics reproduces correctly the full dynamics of the original model. This allows to use our derivation with confidence in place of the continuum dynamics, reducing simulation time by orders of magnitude.

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“…The key assumption that the film is thin in the contact region is then formalized with the help of a multi-scale expansion defining the lubrication limit 34 . This limit, widely employed in engineering (trust bearing) 30 , physics (nanoscale dewetting) 35,36 and biophysical models (membranes) 37,38 , results in nonlinear and nonlocal thin film evolution equations for the profile of the crystal surface. The end of section II presents equations for pressure solution in single contacts with some simplifying assumptions such as equal densities between the liquid and the solid, imposed symmetry (left-right symmetric ridge or axisymmetric contact), and dilute limit.…”

Section: Introductionmentioning

confidence: 99%

Thin film modeling of crystal dissolution and growth in confinement

Gagliardi

Pierre-Louis

2018

Phys. Rev. E

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We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the non-equilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution. We find that in steadystate, diverging (power-law) crystal-surface repulsions lead to flat contacts with a monotonic increase of the dissolution rate as a function of the load. Forces induced by viscous dissipation then surpass those due to disjoining pressure at large enough loads. In contrast, finite repulsions (exponential) lead to sharp pointy contacts with a dissolution rate independent on the load and on the liquid viscosity. Ultimately, in steady-state the crystal never touches the substrate when pressed against it, independently from the nature of the crystal-surface interaction due to the combined effects of viscosity and surface tension.

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Frozen states and order-disorder transition in the dynamics of confined membranes

Cited by 10 publications

References 37 publications

Transition to coarsening for confined one-dimensional interfaces with bending rigidity

Transition to coarsening for confined one-dimensional interfaces with bending rigidity

Kink dynamics with oscillating forces

Thin film modeling of crystal dissolution and growth in confinement

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