Fluctuations of elastic interfaces in fluids: Theory, lattice-Boltzmann model, and simulation

Stelitano, D.; Rothman, Daniel H.

doi:10.1103/physreve.62.6667

Cited by 12 publications

(7 citation statements)

References 53 publications

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“…It is obvious that this heterogenization will fundamentally change the overall properties of a material formed by the same substance but with such a multiphase hierarchal structure. Particularly in all surface and interfacial phenomena, heterogeneities of the surfaces play even more dominant role that is only partially understood 18,19 .…”

Section: B Basic Manifestations Of System Hierarchymentioning

confidence: 99%

Exploring the significance of structural hierarchy in material systems—A review

Pan

2014

Applied Physics Reviews

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Structural hierarchy and heterogeneity are inherent features in biological materials, but their significance in affecting the system behaviors is yet to be fully understood. In Section 1, this article first identifies the major characteristics that manifest, or are resulted from, such hierarchy and heterogeneity in materials. Then in Section 2, it presents several typical natural material systems including wood, bone and others from animals to illustrate the proposed views. The paper also discusses a man-made smart material, textiles, to demonstrate that textiles are hierarchal, multifunctional, highly complex and arguably the engineered material closest on a par with biological materials in complexity, and more importantly we can still learn quite a few new things from them in development of novel materials.In Section 3, the paper summarizes several general approaches in developing a hierarchal material system at various scales, including structure thinning and splitting, laminating and layering, spatial and angular orientation, heterogenization and hybridization, and analyzes the advantages associated with them. It also stresses the adverse consequences once the existing structural hierarchy breaks down due to various mutations in biological systems. It discusses in particular the influences of moisture and air on material properties, given the near ubiquitousness of both air and water in materials.It next deals with in Section 4 some theoretical issues in material research including packing and ordering, the bi-modular mechanics, the behavior non-affinities due to disparity in hierarchal levels, the importance of system dimensionality in a hierarchal material system, and more philosophically, the issues of Nature's wisdom versus Intelligent Design. Section 5 then offers some concluding remarks, including a recap of the major issues covered in this article, and some general conclusions derived from the analyses and discussions. The main purpose of this paper is to make an effort to explore, identify, derive or theorize some generic principles based on the existing results, not to offer another comprehensive review of current research activities in the fields for that there already exist some excellent ones. This paper examines the related topics with several approaches to not only reveal the underlying geometrical and physical mechanisms, but also to emphasize the ways in which such mechanisms may be applied to developing engineered material systems with novel properties.

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Section: B Basic Manifestations Of System Hierarchymentioning

confidence: 99%

Exploring the significance of structural hierarchy in material systems—A review

Pan

2014

Applied Physics Reviews

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“…As a basic example for such a fluctuating non-linear system we investigate, in the following, capillary fluctuations of a liquid-vapor interface [66,67]. We mention a number of previous simulations of fluctuating interfaces using lattice gas automata [68,69] and a fluctuating ideal gas LBM [70]. Note that in the latter work, the interface was modeled as an elastic membrane, which is different from the present approach, where the interface is represented by a smoothly varying order parameter.…”

Section: Capillary Fluctuationsmentioning

confidence: 99%

Langevin theory of fluctuations in the discrete Boltzmann equation

Groß¹,

Cates²,

Varnik³

et al. 2011

J. Stat. Mech.

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The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuationdissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, a fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.fluid at all length scales, not only the largest ones. Notably, the general theory of LB-Langevin equations was also derived in an early account by [17].Recently, the Langevin approach of [15,17], originally devised for the ideal gas, has been generalized to describe thermal fluctuations in the LBE for a class of non-ideal fluids [18]. There, non-ideal fluid models based on a squaregradient (Ginzburg-Landau) free energy functionals were considered, implying that density fluctuations in such a fluid are spatially correlated with a correlation length which is proportional to the theoretical width of the diffuse liquid-vapor interface. This is in contrast to the ideal gas, where equilibrium correlations are generally absent for all degrees of freedom. Clearly, the non-trivial structure factor of a non-ideal fluid has to be faithfully represented by the correlations of the LB population densities. Using results of continuum kinetic theory, a general ansatz for these correlations has been proposed, noticing, however, that certain models might require modifications to account for implementation-specific details [18]. This was, in particular, found to be the case for the model of Swift et al. [19], where, owing to the underlying modified equilibrium distribution, a spatially correlated form of thermal noise arises.In the present paper, we show how thermal noise can be incorporated into both ideal and non-ideal fluid versions of the discrete-velocity Boltzmann equation (DBE). The DBE is a precursor of the LBE that arises from the continuum Boltzmann equation by restricting velocity space to a finite number of velocities, while keeping position space and time continuous [20,21]. The fluctuating DBE (FDBE) is put forward here as a unifying starting point to construct fluctuating LB models and as a theoretical link between two successful frameworks of non-equilibrium physics: the LB method and the theory of linear regression of fluctuations due to Onsager and Machlup [22,23]. The utility of the FDBE is illustrated by re-deriving the fluctuating LBEs of the ideal gas [15] and the modified-equilibrium model [18]. Moreover, based on the model of He, Shan and Doolen [24], we propose a FDBE ...

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“…When the membrane moves, its computational boundary varies and this variation causes fluctuations in the resulting computation of the forces and velocities of the membrane [10,11]. In a different approach, Stelitano and Rothman [19] have modified a multicomponent LBM model to produce the desired membrane tension and bending stiffness. However, such an approach is difficult to apply to systems with specific membrane mechanics, for example, the constitutive relationship for RBC membrane.…”

Section: Introductionmentioning

confidence: 99%

An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows

2007

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In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid-membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was validated for the Laplace relationship, the dispersion relationship for interfacial waves and the drag coefficient for cylinders; excellent agreement with theoretical results was observed. Furthermore, simulations of single and multiple red blood cells in shear and channel flows were performed. Several characteristic hemodynamic and hemorheological features were successfully reproduced, including the tank-treading motions, cell migration from the vessel wall, slipper-shaped cell deformation, cell-free layers, blunt velocity profiles and the Fahraeus effect. These simulations therefore demonstrate the potential usefulness of this computational model for microscopic biofluidic systems. However, extension of this algorithm to three-dimensional situations is necessary for more realistic simulations.

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Fluctuations of elastic interfaces in fluids: Theory, lattice-Boltzmann model, and simulation

Cited by 12 publications

References 53 publications

Exploring the significance of structural hierarchy in material systems—A review

Exploring the significance of structural hierarchy in material systems—A review

Langevin theory of fluctuations in the discrete Boltzmann equation

An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows

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