Irreversible thermodynamics of curved lipid membranes

Sahu, Amaresh; Sauer, Roger A.; Mandadapu, Kranthi K.

doi:10.1103/physreve.96.042409

Cited by 47 publications

(97 citation statements)

References 96 publications

(300 reference statements)

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“…In our previous work [43], as well as the theoretical developments of Sec. 2.3, we presented surface integrals as being of the general form P (.…”

Section: Weak Formulationmentioning

confidence: 94%

“…For a more complete description of surface geometry, we refer the reader to Ref. [43,Sec. II] and the references provided therein, in particular Ref.…”

Section: Surface Geometrymentioning

confidence: 99%

“…While a framework to determine the equations of motion governing arbitrarily curved and deforming two-dimensional materials with in-plane fluidity was developed in Ref. [43], as was summarized in Sec. 2.3, solving the resultant equations is nontrivial.…”

Section: Arbitrary Lagrangian-eulerian Theorymentioning

confidence: 99%

“…(55)-(57) are the weak forms corresponding to the strong forms given respectively by Eqs. (18), (43), and (15). By summing them together and introducing a shorthand for the vector of unknowns, u, as u T := (v T , (v m ) T , λ) T , its variation δu as δu T := (δv T , (δv m ) T , δλ) T , and the space of arbitrary variations U 0 as U 0 := V 0 × V × Λ, we obtain the overall weak formulation, given by…”

Section: Weak Formulationmentioning

confidence: 99%

“…While such theoretical developments have had success in modeling certain membrane phenomena, they were difficult to extend to study how elastic out-of-plane membrane bending is coupled to different irreversible phenomena, such as in-plane lipid flow, in-plane phase transitions involving multiple components, and chemical reactions between membrane components and species in the surrounding bulk. Our recent work [43], inspired by the pioneering works of I. Prigogine [44], L. Onsager [45,46], and S.R. de Groot & P. Mazur [47], developed the general theory of irreversible thermodynamics for arbitrarily curved lipid membranes, provided a formalism to determine the equations governing membrane dynamics, and presented comprehensive models for all of the irreversible phenomena described thus far.…”

mentioning

confidence: 99%

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Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces

Sahu

Omar

Sauer

et al. 2020

Journal of Computational Physics

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An arbitrary Lagrangian-Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. A formalism is provided for determining the equations of motion of a two-dimensional material using an irreversible thermodynamic analysis of curved surfaces. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity is independent of the in-plane material velocity, and which can be specified arbitrarily. A finite element implementation of the theory is formulated and applied to curved and deforming surfaces with in-plane incompressible flows. Numerical inf-sup instabilities associated with in-plane incompressibility are removed by locally projecting the surface tension onto a discontinuous space of piecewise linear functions. The general isoparametric finite element method, based on an arbitrary surface parametrization with curvilinear coordinates, is tested and validated against several numerical benchmarks-including the lid-driven cavity problem. A new physical insight is obtained by applying the ALE developments to cylindrical fluid films, which are numerically and analytically found to be unstable with respect to long-wavelength perturbations when their length exceeds their circumference.In this paper, and the subsequent manuscript in the series ‡ [1], we develop an arbitrary Lagrangian-Eulerian (ALE) theory for arbitrarily curved and deforming two-dimensional interfaces with in-plane fluidity. The theory is based on a surface discretization which is independent of the in-plane material flow, such that the surface mesh need not convect with the material. Consequently, two-dimensional materials with large in-plane flows on arbitrarily deforming surfaces can be modeled. In Part I, we apply our theory and use standard numerical techniques to devise an isoparametric ALE finite element method for incompressible fluid films. We then implement the finite element formulation, model the deformations and flows of such materials over time, and provide several numerical results for both flat and cylindrical geometries. In Part II, we extend the finite element formulation to lipid membranes and study membrane behavior in several biologically relevant situations. As the equations governing single-and multi-component lipid membranes reduce to the fluid film equations in the limit where no elastic energy is stored in the membrane, such a separation is natural and allows us to present our results in a more accessible manner.Two-dimensional fluids have played an increasingly important role in many engineering applications, in which they often arise at phase boundaries in multiphase systems [2]. For example, under the influence of gravity and capillary forces, foams will drain over time until the constituent bubbles burst [3]. Foam lifetime plays a key role in their viability for engineering applications, and there have consequently been many efforts to improve foam stability [2]. Similar efforts have been made to stabilize emulsions and collo...

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“…In our previous work [43], as well as the theoretical developments of Sec. 2.3, we presented surface integrals as being of the general form P (.…”

Section: Weak Formulationmentioning

confidence: 94%

“…For a more complete description of surface geometry, we refer the reader to Ref. [43,Sec. II] and the references provided therein, in particular Ref.…”

Section: Surface Geometrymentioning

confidence: 99%

Section: Arbitrary Lagrangian-eulerian Theorymentioning

confidence: 99%

Section: Weak Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces

Sahu

Omar

Sauer

et al. 2020

Journal of Computational Physics

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Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

et al. 2020

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The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green-Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux-flux time correlations. The relationship between the derived transport coefficients and those of the Stefan-Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green-Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements. K E Y W O R D S electrochemistry, nonequilibrium thermodynamics, thermodynamics/statistical, transport where c i is the concentration of species i and K ij are the Stefan-Maxwell transport coefficients. These equations may be interpreted

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Finite element simulation of multi‐component vesicle morphologies undergoing phase separation

Savitha

Mandadapu

Sauer

2021

Proc Appl Math and Mech

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Morphological changes in lipid bilayer vesicles are due to phase transitions and surface deformations occurring in unison. We present a dynamic chemo-mechanical finite element model to study such changes. This is achieved by coupling two fourth order partial differential equations (PDEs): The Cahn-Hilliard [2] mass balance equation based on irreversible thermodynamics, and the Kirchhoff-Love [1] rotation free thin shell equation. The Helmholtz free energy consists of Helfrich energy to model elastic bending, and also includes in-plane elastic energy with a finite shear modulus for the purpose of regularization. The geometry is discretized by C1-continuous NURBS shape functions. An implicit second order accurate generalized-α scheme is used for time integration. Newton-Raphson iterations are utilized to solve the resulting linearized weak form monolithically. The proposed formulation is illustrated by a numerical example.

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Irreversible thermodynamics of curved lipid membranes

Cited by 47 publications

References 96 publications

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces

Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

Finite element simulation of multi‐component vesicle morphologies undergoing phase separation

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