arXiv subjects

Prerna Gera

Publications and source records attributed to Prerna Gera.

7 recordsLinked to original sources

arXiv2021

Swinging and tumbling of multicomponent vesicles in flow

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations we develop a reduced order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane in two dimensions with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid body tumbling behavior. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.

cond-mat.soft↗

arXiv2018

Three-Dimensional Multicomponent Vesicles: Dynamics & Influence of Material Properties

In this work, the nonlinear dynamics of a fully three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase method, the dynamics are systematically studied as a function of the membrane bending rigidity difference between the components, the speed of diffusion compared to the underlying shear flow, and the strength of the phase domain energy compared to the bending energy. Using a pre-segregated vesicle, three dynamics are observed: stationary phase, phase-treading, and a new dynamic called vertical banding. These regimes are very sensitive to the strength of the domain line energy, as the vertical banding regime is not observed when line energy is larger than the bending energy. These findings demonstrate that a complete understanding of multicomponent vesicle dynamics require that the full three-dimensional system be modeled, and show the complexity obtained when considering heterogeneous material properties.

cond-mat.soft↗

arXiv2017

Modeling of Multicomponent Three-Dimensional Vesicles

In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled using a two-phase surface Cahn-Hilliard system, while the interface is captured using a level set jet scheme. The interface is coupled to the surrounding fluid via a variation of energy approach. Sample energies considered include the total bending, variable surface tension energy, and phase segregation energy. The fully coupled system for surface inhomogeneities, and thus varying interface material properties is presented, as are the associated numerical methods. Numerical convergence and sample results demonstrate the validity of the model.

cond-mat.soft↗

arXiv2017

Stochastic Phase Segregation on Surfaces

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modeled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analyzed on two sample surfaces: a unit sphere and a dumbbell using a variety and a statistical analysis of the growth rate is performed. The influence of noise level and mobility is also investigated. It is also shown that a log-normal distribution fits the results well.

cond-mat.soft↗

arXiv2016

Cahn-Hilliard on Surfaces: A Numerical Study

The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme is investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an incomplete Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.

math.NA↗

arXiv2016

Energy Variation of Soft Matter Interfaces

The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total curvature and an underlying surface concentration field, the energy due to an external field, and a phase segregation energy. When considering these energies the variation of material properties such a bending rigidity are taken into account, which results in more general variation expressions. These variations can be used to determine the equilibrium interface and concentration configuration or to determine the driving forces for non-equilibrium situations. While the focus of this work are energies associated with multicomponent vesicles, it can easily be extended to any soft matter interface.

cond-mat.soft↗

arXiv2013

The Three-Dimensional Jump Conditions for the Stokes Equations with Discontinuous Viscosity, Singular Forces, and an Incompressible Interface

The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interface exerts singular forces on the surround fluids. This gives rise to discontinuous solutions in the pressure and velocity field. These jump conditions are required to develop accurate numerical methods, such as the Immersed Interface Method, for the solutions of the Stokes equations in such situations.

physics.flu-dyn↗