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We study the instability of a thin film composed of two miscible fluids (binary fluid) placed on a solid planar surface. We include the fact that both the free surface and wetting energies depend on the mixture concentration. By assuming a…
The problem of multiphase materials (fluid or solid) interacting with the rigid body structure is studied by proposing a novel VMS-FEM (variational multi-scale finite element method) in the Eulerian framework using the fixed mesh. The…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Dispersions of immiscible liquids, such as emulsions and polymer blends, are at the core of many industrial applications which makes the understanding of their properties (morphology, stability, etc.) of great interest. A wide range of…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed…
This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for…
Liquid films on moving substrates are used in dip-coating processes to form uniform protective layers. Controlling free-surface waves is essential due to the film's inherent linear instability. Therefore, we develop a linear feedback…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We develop a sharp-interface model for solid-state dewetting of double-bubble thin films using an energy variational approach based on a newly proposed interfacial energy. This model characterizes the dynamic evolution of interfaces in…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at…
We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal…
We present a variationally consistent wrinkling model based on spectral decomposition of the stress tensor, providing a unified formulation that captures the three distinct membrane states. Compared to the previous strain-based spectral…
Continuum modeling of a free-standing graphene monolayer, viewed as a two dimensional 2-lattice, requires specifications of the components of the shift vector that act as an auxiliary variable. The field equations are then the equations…
We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…