A fourth–order derivation for smoothed particle hydrodynamics to model thermodynamically–based phase decomposition

Phase decomposition and phase separation play important roles in the preparation of precipitation membranes. Phase decomposition is a diffusion–controlled process on a short time scale. Phase separation is a convection–controlled process on a long time scale. It is necessary to describe the coarsening dynamics of different time scales in only one model, to simulate the complete preparation process of precipitation membranes. In a first step, we will present a Smoothed Particle Hydrodynamics (SPH) model to describe diffusion–controlled phase decomposition. Therefore, an approximation for the fourth–order derivation for SPH is introduced and validated with a power law for coarsening dynamics. Finally, we will present the results of pseudo–binary phase decomposition of the preparation process for polymer membranes

Modeling the dynamics of partial wetting

The behavior of interfaces and contact lines arises from intermolecular interactions like Van der Waals forces. To consider this multi–phase behavior on the continuum scale, appropriate physical descriptions must be formulated. While the Continuum Surface Force model is well–engineered for the description of interfaces, there is still a lack of treatment of contact lines, which are represented by the intersection of a fluid–fluid interface and a solid boundary surface. In our approach we use the “non compensated Young force” to model contact line dynamics and therefore use an extension to the Navier–Stokes equations in analogy to the extension of a two–phase interface in the CSF model. Because particle–based descriptions are well–suited for changing and moving interfaces we use Smoothed Particle Hydrodynamics. In this way we are not only able to calculate the equilibrium state of a two–phase interface with a static contact angle, but also for instance able to simulate droplet shapes and their dynamical evolution with corresponding contact angles towards the equilibrium state, as well as different pore wetting behavior. Together with the capability to model density differences, this approach has a high potential to model recent challenges of two–phase transport in porous media. Especially with respect to moving contact lines this is a novelty and indispensable for problems, where the dynamic contact angle dominates the system behavior

An application of the Cahn-Hilliard approach to smoothed particle hydrodynamics

The development of a methodology for the simulation of structure forming processes is highly desirable. The smoothed particle hydrodynamics (SPH) approach provides a respective framework for modeling the self-structuring of complex geometries. In this paper, we describe a diffusion-controlled phase separation process based on the Cahn-Hilliard approach using the SPH method. As a novelty for SPH method, we derive an approximation for a fourth-order derivative and validate it. Since boundary conditions strongly affect the solution of the phase separation model, we apply boundary conditions at free surfaces and solid walls. The results are in good agreement with the universal power law of coarsening and physical theory. It is possible to combine the presented model with existing SPH models

A fourth–order derivation for smoothed particle hydrodynamics to model thermodynamically–based phase decomposition

Phase decomposition and phase separation play important roles in the preparation of precipitation membranes. Phase decomposition is a diffusion–controlled process on a short time scale. Phase separation is a convection–controlled process on a long time scale. It is necessary to describe the coarsening dynamics of different time scales in only one model, to simulate the complete preparation process of precipitation membranes. In a first step, we will present a Smoothed Particle Hydrodynamics (SPH) model to describe diffusion–controlled phase decomposition. Therefore, an approximation for the fourth–order derivation for SPH is introduced and validated with a power law for coarsening dynamics. Finally, we will present the results of pseudo–binary phase decomposition of the preparation process for polymer membranes

Modeling the dynamics of partial wetting

The behavior of interfaces and contact lines arises from intermolecular interactions like Van der Waals forces. To consider this multi–phase behavior on the continuum scale, appropriate physical descriptions must be formulated. While the Continuum Surface Force model is well–engineered for the description of interfaces, there is still a lack of treatment of contact lines, which are represented by the intersection of a fluid–fluid interface and a solid boundary surface. In our approach we use the “non compensated Young force” to model contact line dynamics and therefore use an extension to the Navier–Stokes equations in analogy to the extension of a two–phase interface in the CSF model. Because particle–based descriptions are well–suited for changing and moving interfaces we use Smoothed Particle Hydrodynamics. In this way we are not only able to calculate the equilibrium state of a two–phase interface with a static contact angle, but also for instance able to simulate droplet shapes and their dynamical evolution with corresponding contact angles towards the equilibrium state, as well as different pore wetting behavior. Together with the capability to model density differences, this approach has a high potential to model recent challenges of two–phase transport in porous media. Especially with respect to moving contact lines this is a novelty and indispensable for problems, where the dynamic contact angle dominates the system behavior