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This work describes the development of a continuum phase field model that can describe static as well as dynamic wetting scenarios on the nano- and microscale.
The model reaches this goal by a direct integration of an equation of state as well as a direct integration of the dissipative properties of a specific fluid, which are both obtained from molecular simulations. The presented approach leads to good agreement between the predictions of the phase field model and the physical properties of the regarded fluid.
The implementation of the model employs a mixed finite element formulation, a newly developed semi-implicit time integration scheme, as well as the concept of hyper-dual numbers. This ensures a straightforward and robust exchangeability of the constitutive equation for the regarded fluid.
The presented simulations show good agreement between the results of the present phase field model and results from molecular dynamics simulations. Furthermore, the results show that the model enables the investigation of wetting scenarios on the microscale. The continuum phase field model of this work bridges the gap between the molecular models on the nanoscale and the phenomenologically motivated continuum models on the macroscale.
Manufacturing techniques that can produce surfaces with a defined microstructure are in the focus of current research efforts. The ability to manufacture such surfaces gives rise to the need for numerical models that can predict the wetting properties of a given microstructure and can help to optimize these surfaces with respect to certain wetting properties. The present phase field (PF) model for wetting is linked to molecular dynamics (MD) simulations by the usage of the MD based perturbed Lennard-Jones truncated and shifted (PeTS) equation of state as well as a MD based viscosity correlation. The lower computational effort of the PF simulations compared to MD simulations enables the model to simulate wetting scenarios on the microscale.
Surface wetting can be described by using phase field models [1]. In these models, often either the contact angle or the surface tensions between the solid and the fluid are prescribed directly on the wall in order to represent the solid-fluid interaction. However, the interaction of the wall and the fluid are not strictly local. The influence of the wall, which can be described by wall potentials [2], reaches out into the fluid, which is the reason for the formation of adsorbate layers. The investigation shows how such a wall potential can be included into a phase field model of wetting. It is found that by considering this energy contribution, the model is able to capture the adsorbate layer.
Surface wetting can be simulated using a phase field approach which describes the continuous liquid-gas transition with the help of an order parameter. In this publication, wetting of non-planar surfaces is investigated based on a phase field model by Diewald et al. [1, 2]. Different scenarios of droplets on rough surfaces are simulated. The static equilibrium for those scenarios is calculated using an Allen-Cahn evolution equation. The influence of the surface morphology on the resulting contact angle is investigated while the width of the phase transition from liquid to gas is varied as a model parameter.