Phase-field model for the Brownian motion of droplets
ORAL
Abstract
Brownian motion (BM) plays an important role in natural science for the stochastic
motion of particles. Despite of its importance, BM was originally applied for a single
solid-particle, the modelling of BM for droplets coupling with hydrodynamics remains
a knotty issue. We present a multicomponent phase-field model coupled with the
full Navier-Stokes equation to simulate BM of droplets which is perturbed by the
thermal composition noise amid a liquid matrix. The model validation is proceeded for
different mesh finenesses, various droplet radii, diverse interfacial tensions, and distinct
viscosities of the droplet-matrix system. In addition, the structure factor of the disturbed
droplet interface is compared with the capillary wave theory (CWT). We find that
the composition noise induced BM shows distinct behaviors from the viscosity related
random body force in the Langevin mechanics. Similar to the quintessential scaling
law D∼kBT/(6πηr) in Einstein’s theory for BM, we demonstrate the scaling laws
also depending on the surface tension, and droplet viscosity. Our finding paves an
alternative way for comprehending the microstructural formation consisting of droplets
in soft matters.
motion of particles. Despite of its importance, BM was originally applied for a single
solid-particle, the modelling of BM for droplets coupling with hydrodynamics remains
a knotty issue. We present a multicomponent phase-field model coupled with the
full Navier-Stokes equation to simulate BM of droplets which is perturbed by the
thermal composition noise amid a liquid matrix. The model validation is proceeded for
different mesh finenesses, various droplet radii, diverse interfacial tensions, and distinct
viscosities of the droplet-matrix system. In addition, the structure factor of the disturbed
droplet interface is compared with the capillary wave theory (CWT). We find that
the composition noise induced BM shows distinct behaviors from the viscosity related
random body force in the Langevin mechanics. Similar to the quintessential scaling
law D∼kBT/(6πηr) in Einstein’s theory for BM, we demonstrate the scaling laws
also depending on the surface tension, and droplet viscosity. Our finding paves an
alternative way for comprehending the microstructural formation consisting of droplets
in soft matters.
*H.Z. thanks the Gottfried-Wilhelm Leibniz prize NE 822/31-1 of the German Research Foundation (DFG) for funding this research.F.W. is grateful to the VirtMat project P09 of the Helmholtz association.The authors acknowledge support by the state of Baden-Wuerttemberg through bwHPC.
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Publication: Phase-field modelling for the Brownian motion of droplets with stochastic Cahn-Hilliard-Navier-Stokes model, in manuscript
Presenters
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Haodong Zhang
- KIT