Spontaneous shrinkage of droplet on a wetting surface in the phase-field model

Abstract

Phase field theory is widely used to model multi-phase flows. A drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy.In this paper, the spontaneous behaviour of a drop on a flat surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size and the interface width, below which the droplet will eventually disappear. In particular, the critical radius can be very large when the contact angle is hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes and the interface widths.

Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic modeling

“…Figures 2(a As analyzed in the literature, the critical diameter scales as D * ∝ (VW ) 1/3 in 2D [59,60] and D * ∝ (VW ) 1/4 in 3D [59,61], with V being the system volume, which is also confirmed by our results [seen in Fig. 2(f)].…”

“…Like other diffuse-interface numerical models, the adopted LB model also suffers from shrinkage effects, meaning that droplets below a critical size shrink spontaneously due to the redistribution of interface and bulk energies to minimize the system energy [59][60][61]. The critical size D * is defined as the 025101-4 size when shrinkage starts to take place and depends on the system size L, interface thickness W for suspending droplets [59,60], and also on the contact angle for sessile droplets [61]. Such a shrinkage effect needs to be carefully addressed in the present investigation.…”

Bubble rising and interaction in ternary fluid flow: a phase field study

“…Though the Cahn–Hilliard model can well conserve the total mass of a binary phase flow, the mass of one component may not be conserved, which has been also observed. 40,41 The shrinkage of drops can be reduced with the Cn number set below a critical value, typically on the order of magnitude of O (10 −2 ) as suggested by Yue et al 40…”

“…Though the Cahn-Hilliard model can well conserve the total mass of a binary phase ow, the mass of one component may not be conserved, which has been also observed. 40,41 The shrinkage of drops can be reduced with the Cn number set below a critical value, typically on the order of magnitude of O(10 −2 ) as suggested by Yue et al 40 Given the result of the mesh sensitivity study here, the grid with Dx = 5 × 10 −5 m or Cn = 1/54 is employed, unless otherwise stated, throughout the paper. Another issue is the choice of the phase eld mobility, which has been adjusted according to the mesh size M ∼ 0.2Dx to achieve the sharp interface limit.…”

Study of a droplet breakup process in decaying homogeneous isotropic turbulence based on the phase-field DUGKS approach

“…For a fixed position near the interface, φ decreases slightly, which indicates that the droplet becomes slightly smaller over time because of the minor mass loss. 56,[64][65][66] At t * = 39.1, i.e., after 1 × 10 6 time steps, the volume…”