Lattice Boltzmann modeling for the coalescence between a free droplet in gases and a sessile droplet on wettable substrate with contact angle hysteresis

Abstract

The coalescence between a free droplet and a sessile droplet on wettable substrate is numerically studied. The axisymmetric lattice Boltzmann method for two-phase flows is used in modeling. Here the contact angle hysteresis (prescribed by advancing angle [Formula: see text] and receding angle [Formula: see text]) is taken into account. The effects of Ohnesorge number ( Oh), contact angle and its hysteresis, and the radius of the free droplet on the coalescence dynamics are investigated in detail. The Oh numbers ranging from 0.02 to 0.15 here makes the radius of the liquid bridge r and the time t follow power law. Also, Oh has remarkable impact on the development of capillary wave and on the amount of kinetic energy released from coalescence. It is found that the curve of the wetting radius varying with time includes several plateau stages, which is a typical characteristic for the effect of contact angle hysteresis. The larger window of contact angle hysteresis would result in smaller steady wetting radius after coalescence. Compared with the existence of contact angle hysteresis, the absence of contact angle hysteresis makes the droplets system release more kinetic energy during the coalescence but the released kinetic energy decays more rapidly and soon reduces to zero. Oppositely, if the contact angle hysteresis exists, the released kinetic energy would oscillate for a period of time before approaching zero.

Substrate Wettability Influences Internal Jet Formation and Mixing during Droplet Coalescence

“…The rate of collapse temporarily reduces at t ≈ 9.5 ms in both the experiment and simulations, which coincides with the disappearance of the column, appearing as a shoulder in Figure b. This shoulder is a consequence of contact angle hysteresis delaying outward spreading and has been seen before for similar droplet configurations but higher Ohnesorge number and lower hydrophobicity . Note that the central depression between t ≈ 11.0 and 14.0 ms cannot be perceived from the external side view for image processing and so appears as a straight line, whereas a dip is correctly seen in the simulation results.…”

“…This shoulder is a consequence of contact angle hysteresis delaying outward spreading and has been seen before for similar droplet configurations but higher Ohnesorge number and lower hydrophobicity. 43 Note that the central depression between t ≈ 11.0 and 14.0 ms cannot be perceived from the external side view for image processing and so appears as a straight line, whereas a dip is correctly seen in the simulation results. Slightly quicker droplet recoil is seen in the experiment, again due to the differences in spreading.…”

Inertial to viscous coalescence of liquid lenses: a lattice Boltzmann investigation

“…The growth of the bridge width reported in the left panel of Fig. 6 scales as w 0 ∼ t 1/2 , which agrees with experiments [20,21,29,31], analytical [4,35] and numerical studies [52,53] for freely suspended, respectively spherical droplets. The evolution of the bridge height h 0 , on the contrary, does not behave as in the quasi two-dimensional case (t 2/3 scaling), but follows again the scaling h 0 ∼ t 1/2 found for the width, as reported in the right panel of Fig.…”

Surveying the effects of concave obstacles with different edge walls on hollow glycerin droplet impacting using the volume of fluid approach

“…10 Using a 3-D model, scientists numerically investigated the impact and solidification of a molten tin droplet on another formed frozen splat. 11 Heat transfer and energy conversion 12–14 were studied in the channel and on the surfaces 15,16 with a different structures.…”