| Two-phase flows with moving contact lines are popular in nature and practical applications of industrial field. Numerical investigation of these problems has many advantages than experimental and theoretical studies. Different CFD (Computational Fluid Dynamics) methods have been applied to study moving contact line problems in the past thirty years. The lattice Boltzmann method (LBM) has developed very fast in recent20years and has become a useful CFD tool. Due to its simplicity and capability of incorporating different physical models, it has been applied to study many two-phase flows. However, studies about contact angle hysteresis using the LBM are rare. Here first a model of contact angle hysteresis is successfully incorporated into the He-Chen-Zhang (HCZ) multiphase LBM. After validation of the numerical method, it is applied to study the dewetting dynamics of a thin liquid film and the fusion kinetics of a free droplet coalescence with a sessile droplet. The results and conclusions in this dissertation are summarized as follows:(1) A model of specifying contact angle and its hysteresis is successfully incorporated into the HCZ LBM. The scheme is validated through investigations of the dy-namic behaviors of a droplet sliding along two kinds of walls:a smooth (ideal) wall and a rough or chemically inhomogeneous (nonideal) wall. For an ideal wall, the wettability of solid substrates can be prescribed exactly in our method. For a nonideal wall, arbitrary contact angle hysteresis can be obtained through adjusting advancing and receding angles. In our scheme, significantly different phenomena can be recovered for the two kinds of walls. For instance, a droplet on an inclined ideal wall under gravity is impossible to stay stationary. However, the droplet on a nonideal wall may be pinned due to contact angle hysteresis. The steady shapes of the droplet on an inclined nonideal wall under gravity or in a shear flow quantitatively agree well with the previous numerical studies. Besides, the complex motion of a droplet creeping like an inchworm is reproduced. The scheme is found suitable for the study of contact line problems with and without contact angle hysteresis.(2) The axisymmetric HCZ LBM is applied to simulate the dewetting dynamics of a thin liquid film with an initial dry spot (a circular hole with a radius R). In sim-ulations, the film dewetting on both smooth and rough substrates is investigated. At first, on smooth substrate, the contact line is observed receding ceaselessly, i.e., the circular hole expands, and the removed liquid accumulates into a rim. The velocity of the contact line, V=dR/dt, keeps constant. The effects of contact angle (θeq), Ohnesorge number(Oh), and the viscosity ratio (λμ) are investi-gated systematically. When θeq<40°, V is found approximately proportional to θ3/eq, i.e., VâˆÎ¸3/eq, which is consistent with the experimental data. Here, the effect of θeq is investigated comprehensively. When θeq is large (e.g.,θeq>40°), V is found to have a linear relationship with θeq, i.e., dVâˆdθeq, which has never been addressed in the literature. It is confirmed that liquid films thickness may not af-fect the dewetting velocity. Second, the liquid film dewetting on rough substrates of uniformly distributed pillars is studied. Under the circumstances of same Oh, λμ, and θeq, it is found that the film dewets in Cassie state slightly faster than that in smooth substrate, but much faster than that in Wenzel state. Wenzel state seems always hold back the movement of the receding interface. The possi-ble mechanism is analyzed. The geometric effects of the pillars are discussed in detail.(3) The axisymmetric HCZ LBM is also used to study a free droplet (radius R2) coa-lescence with a sessile droplet (the volume is fixed). The study was carried out for two typical substrates (wetting and non-wetting). The effects of Ohnesorge num-ber, contact angle and its hysteresis, the radius of the free droplet are investigated in detail. According to the dynamics, five modes in the coalescence are identified. In inertial coalescence regime, the radius of the liquid bridge formed between the two droplets and the time follows the power law, i.e., r/Rc=k(t/tc)0.5, where, the coefficient k is function of Oh and R2, and k increases with the decrement of Oh and with the increment of R2.However, it is confirmed that k is not rele-vant to contact angle (or its hysteresis). In other words, the spread of the liquid bridge is not affected by the wetting properties of the substrate. As a free droplet coalesced with a sessile droplet on wetting substrates, contact angle hysteresis may reduce the wetting radius of the fused droplet when it reaches a steady state finally. Meanwhile, due to the existence of contact angle hysteresis, more kinetic energy would be released from the droplet system, but it also decays more rapidly. As a free droplet coalesced with a sessile droplet on non-wetting substrates, con-tact angle (hysteresis not considered) may play an important role in determining coalescence modes. For instance, when contact angle is set to be90°, the free droplet could be absorbed into the sessile droplet, and finally the formed large droplet would reach equilibrium state on the substrate, however, when contact angle equals to150°, the sessile droplet could be absorbed into the free droplet, and finally the formed large droplet would reach equilibrium state in the air. It is also found that coalescence mode also depends on the radius of the free droplet R2.When R2becomes relatively small, the sessile droplet only departs from the substrate temporarily, subsequently because of the oscillating of capillary wave, the droplet contacts the substrate again and finally stays on the substrate. A reasonable conjecture is that when R2is small enough, the free droplet would be unable to make the sessile droplet leave the substrate from beginning to end. Besides, Oh may significantly affect the dynamics. The smaller Oh is, the more kinetic energy the system releases. |
