Theoretical And Numerical Study Of The Ratchet Motion Of Droplets On A Vibrating Substrate

The ratchet motion of liquid drops,which is commonly seen in nature and industry,is one of the hottest issues in fluid mechanics.The understanding of the underlying mechanisms has scientific significance in biomedicine,material science and bionics.For this purpose,this thesis investigates numerically the climbing of a droplet on a vibrat-ing tilted plate,the mechanism of the ratchet motion of a drop on a vibrating plate with oblique teeth and moving compound droplets on a horizontal plate with oblique vibration.Major findings and significance of the thesis are as follows:(1)We reveal the ratchet mechanism of drops climbing a vibrated oblique plate.For the first time,the three-dimensional direct numerical simulations reproduce the existing experiment(Brunet et al.,2007).With the help of numerical simulations,we identify an interesting and important wetting behaviour of the climbing drop;that is,the breaking of symmetry due to the inclination of the plate with respect to the acceleration leads to a hysteresis of the wetted area in one period of harmonic vibration.In particular,the average wetted area in the downhill stage is larger than that in the uphill stage,which is found to be responsible for the uphill net motion of the drop.A new hydrodynamic model is proposed to interpret the ratchet,mechanism,taking account of the effects of the acceleration,gravity and contact angle hysteresis.The predictions of the theoretical analysis are in good agreement with the numerical results.(2)The two modes and corresponding ratchet mechanisms of a droplet on a vibrating plate with oblique teeth are studied.In numerical simulation,the anisotropy caused by oblique teeth is simplified to asymmetric wettability difference,that is,the different advancing angles of the droplet following and reversing the direction of the teeth.The numerical results show that droplets tend to move towards the side of the plate with smaller contact angle hysteresis.Two modes of ratchet motion have been identified.The resonant mode is defined as the mode with synchronous motion of advancing and receding contact lines,while the hysteretic mode is referred to as the hysteretic motion of advancing and receding contact lines.In the hysteretic mode,the ratchet motion is dominated by capillary waves due to the combined effect of inertia and capillarity.In the resonant mode,ratchet motion is dominated by the asymmetric capillary force.In the latter,a scaling law is proposed and agrees well with the numerical results.(3)The ratchet motion of compound droplets subjected to oblique vibration on a horizontal plate is studied.Two droplets contacting each other are initially inbalance and immiscible with a wettability difference.For the two different wet-tability configurations considered,we observe the ratchet motion with directional motion to the left(Leftward mode),bubble entrainment,static drops and separa-tion of compound drops.The vibration amplitude,frequency and the wettability of the compound droplets are found to have significant effects on the occurrence of these phenomena.Moreover,it is found the alignment sequence of compound droplets in horizontal direction might change the mode of ratchet motion.In the leftward mode,the mean velocity of the compound drops is linearly related to the square of the vibration amplitude,which is consistent with the theory of John&Thiele(2010)for two-dimensional single drop ratchet motion.