| Evaporation of sessile droplet is quite common in daily life,which is a quite complicated thermophysical process involving phase change,heat and mass transfer,and Marangoni convection.Marangoni convection within evaporating droplets not only enhances heat and mass transport,but also affects the morphology of the deposition pattern for droplets containing particles,and thus it has a vast variety of industrial applications,such as DNA mapping,spray cooling,and inkjet printing.Ideally,the droplet often evaporates at constant contact line mode(CCL)and constant contact angle mode(CCA).Compared with that at CCA mode,the droplet morphology,evaporation rate,heat and mass transfer at the liquid-gas interface,as well as internal flow and heat transfer always change during the evaporation at CCL mode,and the morphology and strength of the Marangoni convection inside the droplet also change accordingly.Thus,the Marangoni convection in the evaporating droplet at CCL mode would become more complex compared with that evaporating at CCA mode.At present,most of the studies focus on the Marangoni convective instability inside droplets with spherical shape and the condition that on an isothermal substrate.However,due to the actual conditions such as rough or heterogeneous substrate surface,the droplet shape is often non-spherical and the temperature at the bottom of the droplet is not uniformly distributed.Besides,most of the researches are aimed at the single type of Marangoni instability mode,while few studies are aimed at the transition of Marangoni instabilities.Therefore,in this paper,Marangoni convection instability and transition in droplets evaporating at CCL mode are deeply studied by means of experiment and numerical simulation.The main contents are summarized as follows:Firstly,the Marangoni convection and corresponding instability in evaporating spherical droplets with moderate volatility were studied.When the substrtate temperature(Ts)is higher than the ambient temperature(Ta),the steady thermocapillary convection,longitudinal rolls,and irregular oscillatory Bénard-Marangoni(BM)convection appear in sequence,and the ratio of the normal Marangoni number(Mav)to the tangential Marangoni number(Mah)b increases during evaporation.The total number of longitudinal rolls increases linearly with increasing Ts.When increasing Ts,the thermocapillary convection becomes easier to lose its instability and the critical contact angles for the onset of longitudinal rolls and BM convection cells increase.For Ts < Ta,the internal flow is always irrregulary oscillatory BM convection when Ts >10.6 ℃.When Ts ≤ 10.6 ℃,the internal flow is steady thermocapillary convection with no instability patterns observed.When increasing Ts,the growing and drifting speed of BM cells become faster and the number of them is larger.Secondly,Marangoni convection instabilities in serval types of well-defined non-spherical droplets were investigated experimentally,and the effects of substrate temperature,contact line curvature(kcl),and contact angle were analyzed.The longitudinal rolls always appear first at the region where kcl is the largest with serval cold bands connecting the droplet apex with the end of rolls.These rolls are non-uniformly distributed along the azimuthal direction,and they always drift from the lower kcl region to the higher kcl region.The total number of longitudinal rolls increase linearly with increasing Ts,and the droplet of spherical shape is more capable to hold these rolls especially under a higher Ts.With increasing the Marangoni number(Ma),the crtical contact angle for the onset of these rolls at the middle of straight sides in the polygonal droplet increases,while it decreases at the negative kcl region in the droplet of kidney shape.Furtherly,Marangoni convection and corresponding instabilities inside an evaporating droplet on a non-isothermal substrate were studied,and the influences of substrate temperature,temperature gradient(▽T)were analyzed.The longitudinal rolls,the coexistence of longitudinal rolls and BM convection,and the irregular oscillatory BM convection occur sequentially with droplet evaporation.The longitudinal rolls and BM cells preferentially appear at the cold side of the droplet where the normal Marangoni force is relatively larger.The longitudinal rolls are continuously propagating from the hot side towards the cold side driven by the azimuthal thermocapillary convection near the contact line,and the propagation speed increases with increasing▽T.When increasing Ma and ▽T,The gradually dominant tangential Marangoni force makes the thermocapillary convection inside the droplet more stable,and thus the number of longitudinal rolls and the cirtical contact angles for the onset of them decreases.Further,a three-dimensional unsteady model was established to study the Marangoni convection instability and transition inside an evaporating droplet with high volatility,and the influences of substrate temperature,contact angle(θ),and the relative thermal conductivity(k R)were analyzed.Besides the longitudinal rolls and BM cells,the fan-like hydrothermal waves with three spiral blade-shaped waves are observed,which propagate in counterclockwise or clockwise direction during evaporation process.For k R < 0.1,the BM convection and longitudinal rolls,longitudinal rolls,and irregular oscillatory BM convection appear in sequence.For 0.1 ≤ kR < 1.0,the hydrothermal waves and longitudinal rolls,longitudinal rolls,and irregular oscillatory BM convection occur sequentially in droplet.For k R ≥ 1.0,the hydrothermal waves,hydrothermal waves and longitudinal rolls,longitudinal rolls,and irregular oscillatory BM convection appear successively with evaporation.Finally,the Marangoni convection instability in an evaporating droplet floating on a liquid layer was observed.When the droplet is fully floating on a liquid layer,the evaporating mode is CCA mode,with the square of droplet radius decreasing linearly with evaporation.The droplet is always located at the junction of BM cells in the liquid layer during the evaporation process,and the hydrothermal waves propagating in the azimuthal direction are observed inside the droplet,whose number follows a power law decay with decreasing of dimensionless wetting radius(r/r0)of the droplet.When the droplet is partially floating on a liquid layer,the evaporating mode is CCL mode and the internal flow is irregulary oscillatory BM convection.BM cells always appears at the region near the contact line first and move inwards along the radial direction.Meanwhile,serval gaps are observed on the contact line which is actually the local high temperature region.These gaps are always located at the junction of adjacent BM cells in the liquid layer and they are actually the origins of the BM cells in droplet,and the number of which increases with evaporation and decreases sharply at the end of evaporation process.The critical thickness of the liquid layer for the onset of hydrothermal waves inside the evaporating droplet is equal to that of the transition from partially floating state to fully floating state,which increases slightly with increasing Ma.The critical thickness of liquid layer for the onset of BM convection inside the evaporating droplet of partially floating state increases with increasing Ma. |
