| Droplet evaporation is a common phenomenon in daily life,which is a thermophysical process involving phase changes,heat and mass transfer,and thermocapillary convection.Thermocapillary convection within evaporating droplets not only enhances heat and mass transport,but also affects the morphology of the deposition pattern for droplets containing particles.The droplet evaporation therefore has important applications in many technologies,such as inkjet printing and spray cooling.Although a great deal of research has been carried out on droplet evaporation,few studies have been done on thermocapillary convection within evaporating droplets.Particularly,the understanding of Marangoni instability in droplets evaporating at constant contact angle mode is still lack.Therefore,the purpose of this paper is to study droplets evaporating at constant contact angle mode,and the thermocapillay convection and its instability within evaporative droplets.Firstly,the Benard-Marangoni(BM)convective instability within evaporating droplets was experimentally investigated,and the effects of substrate temperature,contact angle and wetting radius on BM convective instability and its evolution pattern were analyzed.When the normal temperature gradient along the evaporating droplet surface dominates,the Benard-Marangoni(BM)convection occurs.It shows a flower-like cell pattern,with higher temperature in central region than that near the edges.The wavelength of BM cells is approximately 3.0 times of the thickness of droplet.The thermocapillary convection becomes even unstable with increasing the substrate temperature or normal Marangoni number(Man)whereas it is stabilized with increasing contact angle.The cells number decreases with decreasing wetting radius.The dimensionless cells number linearly decreases with the square of dimensionless evaporation time.Secondly,the longitudinal rolls within the evaporating droplets was experimentally investigated.Influences of substrate temperature,contact angle,ambient temperature and wetting radius on longitudinal rolls and their evolution were analyzed.When the ratio of normal to tangential temperature gradient on the droplet surface is about 11.1,the longitudinal rolls are generated within evaporating droplets.They extend straightly from the triple line to the center of droplet.Longitudinal rolls uniformly distribute along the circumference,forming a spoke-like pattern.The number of longitudinal rolls linearly decreases as the droplet wetting radius decreases.With increasing substrate temperature or contact angle,both the number of longitudinal rolls and the corresponding Man increase.However,the ambient temperature gives no significant effect on evolution of the longitudinal rolls pattern,rolls number and Man.Thirdly,the arbitrary Lagrangian-Euler method was adopted to track the dynamic deformation of evaporating droplet profile.A three-dimensional unsteady model was established to study the hydrothermal waves in evaporating droplet.The influences of substrate temperature,initial wetting radius and contact angle on hydrothermal waves were analyzed carefully.When the tangential temperature gradient dominates on the droplet surface,the hydrothermal waves occur in droplets.They consist of three spiral blade-shaped waves.Waves are uniformly distributed along circumference in the central region,forming a fan-like pattern.As the wetting radius decreases,they propagate in counterclockwise or clockwise direction.With increasing the substrate temperature or initial wetting radius,the hydrothermal waves become more unstable.However,the hydrothermal waves and longitudinal rolls coexist in droplet with decreasing contact angle.In addition,the hydrothermal waves only occur for θ>36°.Further,the thermocapillay convection and its instability in droplet evaporating on the lyophilic surface(such as θ=50°)were investigated by numerical simulations.The influences of Marangoni number(Ma),evaporative cooling number(E),the ratio of substrate thermal conductivity to droplet thermal conductivity(kR)and Prandtl number(Pr)on the thermocapillary convection instability and its heat transfer performance were analyzed.For Ma>3950 or E≥ 45,the hydrothermal waves appear in droplet.As Ma or E increases,they become less stable,leading to an increase in both the propagation velocity of hydrothermal waves,the kinetic energy of the fluid flow in droplet and heat transfer performance.For kR<0.1,the BM convection and longitudinal rolls coexist in droplet.For 0.1 ≤kR<0.5,the BM convection and longitudinal rolls,longitudinal rolls and hydrothermal waves,occurs sequentially in droplet,while only hydrothermal waves appear for kR>0.5.For Pr<9.0,the hydrothermal waves are generated.As Pr increases,the thermocapillary convection become more stable.The hydrothermal waves thus become more regular and the oscillation of surface temperature is reduced.The critical Mac for the incipience of hydrothermal waves and heat transfer performance increase with increasing Pr.Finally,influences of Ma,E,kR and Pr on the thermocapillary convection instability and heat transfer performance for droplet evaporating on the lyophobic surface(such as θ=120°)were investigated by three-dimensional simulations.For Ma≥4750 or E≥4.0,the transition between longitudinal hydrothermal waves and hydrothermal waves were found in droplets,enhancing the heat transfer performance.As Ma increases,the kinetic energy,the droplet surface temperature and the temperature oscillation frequency gradually increase,whereas the temperature amplitude decreases.The kinetic energy and the surface heat loss increase,whereas the surface temperature gradually decreases with increase of E.For kR<0.5,BM convection and longitudinal hydrothermal waves appear in sequence.The longitudinal hydrothermal waves and then hydrothermal waves are generated for kR≥0.5.Only hydrothermal waves are generated for Pr≤5.5 whereas longitudinal hydrothermal waves were produced for Pr>5.5. |
