The Unstable Spreading Of A Surfactant-laden Droplet Over Complex Substrates

When a surfactant or its solution is placed on the surface of another liquid film,the liquid will spontaneously spread due to the surface tension gradient.During the spreading,due to the strong nonlinearity of the physical mechanisms involved,the leading edge exhibits a complex instability that is closely related to the substrate property.The study of this instability is beneficial to numerous industrial applications including spraying,printing,and inhalation therapy.There have been many theoretical and experimental studies on the spreading of surfactant-laden droplets on flat non-heated substrates,and physical models have been established and verified.However,when the substrate is more complicated,such studies still need to be further developed.Therefore,in this study,a two-dimensional model for simulating and analyzing the instability is established for the spreading of droplets laden with insoluble surfactants on topographic substrates and on heated substrates with variable viscosity considered.The Marangoni effect,dominant wavenumbers,disturbance energy,and other factors in the spreading are analyzed.The main contents are as follows:(1)For the spreading of droplets laden with insoluble surfactants on topographic substrates,a mathematical model was established based on N-S equation,mass conservation,convection-diffusion equation,and lubrication approximation,and the influence of substrate topography on disturbance energy and dominant wavenumbers was analyzed.According to the driving force,the mechanism of the instability phenomenon is examined.The substrate topography does not change the long-term wavelength selection mechanism,but on the corrugated substrate,a low wavenumber perturbation in the early stage of spreading will be strengthened,the notch substrate has an inhibitory effect on the development of the disturbance,while the corrugated substrate can promote the development of the disturbance.The substrate topography affects the Marangoni effect by affecting the surfactant concentration distribution,and inhibits or promotes the development of disturbances,thereby affecting the spreading stability.(2)For the spreading of droplets laden with insoluble surfactants on heated substrates,a mathematical model was established based on the N-S equation,continuity equation,convection-diffusion equation,energy equation and lubrication approximation,dominate perturbation wavenumbers of spreading over heated substrates are screened out,the mechanism of the instability is analyzed according to the velocity field and driving force.The heating mode of the substrate has a certain influence on the wavelength selection mechanism.When the substrate is heated,the liquid tends to flow out of the heating area,and the fingering is rounder.Decomposing the Marangoni effect into solutocapillary and thermocapillary,both of which have a destabilizing effect on the spreading.The inhomogeneity of the surfactant and temperature distribution is exacerbated by the Marangoni flow,which in turn leads to a stronger Marangoni effect,making the flow more unstable.(3)When the liquid viscosity varies with temperature,due to the uneven temperature distribution of the substrate,the liquids in different regions have different viscosities,which will have different effects on the spreading and instability.On the non-isothermally heated substrate,the liquid in the high-temperature area has a lower viscosity,and its higher fluidity will aggravate the unevenness of the surfactant and temperature distribution,making the flow more unstable;but on the isothermally heated substrate,the overall higher temperature does not exacerbate the unevenness of the surfactant and temperature distribution,but results in an overall increase in fluidity,thereby accelerating spreading.The Marangoni effect is destabilizing to spreading,and anything that exacerbates the uneven distribution of surfactant and temperature will make the flow more unstable.