Marangoni effect

About: Marangoni effect is a research topic. Over the lifetime, 5336 publications have been published within this topic receiving 98562 citations. The topic is also known as: Gibbs–Marangoni effect.

Evaluation of thermocapillary driving forces in the development of striations during the spin coating process

Abstract: The evolution of a temperature gradient at the free surface of a coating solution during the spin coating process is examined. Solvent evaporation causes localized cooling at the top that can result in thermocapillary instability within the coating solution, and thereby driving convective flows that may result in non-uniform coatings. We examine the evolution of these temperature gradients by using a one dimensional finite difference model that simultaneously describes the thinning behavior (both by flow and by evaporation) and the temperature evolution within the solution. The entire system is initially isothermal but is subject to evaporation-driven cooling at the free surface of the gradually thinning fluid. The model is then used to determine the magnitude of the thermocapillary effects during the spin coating process. As test systems we simulate the spin coating of several pure alcohol solutions having different volatilities and therefore different evaporative-cooling powers. As the fluid thins, we calculate the instantaneous Marangoni (Mn) number, which signifies the magnitude of thermocapillary-driven convection. We compare these Mn values against their relevant threshold values, determined from prior reports in the literature, in order to deduce the magnitude of the instabilities they represent. If the Mn value is super-critical, then the instability that it represents will be sufficient for the onset of convection cells within a stagnant fluid layer of corresponding thickness. Because the radial outflow is fully laminar under normal conditions, super-critical Mn values imply that similar instabilities would arise within a spinning solution. Super-critical Mn values were observed under numerous conditions suggesting that thermocapillary instability may be responsible for striation features that develop in coatings made by spin coating. Trends related to spin-speed, solvent volatility, and initial solution thickness are discussed with the goal of improving the flatness of coatings that are made by this process.

Marangoni flow and the shapes of laser-melted pools

Abstract: The incidence of a concentrated flux of energy onto a conducting substrate which leads to localized melting as with a laser beam striking a metal is currently of interest in various material technologies, such as welding [1], in amorphous surface layer formation, as well as in the related problem of plasma disruptions on the first wall of projected thermonuclear fusion reactors [2]. Here we have modeled the process and consider the contribution of Marangoni or capillary gradient convection to the steady-state molten zone configuration. In the small-scale hydrodynamics involved in these phenomena and with high-surface-tension substances, Marangoni flow dominates over buoyancy flow. Tested on an important steel for laser powers up to 4 kW, the model predicts that the system capillarity, related to temperature and chemical composition, determines in a remarkable way the profile of the molten pool and explains observations made in metallurgical practice. This two-dimensional transient analysis refers to a model of a laser beam with a Gaussian power distribution normal to a flat substrate. Part of the incident radiation is reflected, while the absorbed part raises the temperature and produces a molten pool. Because of the steep temperature distribution, the surface tension decreases or increases radially from the center depending upon the surface chemistry of the system. Classical Marangoni flow arises from thermal or chemical capiUary gradients at the fluid surface, the direction of flow being from a locality of low to one of high surface tension. A detailed description of the present modeling will be published elsewhere. In summary, for the treatment of the flow hydrodynamics, we consider the Navier-Stokes governing equations with an additional relation expressing surface tension as a linear function of temperature. The analysis incorporates the problem of the moving boundary, as treated by Szekely [3] and exemplified in typical melting and solidification processes. Here, for a single-component system, the temperatures of the solid and the molten phases are equal at the meltsolid interface. In addition, a relationship has been established between the movement of the liquefaction front and the heat flux crossing the melt-solid interface. This is simply an expression of a balance between the heat flux arriving at the interface from the melt and passing into the solid, to the rate of advance of the interface. For the free surface, we consider the heat flux lost by evaporation, whereas heat losses by radiation and convection are neglected. Computations have been restricted to the case where the surface temperature never exceeds the boiling temperature. Furthermore, we assume at this stage as a first approximation, that the thermal conductivity and density are the same for both liquid and solid, that all physical properties such as viscosity and density of the liquid and solid are invariant with respect to temperature, and that the surface of the melt pool remains flat (a treatment under development will make allowance for a changing liquid/vapor interface). By considering cylindrical geometry, the governing equations have been discretized by finite difference methods using an unevenly spaced grid. As a starting point, a constant temperature field without fluid motion is considrently of interest as a candidate for first wall material for the next step of tokamak-type thermonuclear fusion reactor, where localized surface melting is expected to occur due to energy bursts resulting from plasma disruptions, a phenomenon which has been simulated by Schiller et al. [2] using electron beams. The present alloy has been studied in connection with anomalous welding behavior [4-8] and it has been demonstrated experimentally [1] that a steel with a high impurity content is associated with a deep, narrow weld pool (good penetrability) while the converse holds for a \"clean\" steel. The weld pool geometry is convincingly related to the sulfur impurity content of the steel. We apply the present model to test the notion that the role of the sulfur is through its effect on capillarity, which in turn influences the flow hydrodynamics. In essence, we attempt through the present model to predict the resulting pool shapes from the surface thermodynamic data. The surface tensions of this family of alloys have been measured recently by Mills et al. [1], using an elegant levitated molten-drop technique in a well controlled environment. These are currently the most rigorous data available on high-temperature alloy systems. We have applied the following quantities: Steel A (\"clean\" steel with very low impurity levels) which has a temperature coefficient of surface tension of -0 .30 mNm-lK -1 in a temperature range of 1400-1800 ~ Steel B, containing 140 ppm of sulfur (which displays good weld pool penetration) has a value + 0.36 mNm-lK -1. The negative coefficient for steel A is consistent with thermodynamic expectation for a system in which the bulk and surface compositions are identical; whereas the positive coefficient for steel B reflects