Thermal Marangoni flow

However, it remains questionable as to whether the Pearson-Nield model can be accurately applied to volatile liquid systems [72], This is because experimental results show that energy is transported from the vapor phase to the liquid-vapor interface which is opposite to the assumption made in the Pearson-Nield model. Moreover, it was predicted that thermally driven Marangoni flow would exist in an evaporating water droplet, which was not observed in experiments [58, 73]. The suppression of Marangoni flow in a water droplet may be attributed to the surfactant contaminants [74]. In addition, whether the temperature at the contact line is cooler than the top of the droplet is also unclear [11, 75]. 

EiJ, where x is determined by thermal fluctuations. Generally, the tail-water interaction energy is considerably higher than that of the tail-air interaction (E nE, where El is an interaction energy per hydrophobic unit, and is a number of those units in each tail). Consequently, x /x = exp 2( - EjJ 1, and transfer from the interface to bulk is a much slower process than the reverse one. If the duration of a spreading experiment is shorter than x, then, during that experiment, the surfactant can be considered as insoluble. Otherwise, if t > x, the solubihty of the surfactant in the liquid must be taken into account, hi the latter case, surfactant transfer to the bulk liquid tends to make concentration uniform both in the bulk and at the interface, and the result is a substantial decrease of the surfactant influence of that type (Marangoni flow). 

All of these disturbances cause a many-fold increase in the rate of transfer of solute across the interface. If a chemical or thermal difference along an interface causes an interfacial tension gradient, violent flow in the direction of low a will result. This action is usually termed the Marangoni effect. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

In equation 13, C1 and Cs are the total concentrations in the liquid and solid phases, respectively. This statement of the problem assumes that the convective flux due to the moving boundary (growing surface) is small, the diffusion coefficients are mutual and independent of concentration, the area of the substrate is equal to the area of the solution, the liquid density is constant, and no transport occurs in the solid phase. Further, the conservation equations are uncoupled from the equations for the conservation of energy and momentum. Mass flows resulting from other forces (e.g., thermal diffusion and Marangoni or slider-motion-induced convective flow) are neglected. 

This parameter is termed the Marangoni number. As discussed beJow, if Ma exceeds a critical value, an unstable convective flow will develop. The Marangoni number can also be interpreted as a thermal Peclet number (Eq. 3.5.16) if the characteristic velocity for the surface tension driven viscous flow is taken to be that of Eq. (10.5.5). We emphasize that this velocity is not a given parameter but rather a derived quantity. Expressing this velocity in terms of the imposed uniform temperature gradient p, with the aid of continuity, we arrive at Eq. (10.6.10). Interpreted as a Peclet number, the Marangoni number is a measure of the heat transport by convection due to surface tension gradients to the bulk heat transport by conduction. 

The strength of the thermocapillary flow is determined by the non-dimensional Marangoni number (Ma) defined in Equation 11 where (dy/dx) is the temperature gradient, Tj is the viscosity, a is the thermal diffusivity and L is the characteristic... 

The hydrodynamic instability leading to convective flow in the biochemical systems is driven by unbalanced forces (surface tension) at the liquid/gas interface, mainly caused by temperature gradients due to evaporative cooling [1,4]. Our experiments show that the chemical composition of the solution has to be accounted for as well. The significant parameters for the onset of pattern formation are the thermal and the solutal Marangoni numbers. Both are also important for spatial patterning in biochemically reactive liquid layers. 

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