Surface tension gradient based flow

Surface tension on the surface of a liquid at gas-Uquid or vapor-liquid interfaces can vary due to a variation in temperamre or species concentration. The components of the tangential stress, Tj Ty and are related to the corresponding gradients in interfacial tension, between the liquid phase, j = 1, and the gas/vapor phase, y = 2 by (Bird et al, 2002)  

Assume that there are no variations of temperamre or composition in the jc-direction these vary only in the z-direction. For example. 

Note that surface tension decreases with an increase in temperamre. The height of the liquid, h, will depend on the axial location in the pan, i.e. h(z). At the top surface of the liquid, the maximum flow velocity toward the cold surface. 

Force per unit area in the tangential direction on a surface whose normal is in the jz-direction the two components of this stress, namely and are relevant here. 

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In their studies of three-phase capillary air slug (bubble) flow, Stebe and Maldarelli [47] correlated surfactant concentration to equivalent flow rate invoking similar reasoning. At a higher surfactant concentration, flow rate increased with surfactant concentration, due to the relief of surface tension gradients at the air bubble surface. When using protein-based surfactants, retardation of flow due to surface viscous effects (flow rate decreased with an increase in protein concentration) was observed. 

Velocimetry. - An analytic model for the velocity field within a tubeless siphon (Fano flow) was presented. The model was based on a simple differential equation in which extensional, shear and gravitational pressure gradient forces are balanced. The role of surface tension in determining boundary conditions for the flow is considered. The analysis is applied to NMR velocimetry data (Xia and Callaghan, J. Magn. Reson., 2003, 16, 365) on a... 

The analysis of the preceding section is based on the assumption that the interfacial tension at the drop surface is uniform so that grad y = 0 and the condition (2 141) reduces to the requirement that the tangential components of stress in the two fluids are equal at the drop interface. However, the interfacial tension at any point on the interface depends on the thermodynamic state (p and 7) as well as the concentrations of any solute molecules that are adsorbed at the interface. Hence, in a real flow system, we must often expect y to vary from point to point on the interface, and it is important to consider how gradients of y may influence the flow. 

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