Complications to Capillary Flow Analysis

Other than capillary phenomena. Some of those systems will be encountered in later chapters. 

Marangoni effects can be encountered in both single- and multicomponent liquid systems. In a pure liquid, surface tension gradients result from differences in temperature (or evaporation rate) from one point to another in the system. It is generally found that an increase in temperature lowers ctlv so that where hot spots occur, liquid flows away to cooler regions of the liquid (Fig. 6.13 ). The result of such a phenomenon can be the formation of dimples in a surface that dries or solidifies under uneven temperature conditions. 

In multicomponent systems (e.g., surfactant solutions), surface tension gradients usually are due to adsorption-related phenomena or, where possible, to different rates of evaporation from the system (although simple temperature variations can also be important). If the system contains two liquid components of differing volatility, the more volatile liquid may evaporate more quickly from the LV interface, resulting in localized compositional—and therefore surface tension—differences. It is also commonly found that when two or more components are present, one will be preferentially adsorbed at the LV interface and lower ctlv of the system. If a surface-active component 

FIGURE 6.13. The Marangoni effect results from the presence of surface tension gradients in a liquid surface (a) the presence of a hot spot will lower the surface tension near the heated area, causing flow in the direction of the cooler (higher surface tension) areas (b) if a volatile surface-active material evaporates from a liquid surface, the local surface tension will increase resulting in flow toward the depleted area and the formation of a bump or drop as in wine tears.  

Multicomponent systems may also involve the selective adsorption of one component at the SL interface. Since the component that lowers the interfacial tension will be preferentially adsorbed, the rate of the adsorption process can affect the local tension and the contact angle. In many systems, the rate of adsorption at the solid surface is found to be quite slow compared to the rate of movement of the SLV contact line. As a result, the system does not have time for the various interfacial tensions to achieve their equilibrium values. Most surfactants, for example, require several seconds to attain adsorption equihbrium at a LV interface, and longer times at the SL interface. Therefore, if the hquid is flowing across fresh solid surface, or over any surface at a rate faster than the SL adsorption rate, the effective values of olv and osl (and therefore 6) will not be the equilibrium values one might obtain from more static measurements. More will be said about dynamic contact angles in later chapters. 

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