Spontaneous Capillary Imbibition of Surfactant Solutions into Hydrophobic Capillaries

2 SPONTANEOUS CAPILLARY IMBIBITION OF SURFACTANT SOLUTIONS INTO HYDROPHOBIC CAPILLARIES 

In this section, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and solution concentration reduction close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant 

Pure water does not penetrate spontaneously into hydrophobized quartz capillaries however, surfactant solutions penetrate spontaneously, and the penetration rate depends on the concentration of surfactant. Both the air-Uquid interfacial tension, y, and the contact angle of the moving meniscus, are concentration dependant, where a subscript a indicates the advancing contact angle. 

It is obvious that adsorption of surfactant molecules behind the moving meniscus results in a decrease of the bulk surfactant concentration from the capillary inlet in the direction of the moving meniscus. However, as we show in this section, the major process, which determines penetration of surfactant solutions into hydro-phobic capillaries or spreading of surfactant solutions over hydrophobic substrates, is the adsorption of surfactant molecules onto a bare hydrophobic substrate in front of the moving three-phase contact line. This process results in a partial hydrophilization of the hydrophobic surface in front of the meniscus or drop, which, in its turn, determines spontaneous imbibition or spreading. 

Let us consider expression (1.2) from Section 1.1 in Chapter 1 for the excess free energy, O, of the droplet on a solid substrate  

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