2004
DOI: 10.1007/s00396-004-1107-2
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Adsorption kinetics at air/solution interface studied by maximum bubble pressure method

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Cited by 9 publications
(8 citation statements)
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“…This resulted in accurate expressions of the dynamic surface adsorption for the following cases: (1) short-time limit adsorption (no-back diffusion), (2) adsorption with back diffusion, and (3) long-time limit adsorption. The following equations give the dynamic surface adsorption onto a spherical interface within the short- and long-time approximation, respectively: normalΓ ( t ) = D C 0 t r 0 + 2 C 0 D t π .25ex2ex .25ex2ex normalΓ ( t ) = ( C 0 C s ) D r 0 ( t + 2 r 0 t D π ) + Q ( t t 1 ) where r 0 is radius of capillary, t 1 is a given long time at which the concentration at the subsurface has reached a constant value of C s , and Q is only a function of t 1 and C s .…”
Section: Experimental Sectionmentioning
confidence: 99%
“…This resulted in accurate expressions of the dynamic surface adsorption for the following cases: (1) short-time limit adsorption (no-back diffusion), (2) adsorption with back diffusion, and (3) long-time limit adsorption. The following equations give the dynamic surface adsorption onto a spherical interface within the short- and long-time approximation, respectively: normalΓ ( t ) = D C 0 t r 0 + 2 C 0 D t π .25ex2ex .25ex2ex normalΓ ( t ) = ( C 0 C s ) D r 0 ( t + 2 r 0 t D π ) + Q ( t t 1 ) where r 0 is radius of capillary, t 1 is a given long time at which the concentration at the subsurface has reached a constant value of C s , and Q is only a function of t 1 and C s .…”
Section: Experimental Sectionmentioning
confidence: 99%
“…The subsurface is defined as the surface of the spherical region outside the semi-spherical forming bubble with diameter equal to the capillary. Following the procedure by Liu et al (2004), which is reported in detail in Appendix A, the diffusion equation…”
Section: Transient Surface Accumulationmentioning
confidence: 99%
“…A.1). Following the procedure by Liu et al (2004), the Ward and Tordai equation can be written in spherical coordinates by solving the diffusion equation…”
mentioning
confidence: 99%
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“…The adsorption time scale for most of the known surfactants (we treat the impurities as surfactants) is of the order of few seconds and consequently the surface tension attains the reduced value in this time [31][32][33]. On the contrary, the typical time scale that can be ascribed to the formation or morphological changes (if any) of the surface nanobubbles is at least of the order of 10 minutes [5,34,35].…”
Section: Introductionmentioning
confidence: 99%