Dupre relation

The wetting angle 0 is calculated from the Young Dupre relation + o j cos0. Mean surface energies... 

The Young-Dupre relation is the boundary condition that allows the determination of the shape of the surface between two fluids in contact with a solid wall, such as a liquid drop on a solid wall within a gas (dew) or an air bubble adhering to a sohd wall within a liquid. It is important to emphasize that the Young-Dupre law is applicable only to the case where the triple line is at static equilibrium on the sohd. When the triple line moves (if for example the dew drop slides down the wah), the concept of dynamic contact angle shoirld be substituted for that of static contact angle for better results. ... 

The thermodynamic adhesion (work of adhesion - Wa) between two polymer materials (1 and 2), in ideal contact, is given by the Dupre relation ... 

By relating the work required to force a volume dp" of mercury into the pore of a solid to the work required to form an element d/4 of mercury-solid interface, and making use of the Young-Dupre equation (3.70) one arrives at the expression... 

Figure 9. Variations of uranium (a) and thorium (b) contents in the filtrates of a sample as a function of the filtration size, and relation with the variations of the dissolved organic carbon (DOC). Data sources (1) Viers et al. (1997), (2) Dupre et al. (1999), (3) Porcelh et al. (1997, 2001), (4) Riotte et al. (2003). Filtrates are recovered by tangential ultra-filtration. Low filtration sizes are usually given in Dalton—a molecular weight unit of 1 g/mol—and are ranging between 3 and 300 kD. These filtration sizes have been converted here into an approximate rm pore size.

Armando Aranda So, sorry, is it because in relation to what Dupre has said that I presume that downward causation can be based on something stronger and deeper than correlations ... 

A relation between rupture phenomena and (specific) surface energy 7 was postulated by Dupre 4 almost simultaneously with the hypothesis of Quincke. Let a cylindrical rod be broken in tension. After rupture, two new gas — solid interfaces of vr2 each are present, r being the radius of the rupture surface. Consequently, the work of rupture ought to contain a term 2 nr2 7 . Dupre did not indicate how to separate this term from the main component of the work of rupture, which is the work required to extend the rod to its maximum elongation (or strain). The modern development of Dupre s ideas is reviewed in Section III.3. below. 

Calcagni, A., Ciattini, P. G., Di Stefano, A., Dupre, S., Luisi, G., Pinnen, F., Rossi, D., and Spirito, A. (1999). psi(S02NH) transition state isosters of peptides. Synthesis and bioactivity of sulfonamido pseudopeptides related to camosine. Farmaco 54, 673-677. 

The equation relating contact angle to surface tension, generally ascribed to Young or Dupre, is... 

Substituting in the Dupre equation, the spreading coefficient can be related to the work of adhesion and cohesion... 

If the various equations introduced above are taken into consideration, to a reasonable approximation the optimum conditions for herbicide activity will be realized when the quantity yL cos 6 is at a maximum. From the well-known relation of Dupre, it follows that... 

This important relation is due to Dupr. 1 It is so much easier to visualize the attraction WAB, which one liquid has for another, than the surface tension, or inward pull on the surface molecules, that an insight into the... 

This equation has been known for over a century it was given by Young2 (without proof ) and by Dupre 3 it can be deduced also from Laplace s theory of Capillarity, or indeed from any theory of the cohesive forces, since it can be obtained from consideration of energies only. Until recent years it has been little noticed, which is unfortunate, as the meaning of the contact angles is much clarified when the work of adhesion is introduced, and the surface tensions of the solid surfaces, which are not measurable, are eliminated. Most authors are now, however, expressing their results in terms of the work of adhesion or of closely related expressions. 

Adhesion — (a) When two compact materials, be they solid or liquid, are in intimate contact, attractive forces may act between their surface atoms or molecules. These forces are typically - van der Waals forces and electrostatic forces. The work of adhesion W (b)b(a) between the two phases (denoted A and B) is WAB = yA+yB -yAB> where yA and yg are the - interfacial tensions of A and B when each is interfaced only with the vapor phase, and yAB is the interfacial tension of the interface between A and B. In a more rigorous treatment (at thermodynamic equilibrium) each phase is regarded as saturated with the other phase [i]. In the case of liquid phases the equation for the work of adhesion is referred to as the -> Dupre equation. Adhesion forces between particles, or between particles and surfaces, dominate gravity for small particle sizes (pm and sub-pm range). In electrochemistry, increasing attention is being given to various phenomena related to the adhesion of vesicles [ii], particles [iii], droplets [iv], cells [v], etc. to electrode surfaces. 

Athanase Dupr was the first to propose representing by such a formula the relation which exists between the tension of saturated vapor of water or of any other liquid and the tempera ture. 

These relationships lead to the simple consequence that the variability of element concentrations in large data sets of basalt analyses are related to the bulk partition coefficients of these elements (Hofmann, 1988 Dupre et al., 1994). This can be verified by considering a set of trace... 

D. B. DuPre and J. P. McTague. Pair polarizability of hydrogen atoms. Relation to collision induced light scattering and dielectric phenomena in rare gases. J. Chem. Phys., 50 2024-2028 (1969). 

A relation between the interfacial tension between two immiscible liquids I and II and the surface tensions of the separate liquids was given by Dupre.2... 

A. Dupre (1869) represented the relation between the vapour pressures, p, of a substance and the absolute temperature T by the equation... 

It seems essential that the energies of adhesion of the systems involved, the possibility of a contraction of the liquid film in negative systems and the contact angle (Fig. 27) are not taken into account in these relations. This may account for the great differences between calculated and experimental data. Combining the equations after Dupre and after Young yields the following simple relation for the work of adhesion ... 

Another approach avoids specifying the field of inter molecular force between solid and liquid and instead resorts to thermodynamics. The first application of thermodynamics to capillarity appears to have been made by Thompson [101,102] later came the classic and general treatment by J. Willard Gibbs [50]. Nearly 60 years had elapsed after Young s treatment before Dupre [31] introduced the reversible work of adhesion of liquid and solid, and its relation to ygv sl ... 

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