Adams equation

In Equation (83) R is given by Equation (36). Expression (83) is known as the Bashforth-Adams equation. It is conventional to express this equation in dimensionless form by expressing all distances relative to the radius at the apex b ... 

The Bashforth-Adams equation —the composite of Equations (36) and (84) —is a differential equation that may be solved numerically with /5 and 4> as parameters. Bashforth and Adams solved this equation for a large number of values between 0.125 and 100 by compiling values of x/b and z/b for 0° < 4> < 180°. Their tabular results, calculated by hand before the days of computers, were published in 1883. Other workers subsequently extended these... 

What is the Bashforth-Adams equation How would you use it to determine the surface tension of a liquid and the contact angle of a liquid with a surface ... 

At z=0 AP = 2y/b.) Defining /3=Apgb2/y° and substituting into the Young-Laplace equation yields one form of the Bashforth-Adams equation ... 

Equation (481) is known as the Basforth-Adams equation. Small Bond numbers indicate a high liquid surface tension. The (5 parameter is positive for a meniscus in a capillary tube,... 

If the radius of the capillary is large, so that (r/a) > 0.05, then the Basforth-Adams equation (Equation (481)) or the Lane equations (Equations (482) and (483)) can also be used in the surface tension calculation from the maximum bubble pressure method. This method can also be used to determine the surface tension of molten metals. It has been a popular method in the past, but now it is not very common in surface laboratories because of its poor precision. 

Surface tensions of poljuneric fluids or melts may be measured by a variety of direct techniques, with those based upon analysis of the shape of axisymmetric fluid drop profiles (3,72) the most versatile and popular. Discussions of the relative advantages and disadvantages of each technique are presented in Reference 3. Several drop geometries are possible as shown in Figure 18. The shape of these drops is governed by the Bashforth-Adams equation... 

Interfacial tension was measured using an axisymmetric drop shape analysis (ADSA) method [24]. In this method, interfacial tension is obtained by analyzing the change in the shape of a pendant drop of one liquid suspended in a second liqnid. The method is based on the Bashforth-Adams equation, which relates drop shape geometry to interfacial tension [25,26]. A schematic of a pendant drop with the appropriate dimensions for nse in the Bashforth-Adams equation is illustrated in fig. 13.6. 

Fig. 2.6 Images of sessile water drops (a) 3.4 pL, (b) 8.7 pL, (c) 20.7 pL, and (d) 33.2 pL on a completely nonwetting hydrophobic surface made from TFE powder. The curves are theoretical profiles calculated from the Bashforth and Adams equation (Reproduced with permission from [18], Copyright 2010 The American Chemical Society)...

In 2011, Srinivasan et al. [20] systematically assessed the contact angle measurement of superhydrophobic surfaces using a perturbation solution of the Bashforth-Adams equation. The uncertainty in the calculated contact angle is determined by the uncertainty in the drop height measurement. For example, assuming the resolution limit of the imaging camera is 10 jm, for a 0.7 pL water drop of 153° contact angle calculated from Bashforth-Adams equation, will result in an uncertainty of 3° in the... 

---