Sessile drops

Fig. 11-16. Shapes of sessile and hanging drops and bubbles (a) hanging drop (b) sessile drop (c) hanging bubble (d) sessile bubble.

The cases of the sessile drop and bubble are symmetrical, as illustrated in Fig. n-16. The profile is also that of a meniscus 0 is now positive and, as an... 

The usual experimental situation is that of a sessile drop and, as with the pendant drop, it is necessary to determine a shape parameter and some absolute length. Thus /3 may be determined by profile fitting, and Ze measured, where Ze is the distance from the plane at = 90 to the apex. If the drop rests with... 

Very small sessile drops have a shape that depends on the line tension along the circular contact line if large enough it induces a dewetting transition detaching the drop from the surface [84]. 

The following values for the surface tension of a 10 Af solution of sodium oleate at 25°C are reported by various authors (a) by the capillary rise method, y - 43 mN/m (b) by the drop weight method, 7 = 50 mN/m and (c) by the sessile drop method, 7 = 40 mN/m. Explain how these discrepancies might arise. Which value should be the most reliable and why ... 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

Fig. X-8. Use of sessile drops or bubbles for contact angle determination.

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Figure C2.11.8. An illustration of the equilibrium contact (i.e. wetting) angle, ( ), fonned by the balance of interfacial energies for or a liquid (sessile) drop on a flat solid surface.

This equation may be derived by eonsidering the small displaeement from equilibrium of a sessile drop on a plane surface. Fig. 3. If a small length, w, of the edge of the drop (assumed straight) advanees by a distance cLv, such that the drop takes up a new eontaet angle 6 — df ), the energy change will be ... 

Fig. 3. Sessile drop with equilibrium contact angle 6 displacement of edge a distance dx (s solid 1 = liquid v = vapour).

As was shown above (Section 2.2, Eq. 5), Young s equation (Eq. 4) may be derived by considering the small displacement from equilibrium of a sessile drop on a plane surface. If the same derivation is applied to the situation where the solid surface has a roughness factor (Eq. 19) of r, it is readily seen that Eq. 5 becomes [28]... 

Fig. 5. Sessile drop on a rough surface true contact angle BTA and apparent contact angle BTH. Thick curve = surface of solid (s) thin curve = surface of liquid (1) v = vapour. T is the triple point HTR a horizontal AT a tangent to the solid surface BT a tangent to the liquid surface.

The most commonly used techniques for contact angle measurements are the sessile drop method and the Wil-helmy plate method. Results obtained from these two methods are in good agreement. 

We can consider the spreading of a sessile drop on a soft, lossy substrate rather like the advance of a negative crack and thus use fracture mechanics concepts, as was the case in the derivation of Eq. (15) for the separation of an elastomer from a rigid solid. The term negative is used since the spreading of a drop leads to the creation of solid/liquid interface rather than separation. 

To investigate the influence of swelhng of the substrate by the contacting liquid, the contact angle 6 of sessile drops of tricresylphosphate, TCP (drop volume 2 p,L, viscosity t = 70 cP, surface tension = 40.9 mN m ), has been measured as a function of time after deposition, t, on flat, smooth, horizontal surfaces of soft and rigid solids at 20°C. The method of measurement of contact angle is the same as in Section Ill.A. 

Analytical Techniques. Sessile drop contact angles were measured with a NRL C.A. Goniometer (Rame -Hart, Inc.) using triply distilled water. The contact angles reported are averages of 2-8 identically treated samples with at least three measurements taken on each sample. ESCA spectra were obtained on a Kratos ES-300 X-ray Photoelectron Spectrometer under the control of a DS-300 Data System. Peak area measurements and band resolutions were performed with a DuPont 310 Curve Resolver. 

FIGURE 18.1 (a) Drop contact angle and (b) a sessile drop showing characteristic dimensions. 

This type of difficulty associated with measurements using chemical ly iI I-defined substrates was also observed during sessile drop measurements carried out on Athabasca bitumen in D20 T311. Values in the range of 15-20 mN/m were obtained for measurements with several drops of bitumen, while interfacial tensions for other pure aqueous and oleic systems were accurate to 0.5 mN/m. 

The sessile drop method has several drawbacks. Several days elapse between each displacement, and total test times exceeding one month are not uncommon. It can be difficult to determine that the interface has actually advanced across the face of the crystal. Displacement frequency and distance are variable and dependent upon the operator. Tests are conducted on pure mineral surfaces, usually quartz, which does not adequately model the heterogeneous rock surfaces in reservoirs. There is a need for a simple technique that gives reproducible data and can be used to characterize various mineral surfaces. The dynamic Wilhelmy plate technique has such a potential. This paper discusses the dynamic Wilhelmy plate apparatus used to study wetting properties of liquid/liquid/solid systems important to the oil industry. 

Far from a wellbore, the velocity of reservoir fluids is about one linear foot per day. Near a wellbore, the velocity can increase one-hundred fold. A static or quasi-static test such as the sessile drop (contact angle) test may not represent the dynamic behavior of the fluids in the field. The dynamic Wilhelmy device gives results which are comparable in interface velocity to the field displacement rate. The interface in the Wilhelmy test described here moved at a steady rate of 0.127 mm/sec or 36 ft/day. The wetting cycle for a hybrid-wetting crude oil system was not affected by moving at a rate less than 1 ft/day. 

The four-to-six day duration of the dynamic Wilhelmy tests (wherein equilibrium actually occurred after one day) were much shorter than the times generally required for the sessile drop test. The conventional contact angle measurements on oil from the fields mentioned above required up to 48 days (12). 

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