Inclined plate method

The basic setup to determine static interfacial tension based on either the Wilhelmy plate method or the du Noiiy ring method (see Alternate Protocol 2) is shown in Figure D3.6.1. It consists of a force (or pressure) transducer mounted in the top of the tensiometer. A small platinum (Wilhelmy) plate or (du Noiiy) ring can be hooked into the force transducer. The sample container, which in most cases is a simple glass beaker, is located on a pedestal beneath the plate/ring setup. The height of the pedestal can be manually or automatically increased or decreased so that the location of the interface of the fluid sample relative to the ring or plate can be adjusted. The tensiometer should preferably rest on vibration dampers so that external vibrations do not affect the sensitive force transducer. The force transducer and motor are connected to an input/output control box that can be used to transmit the recorded interfacial tension data to an external input device such as a monitor, printer, or computer. The steps outlined below describe measurement at a liquid/gas interface. For a liquid/liquid interface, see the modifications outlined in Alternate Protocol 1. Other variations of the standard Wilhelmy plate method exist (e.g., the inclined plate method), which can also be used to determine static interfacial tension values (see Table D3.6.1). 

Various experimental methods for dynamic surface tension measurements are available. Their operational timescales cover different time intervals. - Methods with a shorter characteristic operational time are the oscillating jet method, the oscillating bubble method, the fast-formed drop technique,the surface wave techniques, and the maximum bubble pressure method. Methods of longer characteristic operational time are the inclined plate method, the drop-weight/volume techniques, the funnel and overflowing cylinder methods, and the axisym-metric drop shape analysis (ADSA) " see References 54, 55, and 85 for a more detailed review. 

Figure 9.2 Determination of contact angle from the sliding drop on an inclined plate method. The advancing contact angle, 9 , is the measured angle at the downhill edge of the drop, the receding contact angle, 0r is measured at the uphill edge, and 0, is the tilt angle.

Fig. 5.28 Dynamic surface tension of two TRITON X-100 solutions measured using the maximum bubble pressure (n- ) and inclined plate ( ) methods Cq= 0.2 ( ) 0.5 ( ) g/1 according to Fainerman et al. (1994a)...

A comparison of the bubble pressure with the inclined plate method, performed with aqueous solutions of Triton X-100 (octylphenol polyglycol ether, C 4H2iO(C2H40) oH from Serva), is displayed in Fig. 5.28. The time interval of the inclined plate from 50 ms to 1000 ms is... 

It has been already indicated (Fig. 7) that micelles can lead to an essential acceleration of the adsorption process. Therefore, special experimental techniques are necessary for its investigation, allowing measurements of the dynamic surface tension in a time interval of milliseconds. The maximum bubble pressure method [78, 81, 83, 89,90,93] and the oscillating jet method [77, 82, 86, 87, 88, 90, 92, 93, 156] are most frequently used for these purposes. The inclined plate method [83, 89, 90, 93], the method of constant surface dilation [85] and the drop volume method [84] have been used also for slow adsorbing surfactants. 

A method based on the comparison of experimental and calculated kinetic dependencies of the dynamic surface tension can be more precise in comparison with the use of Eq. (5.253) [77, 85, 89, 92, 93]. Mitrancheva et al. presented the most detailed data and compared calculated dynamic surface tension with results obtained for solutions of TRITON X-100 using three different experimental methods the inclined plate, the oscillating jet and the maximum bubble pressure methods [93]. The inclined plate method yielded values of i2 different from the results of the two other techniques. This discrepancy is probably connected with the differences in the attainable surface age. Thus the inclined plate method can be used only at relatively high surface life times when the surface tension tends asymptotically to equilibrium, and when the accuracy of determination of i2 decreases. In addition the insufficiently investigated peculiarities of the liquid flow along the inclined plane can be another source of experimental errors [93]. 

Fig. 1.6 Inclined plate method for the determination of advancing and receding Contact angles, and 9 ...

The wettability of a flat plate was quantitatively evaluated in terms of O. This angle and the receding contact angle Or were determined by the inclined plate method, as shown in Fig. 4.43. A water droplet of known volume was placed on a flat plate, and the plate was gradually inclined. The shape of the bubble was observed with... 

However, the experimental studies relate to spatial growth of disturbances as the flow system is always excited by fixed frequency sources. Hence a spatial theory is preferred to study the stability of non-isothermal flows. Despite the distinction between temporal and spatial methods, the neutral curve, however, is identical. Iyer Kelly (1974) reported results using linear spatial theory under parallel flow approximation for free-convection flow past heated, inclined plates. Tumin (2003) also reports the spatial stability of natural convection flow on inclined plates providing the eigen spectrum. 

Inclined-Plate Clarifiers Lamella or inclined-plate separators have achieved increased use for clarification. They contain a multiplicity of plates inchned at 45 to 60° from the horizontal. Various feed methods are employed so that the influent passes into each inclined channel. The geometry of the plates results in the solids having to settle only a short distance in each channel before sliding down the base to the collection zone beneath the plates. The clarified liquid passes in the opposite direction beneath the ceiling of each channel to the overflow connection. 

In coating processes the problem of controlling the flow of liquids down an inclined plate is a key question (Scriven 1960, Kretzschmar 1974). Therefore, the hydrodynamic flow of such films in combination with surface rheological and adsorption kinetics models were described. As the principle of a flowing film can be used also as a separate method to study adsorption processes in the range of milliseconds, the theory is presented here, while the experimental details are given in the next chapter. 

The maximum bubble pressure method, realised as the set-up discussed above, allows measurements in a time interval from 1 ms up to several seconds and longer. At present, it is the only commercial apparatus which produces adsorption data in the millisecond and even sub-millisecond range (Fainerman Miller 1994b, cf. Appendix G). Otherwise data in this time interval can be obtained only from laboratory set-ups of the oscillating jet, inclined plate or other, even more sophisticated, methods. The accuracy of surface tension measurements in... 

Another method applicable over longer times, from 50 ms up to seconds, is the so-called inclined plate (IP) method developed by Van den Bogaert Joos (1979). A surfactant solution is allowed to flow over an inclined plate with an angle of inclination a. The solution is pumped over the plate and the flow rate is measured by the rotameter. The surface tension of the solution surface, freshly formed at the inlet, is measured by using a Wilhelmy plate oriented with its length parallel to the flow direction. The schematic of the set-up is shown in Fig. 5.22. 

The inelined plate technique is applicable to liquid/gas interfaces only. Temperature eontrol seems to be very complicated. As the time is also limited to a small interval of 25 ms up to a few seconds, the application of this method is restricted only to some special cases. However, the eomparison of experimental results of the inclined plate technique with those obtained by other methods exhibits good agreement (Van Hunsel Joos 1987a, Fainerman et al. 1993a, Miller et al. 1994b, d). 

The following so-called dynamic capillary method was developed by Van Hunsel Joos (1987b) and complements the area of application with respect to other methods. This method allows measurements from 50 ms up about 1 s, similar to the inclined plate and growing drop techniques described above, and can be used at liquid/liquid and liquid/gas interfaces without modification. The principle of the experiment is schematically given in Fig. 5.23. Two fluids are contained in a tube of diameter R. The interface (or surface in case of studies at the water/air interface) is located in such a way that its interfacial tension can be measured by the capillary rise of the lower liquid in a narrow capillary c, which connects the both fluids. The height of the capillary rise h is determined via a cathetometer Cat. 

In a recent paper Miller et al. (1994d) discussed parallel experiments with a maximum bubble pressure apparatus and a drop volume method (MPTl and TVTl from LAUDA, respectively), and oscillating jet and inclined plate instruments, performed with the same surfactant solutions. As shown in Fig. 5.27, these methods have different time windows. While the drop volume and bubble pressure methods show only a small overlap, the time windows of the inclined plate and oscillating jet methods are localised completely within that of the bubble pressure instrument. 

A comparison of the bubble pressure method with the oscillating jet method was also performed with aqueous Triton X-100 solutions. Some results are given in Fig. 5.29 as a y/log X3 - plot. In contrast to the inclined plate, the oscillating jet only yields data in the time interval of few milliseconds. Also in this time interval the agreement with the maximiun bubble pressure method is excellent and shows deviations only within the limits of the accuracy of the two methods. 

Dynamic surface tensions of an aqueous l.5510" mol/cm Triton X-100 solution measured with the dynamic capillary (0), inclined plate (A,A), drop volume ( ), strip ( ) and Wilhelmy plate ( ) methods according to Rillaerts Joos (I9S2)... 

The exact form of functional relationship between the resistance force and the contact angle hysteresis depends, of course, on the parameters chosen. Rosano has presented an equation based on the plate method [14] and very recently Furmidge[10] has shown the essential relationship between Rosano s equation and the widely used equation for a droplet moving on an inclined plane. Since the total resistance force that must be overcome before the boimdary line will move is directly proportional to the length of the line, we can tentatively define a force just necessary to start a unit length of boundary line moving as the critical line force. 

Fig. 5.14. Dependence ot T2 on the relative amount ot Triton X-100 aggregated in micelles obtained by different methods of the dynamic surface tension oscillating jet [93] ( ), maximum bubble pressure [93] (A), [89] ( ), [90] (T), inclined plate [83] ( ) open symbols refer to results of relaxation methods for the bulk phase [166, 167] according to [93].

Four methods of interpreting the echo pulse have been tested for their ability to locate an inclined plate target. The first two, taking the peak... 

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