Drop dimensions method

The contact angle may be calculated indirectly from measurement of the dimensions of a sessile drop. In order to carry out such a calculation, the drop should be small enough so 

If h and rb are measured, 0 can be calculated from Equation (651). For large drops, h and rb can be so distorted by gravitation that Equation (651) cannot be used, and much more elaborate calculations are needed. On the other hand, the contact angle may be calculated if the drop volume can be experimentally measured by using advanced syringes. If the contact radius of the liquid drop, rb of known volume, V is measured, then 6 can be calculated from the dimensionless ratio obtained from three-dimensional spherical trigonometry 

Equations (651)—(653) imply that the base of the drop is an exact circle, but it is rarely circular due to the non-uniformity of most of the solid surfaces. This is the main source of error in this method. 

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Figure 9.3 Determination of contact angle from the drop dimensions method h is the height of the drop [/ = R (1 - cos0)], rb is the contact radius of the liquid drop (rb = Rsin (9) and R is the radius of the circle of the spherical segment.

Drop-weight method. Here, the liquid is allowed to flow out from the bottom of a capillary tube. Drops are formed which detach when they reach a critical dimension. The weight of a drop falling out of a capillary is measured. To get a precise measure, this is done for a number of drops and the total weight is divided by this number. 

Most interfacial tension measurements have been made by the pendant drop technique. A drop of a polymer melt is formed in another polymer melt. The shape is recorded photographically and the interfacial tension found from drop dimensions, i,e. maximum width and width at a height equal to the maximum width, using tabulated ratios found from numerical solutions of the equations of Bashforth and Adams. The interfacial tension can also be found by a full analysis of the shape of the drop. The method is preferred over alternatives since equilibration is not a serious problem but accurate density measurements are required. Tabulated values of interfacial tensions are available in the literature and range from about ImNm" for polymers similar in polarity such as polyethylene/polypropylene to llmNm" for dissimilar polymers such as polyethylene poly-(methyl methacrylate). 

The drop weight method measures the weight of a drop (or several drops) emerging from a capillary of known dimensions [318,336,344-347]. Slight vacuum is applied to the apparatus through a tubing until the drop, forming at the outlet of the capillary, assumes almost its full size. The drop is then allowed to detach itself from the capillary. Surface tension is calculated from the equation... 

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

Common to all air cooled heat exchangers is the tube, through which the process fluid flows. To compensate for the poor heat transfer properties of air, which flows across the outside of the tube, and to reduce the overall dimensions of the heat exchanger, external fins are added to the outside of the tube. A wide variety of finned tube types are available for use in air cooled exchangers. These vary in geometry, materials, and methods of construction, which affect both air side thermal performance and air side pressure drop. In addition, particular... 

There have been very few method development processes proposed for 2DLC. One study (Schoenmakers et al., 2006) is titled A protocol for designing comprehensive two-dimensional liquid chromatography separation systems. This study advocates that one initially chooses the first-dimension maximum acceptable analysis time, the first-dimension maximum workable pressure drop, and the smallest first-dimension column diameter. The first two variables are then used to construct a Poppe plot (Poppe, 1997)—pronounced Pop-puh (Eksteen, 2007). 

According to Eq. (27), Stromme et al.125,126 developed systematically the peak-current method to determine the fractal dimension of the electrode surface by using cyclic voltammetry. It must be recalled that this method is valid when the recorded current is limited by diffusion of the electroactive species to and away from the electrode surface. Since the distribution of the reaction sites provides extensive information about the surface geometry, the fractal dimension of the reaction site distribution may agree with the fractal dimension of the electrode surface which is completely electrochemical-active. In addition, it is well known that this method is insensitive to the IR drop in the electrolyte.126... 

The other method is the velocity head method. The term V2/2g has dimensions of length and is commonly called a velocity head. Application of the Bernoulli equation to the problem of frictionless discharge at velocity V through a nozzle at the bottom of a column of liquid of height H shows that H = V2/2g. Thus II is the liquid head corresponding to the velocity V. Use of the velocity head to scale pressure drops has wide application in fluid mechanics. Examination of the Navier-Stokes equations suggests that when the inertial terms dominate the viscous terms, pressure gradients are expected to be proportional to pV2 where V is a characteristic velocity of the flow. 

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