Maximum pressure method

The maximum pressure method establishes the maximum value of pressure required to squeeze a bubble (or a drop of another liquid) through the liquid phase [6,25]. When the outside pressure gradient, Ap, is applied across a calibrated capillary immersed into liquid, a gas bubble (or drop of liquid) starts to grow at the capillary tip (Fig. I-18). As the bubble grows, its curvature radius, r, decreases and finally reaches a minimum value equal to the radius of the capillary, r0. At this point the bubble surface acquires hemispherical... 

Fig. 1-18. Change of the curvature radius of the bubble surface that occurs during the determination of surface tension by the maximum pressure method...

The maximum bubble pressure method is good to a few tenths percent accuracy, does not depend on contact angle (except insofar as to whether the inner or outer radius of the tube is to be used), and requires only an approximate knowledge of the density of the liquid (if twin tubes are used), and the measurements can be made rapidly. The method is also amenable to remote operation and can be used to measure surface tensions of not easily accessible liquids such as molten metals [29]. 

Correction Factors for the Maximum Bubble Pressure Method (Minimum Values of Xjr for Values of r/a from 0 to 1.50)... 

A method for calculating the dimensions of the cavities and narrow necks from the intrusion-extrusion curves has been proposed by Reverberi." " The method is essentially as follows the ascending curve (penetration) branch is measured in the usual way, but the descending curve is mapped out from a series of steps each step commences at the same maximum pressure, proceeds to a pre-determined minimum pressure which is different for... 

Typical methods are those of F. C. Zevnik and R. L. Buchanan [Chem. Eng. Progi , 59, 70-77 (Feb. 1963)] and J. H. Taylor Eng. 6-Proc. Econ., 2, 259-267, 1977). The former is mainly a graphical method of estimating the cost per functional unit (Cp) based on the capacity, the maximum pressure, the maximum temperature, and the materials of construction. The Taylor method requires the determination of the costliness index, which is dependent on the complexity of the process. A simpler method was suggested by S. R. Timms (M.Phil. thesis, Aston University, England, 1980) to give the battery hmits cost for gas phase processes only in U.S. dollars with a Marshall and Swift index of 1000. The simple equation is... 

A number of experimental studies have supplied numerical values for these, using either the classical maximum bubble pressure method, in which tire maximum pressure requhed to form a bubble which just detaches from a cylinder of radius r, immersed in tire liquid to a depth jc, is given by... 

Maximum Pressure and Rate of Pressure Rise and KJ These explosibility parameters are used in assessing whether equipment will contain the maximum pressure developed during deflagration, or to design deflagration relief vents and other explosion prevention systems (see NEPA 68 and 69). The test method is given in ASTM E 1226. 

If the driller s method is used, this maximum pressure Pj can be obtained from... 

Konstantinov et al. [320, 321] investigated the surface tension and density of molten systems K2TaF7 - KC1 and K2TaF7 - KF as well as some molten mixtures containing K2TaF7, KC1, KF and Ta2Os, using the method of maximum pressure in gas bubble. 

There is a method that can be used for this analysis. It is extremely complex so it requires using a computer. In general, equations are generated to determine the moment and thrust created in the invert area of the deflected pipe, where a pressure term is superimposed. This analysis must examine the strains in the outer and innermost fibers of the pipe to verify that its wall structure is adequate and not overstrained. During this analysis the pipe must be examined under conditions of no pressure, minimum pressure, and maximum pressure. 

Hsu and Berger [43] used the maximum bubble pressure method (MBP) to study the dynamic surface tension and surface dilational viscosity of various surfactants including AOS and have correlated their findings to time-related applications such as penetration and wetting. A recent discussion of the MBP method is given by Henderson et al. [44 and references cited therein]. 

In the MBP method, an inert gas passes through a precision bore capillary of radius r which then creates a gas bubble at the tip. The pressure within the bubble is measured and the maximum pressure P(m) in g/cm2 is related to the surface tension y in dyne/cm by means of... 

The importance of the first three of these factors has already been discussed. The temperature factor would include the cost of insulation plus the increase in metal thickness necessary to counteract the poorer structural properties of metals at high temperatures. Zevnik and Buchanan17 have developed curves to obtain the average cost of a unit operation for a given fluid process. They base their method on the production capacity and the calculation of a complexify factor. The complexity factor is based on the maximum temperature (or minimum temperature if the process is a cryogenic one), the maximum pressure (or minimum pressure for vacuum systems) and the material of construction. It is calculated from Equation 2 ... 

Khadilkar and Rebeiro have investigated a new method [107] that overcomes all these problems and is far safer. The authors used closed pressure reactor [108], with no apparent loss of yield. The microwave reactor used for these reactions has a possibility for recording temperature and pressure during irradiation. For example, 1-bu-tyl-3-methylimidazolium chloride was isolated in 91% yield in 24 min [109] at 150 °C and 57 psig was the maximum pressure reached. 

Fig. 4.8 Schematic illustration of the working principle of the dynamic bubble pressure method. If the bubble radius equals the capillary radius, maximum pressure is detected. The pressure minimum occurs on bubble detachment.

Relation 9.77 is usually called the Washburn equation [55,237], One should consider it as a special case of the fundamental Young-Laplace equation [3,9-11], Washburn was the first to propose the use of mercury for measurements of porosity. Now, it is a common method [3,8,53-55] of psd measurements for a range of sizes from several hundreds of microns to 3 to 6 nm. The lower limit is determined by the maximum pressure, which is applied in a mercury porosimeter the limiting size of rWl = 3 nm is achieved under PHg = 4000 bar. The measurements are carried out after vacuum treatment of a sample and filling the gaps between pieces of solid with mercury. Further, the hydraulic system of a device performs the gradual increase of PHg, and the appropriate intmsion of mercury in pores of the decreasing size occurs. 

Leung s method (as given in equation (6.5) below) is applicable if all the above assumptions are true. Assumption (d) above, regarding the use of an average rate of heat release, tends to be the most limiting in terms of the maximum difference that can be allowed between the relief pressure and the maximum pressure. The absolute overpressure (often referred to simply as the "overpressure") has been sometimes used to characterise this. This is given by ... 

The required relief flow area, A, can be calculated using equation (5.1). The two-phase mass flow capacity per unit cross-sectional area, G, can be calculated using a suitable method for hybrid-systems (see Chapter 9). In order to minimise the relief size obtained, G.should befevaluated at the maximum pressure permitted in the reactor during relief, irrespective of the relief pressure. ... 

This method14 is for vapour pressure systems. It solves the material and energy balance equations, on which Leung s method (see 6.3) is based, in a step-wise manner. The method shares most of the conditions of applicability of Leung s method (see 6.3.1) but does not require values of parameters to be constant over the pressure range from the relief pressure to the maximum pressure. Indeed, systems in which there is a discontinuity in rate of reaction or physical properties can be handled by this method, provided that the step boundaries are chosen such that any discontinuity coincides with a boundary (see, for example, Figure A5.1).. 

There are numerous other methods for measuring surface tension that we do not discuss here. These include (a) the measurement of the maximum pressure beyond which an inert gas bubble formed at the tip of a capillary immersed in a liquid breaks away from the tip (the so-called maximum bubble-pressure method) (b) the so-called drop-weight method, in which drops of a liquid (in a gas or in another liquid) formed at the tip of a capillary are collected and weighed and (c) the ring method, in which the force required to detach a ring or a loop of wire is measured. In all these cases, the measured quantities can be related to the surface tension of the liquid through simple equations. The basic concepts involved in these methods do not differ significantly from what we cover in this chapter. The experimental details may be obtained from Adamson (1990). 

For examination of an expl a charge(usually 50 to 300 g) is placed inside the bomb, and, after closing the lid, the air ib evacuated by means of a vacuum pump. Then foe chge Is fired electrically and the pressure diagram ia obtained. Method of computation of results is given in Ref 2. The result thus obtained ia termed foe "maximum pressure of the explosive in its own volume" ... 

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