Mean drop volume

To facilitate the application of mydriatics in neonates and infants, a single-instillation solution may be prepared by combining 3.75 ml cyclopentolate 2% with 7.5 ml tropicamide 1% and 3.75 ml phenylephrine 10%.The final solution contains 0.5% cyclopentolate, 0.5% tropicamide, and 2.5% phenylephrine.This combination produces no major side effects and provides an effective pupillary dilation. Alternatively, equal amounts of 1% tropicamide and 2.5% phenylephrine may be mixed together to yield a single combination solution with final concentrations of 0.5% tropicamide and 1.25% phenylephrine. This too should produce adequate pupillary dilation with no major side effects. Again, these solutions can also be applied as a spray. Cyclopentolate, tropicamide, and phenylephrine administered in microdrops (mean drop volume, 5.6 micro liters, as opposed to commercially available standard drops) have the same efficacy with a decreased risk for systemic side effects. 

Where n and n are number of singlets present initially and at time t, D is the diffusion coefficient and R = 2a, a being particle radius. 0 is the phase volume ratio (0 = 0.04 in our system). If Vm is mean drop volume of n drops after time t, we have -... 

Where Vra is mean drop volume of initial drops, hence,... 

Drop dispersions are hardly ever uniform, and size distribution must be allowed for in calculating a. This can be done by means of the Sauter mean drop diameter, based on the average volume-to-area ratio for N drops. 

Humphrey and Seal9 (U.S.A.) reported in 1959 detailed experiments on the ECT of sarcoma-180 tumors in nearly 500 mice. In a typical experiment, 18 test animals and 18 control animals were used the ECT was done with 3 ma current, at 6 V for 3 hours a day, for 24 days. They observed that after such a lengthy treatment, the mean volume of test tumors was about 15% of the mean tumor volume of the control group seven mice showed complete tumor regression as a result of ECT. Total regression means that the tumor has decreased progressively in volume, hardened, dropped off, leaving a new skin surface at the former tumor site. 

The mean drop diameter should be fixed in the range of the transition region of circulating to oscillating drop, since this gives the most favorable compromise between the possible transfer area per unit volume of the column and mass transfer intensity. 

In liquid-liquid reacting systems, one of the important parameters is the surface area per unit volume, a, in the dispersion, which can be related to the Sauter mean drop diameter dn- In some processes, the drop size distribution and especially the minimum drop size or the maximum stable drop diameter are also important factors in analysing the process results. 

Because the inequalities among the various mean diameters are usually strengthened when the drop sizes are widely dispersed, the ratio of some higher-order moment to a lower-order moment is often useful as a measure of the dispersion of the drop sizes. For example, the coefficient of variation for the surface-weighted size distribution is a function of the ratio of the weight-weighted mean drop size to the volume-surface mean drop size. The variance of the drop-size distribution may also be expressed in terms of the moments of the unweighted size distribution. 

Industrial liquid-liquid extraction most often involves processing two immiscible or partially miscible liquids in the form of a dispersion of droplets of one liquid (the dispersed phase) suspended in the other liquid (the continuous phase). The dispersion will exhibit a distribution of drop diameters d, often characterized by the volume to surface area average diameter or Sauter mean drop diameter. The term emulsion generally refers to a liquid-liquid dispersion with a dispersed-phase mean drop diameter on the order of 1 pm or less. 

The two liquid phases are in equilibrium if no further changes in concentration occur and thus a theoretical stage is established. The interfacial area per unit volume depends directly on the fractional hold-up and is inversely proportional to the mean drop size of the dispersed phase. The former is influenced by the internals of the extractor, the latter by the physical properties of the two phases, such as interfacial tension and the degree of agitation. A large density difference and high interfacial... 

The Sauter mean drop diameter, d M or (32, defined by Equation (9.45), is most commonly used to characterize drop size because it relates to the volume fraction of the dispersed phase, O, and the interfacial area, a. The Sauter mean drop diameter is also known as the volume-to-surface average drop diameter. The interfacial area, a, in Equation (9.45) is also used to deal with mass transfer, such as ki a. Other commonly used terms are d o, dgo, and d They represent the midsize, the 90th percentile, and the largest size in the drop size distribution, respectively, on a volume basis. The... 

In this example, solvent extraction is to be used to recover a product from a fermentation process. Processing information includes broth viscosity j, = 0.3 Pa s (300 cP), interfacial tension o = 0.003 N/m (3.0 dynes/cm), bulk density Pc = 1000 kg/m (1.0 g/cm ), vessel volume = 3.54 m (750 gal), vessel diameter = 1.524 m (5.0 ft), and DIT = 0.4. Laboratory smdies showed that acceptable extraction efficiency was obtained with mean drop sizes of 50 pm. Determine the power and speed required to produce 50-pm drops in the 750-gal extractor. 

Since the interfacial area per unit volume, a, is related to the Sauler mean drop diameter as a = 60/ dji, the coulinuous-phase capacity coefficient for a six-flai-blade turbine, centrally mounted and with radial befiling, is... 

The coefficients a and P are functions of the capillary constant a. When averaging over the interval 0.19 cm < a < 0.39 cm the following mean values a = 0.08 s and p = 0.041 s cm are obtained. The correction of measured drop volumes can be made using the following relation,... 

A different type of experiments was performed by Van Hunsel Joos (1987b). They studied the steady state of adsorption of various alkanols at the alkane/water interface by means of the drop volume method (Fig. 5.35). The steady states differ remarkably from the equilibrium state. A description of the adsorption process has therefore to allow for a transfer of hexanol molecules across the hexane/water interface. The difference of the two studied steady states is... 

Figure 30. Foam lifetime as a function of the Sauter mean drop diameter for two initial emulsified decane volume fractions (33 and 9.1 vol%) for foams from 4 wt% sodium dodecylbenzenesulfonate (Siponate DS-10). (Reproduced with permission from reference 82. Copyright 1992 Academic.)...

For the pressure drop calculations, first we need to determine the fluid densities at the exchanger inlet and outlet (p/ and p ) for each fluid. The mean specific volume on each fluid side is then computed from Eq. 17.66. 

This formula is consistent with the fact that in stable equilibrium the energy of the surface must be a minimum for a given value of bubble or drop volume, and a sphere has the least surface area for a given volume. For general curved surfaces the radius a in Eq. (10.1.6) is frequently taken to be the mean radius of curvature defined as half the sum of the inverse principal radii of curvature. For immiscible liquids a refers to the interfacial tension, which, for example, for benzene over water at 20°C is 35mNm. Obviously for a plane interface, where the mean radius tends to infinity, the pressure difference will be zero. 

In the drop volume technique the volume of a drop formed at the tip of a given capillary has to be determined accurately which is typically realised by means of a precise dosing system. In Fig. 4.13 the principle of the drop volume apparatus TVT2 from Lauda is shown as an example. 

---