Concentration difference

McBain reports the following microtome data for a phenol solution. A solution of 5 g of phenol in 1000 g of water was skimmed the area skimmed was 310 cm and a 3.2-g sample was obtained. An interferometer measurement showed a difference of 1.2 divisions between the bulk and the scooped-up solution, where one division corresponded to 2.1 X 10 g phenol per gram of water concentration difference. Also, for 0.05, 0.127, and 0.268M solutions of phenol at 20°C, the respective surface tensions were 67.7, 60.1, and 51.6 dyn/cm. Calculate the surface excess Fj from (a) the microtome data, (b) for the same concentration but using the surface tension data, and (c) for a horizontally oriented monolayer of phenol (making a reasonable assumption as to its cross-sectional area). 

This subject has a long history and important early papers include those by Deijaguin and Landau [29] (see Ref. 30) and Langmuir [31]. As noted by Langmuir in 1938, the total force acting on the planes can be regarded as the sum of a contribution from osmotic pressure, since the ion concentrations differ from those in the bulk, and a force due to the electric field. The total force must be constant across the gap and since the field, d /jdx is zero at the midpoint, the total force is given the net osmotic pressure at this point. If the solution is dilute, then... 

Analytic teclmiques often use a time-dependent generalization of Landau-Ginzburg ffee-energy fiinctionals. The different universal dynamic behaviours have been classified by Hohenberg and Halperin [94]. In the simple example of a binary fluid (model B) the concentration difference can be used as an order parameter m.. A gradient in the local chemical potential p(r) = 8F/ m(r) gives rise to a current j... 

The most often used subphase is water. Mercury and otlier liquids [12], such as glycerol, have also occasionally been used [13,14]. The water has to be of ultrapure quality. The pH value of tire subphase has to be adjusted and must be controlled, as well as tire ion concentration. Different amphiphiles are differently sensitive to tliese parameters. In general it takes some time until tire whole system is in equilibrium and tire final values of pressure and otlier variables are reached. Organic contaminants cannot always be removed completely. Such contaminants, as well as ions, can have a hannful influence on tire film preparation. In general, all chemicals and materials used in tire film preparation have to be extremely pure and clean. 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

In the case of a less soluble gas such as oxygen, diffusion occurs so slowly through the Hquid film that only a small concentration difference is required to overcome the resistance of the gas film. Thus the Hquid film at the interface is considered to be very close to oxygen saturation and it is not necessary to consider gas film resistance in the calculation (14). 

Circulation of fluid is promoted by surface tension gradients but inhibited by viscosity, which slows the flow, and by molecular diffusion, which tends to even out the concentration differences. The onset of instabibty is described by a critical Marangoni number (Mo), an analogue of the Rayleigh... 

The salt flux, across a reverse osmosis membrane can be described by equation 5 where is a constant and and < 2 the salt concentration differences across the membrane. 

For the solute flux, it is assumed that chemical potential difference owing to pressure is negligible. Thus the driving force is almost entirely a result of concentration differences. The solute flux, J), is defined as in equation 6 ... 

The deposition of ions at the cathode creates a depletion layer across which the ions must migrate in order to deposit. This layer can vary in thickness according to surface morphology. The depletion layer is more or less defined as the region where the ion concentration differs from that of the bulk solution by >1%. The layer thickness can be decreased by agitation. 

The separative capacity of the equivalent theoretical stage in the continuous process is seen to depend on the concentration difference between the countercurrent streams as well as on the concentration difference between the top and bottom of the stage. The separative capacity is zero when V is equal tojy or V is equal to x inspection shows that it attains a maximum value when V is equal to the arithmetic average of x andjy and that this maximum value... 

The number of stages requited to span a given concentration difference in an ideal plant in which all stages have the same separation factor is therefore... 

Back-diffusion is the transport of co-ions, and an equivalent number of counterions, under the influence of the concentration gradients developed between enriched and depleted compartments during ED. Such back-diffusion counteracts the electrical transport of ions and hence causes a decrease in process efficiency. Back-diffusion depends on the concentration difference across the membrane and the selectivity of the membrane the greater the concentration difference and the lower the selectivity, the greater the back-diffusion. Designers of ED apparatus, therefore, try to minimize concentration differences across membranes and utilize highly selective membranes. Back-diffusion between sodium chloride solutions of zero and one normal is generally [Pg.173]

If it is desired to calculate the rate of transfer from the overall concentration difference based on bulk-hquid compositions (x° — x), the appropriate overall coefficient Kl is related to the individual coefficients by the equation... 

Experimentally observed rates of mass transfer often are expressed in terms of overall transfer coefficients even when the eqmlibrium lines are curved. This procedure is empirical, since the theory indicates that in such cases the rates of transfer may not vary in direct proportion to the overall bulk concentration differences y — y°) and (x° — x) at all concentration levels even though the rates may be proportional to the concentration difference in each phase taken separately, i.e., Xi — x) and y — y ). 

T] Low MT rates. Dilute systems, Ap/p 1. Nq,.Nsc < 10 - Use with arithmetic concentration difference, x = length from plate bottom. 

T] Constant-property liquid film with low mass-transfer rates. Use arithmetic concentration difference. 

S] Low mass-flux with constant property system. Use with arithmetic concentration difference. 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

Mass-transfer coefficients are derived from models. They must be employed in a similar model. For example, if an arithmetic concentration difference was used to determine k, that k should only be used in a mass-transfer expression with an arithmetic concentration difference. 

A. Laminar, vertical wetted wall column Ws/, 3.41 — D 5fa (first term of infinite series) [T] Low rates M.T Use with log mean concentration difference. Parabolic velocity distribution in films. 

T] h = distance between plates. Use log mean concentration difference. 

---