Stagnant liquid layer

External transport resistance describes the rate of transport of the reactants from a bulk liquid phase through the stagnant liquid layer around the particles, which has to be overcome to reach the surface. The transport rate is commonly described by the equation... 

Verhallen P.T.H.M., Oomen L.J.P., v.d.Elsen A.J.J.M., Kruger A.J., and Fortuin J.M.H. (1984) The diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water determined from the permeability of a stagnant liquid layer in the quasi-steady state. Chem. Eng. Sci. 39, 1535-1541. 

When a (solid) surface moves in a liquid, or vice versa, there is always a layer of liquid adjacent to the surface that moves with the same velocity as the surface. The distance from the surface over which this stagnant liquid layer extends or, in other words, the location of the boundary between the mobile and the stationary phases, the so-called plane of shear or slip plane, is not exactly known. For smooth surfaces, the plane of shear is within a few liquid (water) molecules from the surface (see Figure 9.4), that is, well within the electrical double layer. The stagnant layer is probably somewhat thicker than the Stern layer, so that the plane of shear is located in the diffuse part of the electrical double layer. It follows that the potential at the plane of shear, that is, the electrokinetic potential or the zeta potential is somewhat lower than the Stern potential /j. Because the largest part of the potential drop in the... 

Zeta-potential (or electrokinetic potential) electric potential at the shear (or slip) plane within an electric double layer (EDL) the zeta-potential can be measured in case of a relative motion between the charged surface (and Stem layer) and the bulk liquid (including the difluse layer)—e.g. by application of an electric field or due to sedimentation the concept of a slip plane assumes a sharp transition between a stagnant liquid layer attached to the smface and a hydrodynamically mobile liquid phase which is located very close to the outer Helmholtz plane (OHP) the zeta-potential is, therefore, equal or lower in magnitude than the diffuse layer potential at the OHP (cf Sect. 3.1.5.1). 

Inside the thermal layer, a much smaller stagnant liquid layer is found. This layer is of constant thickness. Electroactive particles can cross this layer only by diffusion. The layer is independent of external stirring and independent of actual temperature over a broad range of conditions. For aqueous solutions, thickness of this stagnant layer is ca. 8 pm. 

In this accident, the steam was isolated from the reactor containing the unfinished batch and the agitator was switched ofiF. The steam used to heat the reactor was the exhaust from a steam turbine at 190 C but which rose to about 300°C when the plant was shutdown. The reactor walls below the liquid level fell to the same temperature as the liquid, around 160°C. The reactor walls above the liquid level remained hotter because of the high-temperature steam at shutdown (but now isolated). Heat then passed by conduction and radiation from the walls to the top layer of the stagnant liquid, which became hot enough for a runaway reaction to start (see Fig. 9.3). Once started in the upper layer, the reaction then propagated throughout the reactor. If the steam had been cooler, say, 180 C, the runaway could not have occurred. ... 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

Fig. 10-18 A schematic of a stagnant boundary-layer gas exchange model. Cg = gas concentration at the liquid side of the interface Q = gas concentration at the base of the stagnant boundary layer Znim = stagnant boundary layer thickness.

The parameter K is a measure of how fast the molecules diffuse across the stagnant liquid film layer. It is assumed that local equilibrium occurs at the exterior solid particle surface. The average solid phase loading, which is only a function of time, is given by ... 

Two limiting mechanisms for solute retention can be imagined to occur in RPC binding to the stationary phase surface or partitioning into a liquid layer at the surface. In the previous treatment we assumed that retention is caused by eluite interaction with the hydrocarbonaceous surface, i.e., the first type of mechanism prevails. When the eluent is a mixed solvent, however, the less polar solvent component could accumulate near the apolar surface of the stationary phase. In the extreme case, an essentially stagnant layer of the mobile phase rich in the less polar solvent could exist at the surface. As a result eluites could partition between this layer and the bulk mobile phase without interacting directly with the stationary phase proper. 

The example furthermore shows that diffusion from the bulk fluid phase toward the volume near the IRE, which is probed by the evanescent field, has to be accounted for because it may be the limiting step when fast processes are investigated. The importance of diffusion is more pronounced when a catalyst layer is present on the IRE, because of the diffusion in the porous film is much slower than that in the stagnant liquid film. Indeed, the ATR method, because of the measurement geometry, is ideally suited to characterization of diffusion within films (50,66-68). Figure 16 shows the time dependence of absorption signals associated with cyclohexene (top) and i-butyl hydroperoxide (TBHP, bottom). Solutions (with concentrations of 3mmol/L) of the two molecules in cyclohexane and neat cyclohexane were alternately admitted once to... 

C Stagnant film layer at the liquid - solid catalyst interface. 

Comparison with Table I shows also that the effective depth of the stagnant air layer above the liquid is of the order of 10 mm. in still air and 3 mm. in strong wind, van den Honert (16) quotes figures for outside conditions ranging from 10 to 0.4 mm. in a much stronger wind. 

Every solid catalyst in solution is surrounded by a "stagnant diffusion layer which reactants must cross in order to reach the surface. The resulting concentration profile is sketched in Fig. 6. The rate of the reactant s arrival at the solid/liquid interface is determined by its concentration gradient at that interface, (dc/dx)x=0. The diffusion layer therefore has the same effect on the rate as does the simplified layer shown by the dotted lines [63]. The thickness of this so-called Nernst layer is designated 5. It follows from Fick s first law of diffusion that the number of moles of reactant A, nA, that reach the surface in unit time is given by... 

Matty engineering applications such as heat pipes, cooling ponds, and the familiar perspiration involve condensation, evaporation, and transpiration in the presence of a noncondensable gas, and thus the dijfnsioi of a vapor through a stationary (or stagnant) gas. To understand and analyze such processes, consider a liquid layer of species A in a tank surrounded by a gas of species B, such as a layer of liquid water in a tank open to the atmospheric air (Fig. 14-34), at constant pressure P and temperature T. Equilibrium exists between the liquid and vapor phases at the interface (.v - 0), and thus the vapor pressure at the interface must equal the saturation pressure of species A at the specified temperature. We assume the gas to be insoluble in the liquid, and both the gas and the vapor to behave as ideal gases. 

Equations for diffusion through a layer of stagnant liquid can also be developed. The applicability of these equations is, however, limited because diffusivity in a liquid varies with concentration. In addition, unless the solutions are very dilute, the total molar concentration varies from point to point. These complications do not arise with diffusion in gases. 

Nernst diffusion layer, 5 A thin layer of stagnant liquid at the surface of an electrode caused by friction between the surface and the liquid that flows past the surface. 

Individual adsorbent particles within a packed bed are surrounded by a boundary layer, which is looked upon as a stagnant liquid film of the fluid phase. The thickness of the film depends on the fluid distribution in the bulk phase of the packed bed. 

According to the assumptions in Section 6.2.1, the liquid phase concentration changes only in axial direction and is constant in a cross section. Therefore, mass transfer between liquid and solid phase is not defined by a local concentration gradient around the particles. Instead, a general mass transfer resistance is postulated. A common method describes the (external) mass transfer mmt i as a linear function of the concentration difference between the concentration in the bulk phase and on the adsorbent surface, which are separated by a film of stagnant liquid (boundary layer). This so-called linear driving force model (LDF model) has proven to be sufficient in... 

The clathrate hydrate growth model presented by Englezos and Bishnoi is based on crystallization and mass transfer theories. It describes the growth of the hydrate as a three step process. The first step is the transport of the gas molecule into the liquid phase. The second step is the diffusion of the gas molecule through a stagnant liquid diffusion layer which surrounds the hydrate particle. The last step is the incorporation of the gas... 

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