Liquid flow velocity

The number of fluorine equivalents (to toluene) was varied the gas and liquid flow velocities were kept constant to maintain the same flow pattern for all experiments. Liquid products were collected in an ice-cooled roimd-bottomed glass flask containing sodium fluoride to trap the hydrogen fluoride. The flask is connected to a cooling condenser to recover the solvent. Samples were typically collected for 1 h. Waste gases were scrubbed in aqueous 15% potassium hydroxide solution. Samples were degassed with nitrogen and filtered before analysis. 

J. Bouillard, B. Alban, P. Jacques, C. Xuereb 2001, (Liquid flow velocity measurements in stirred tanks by ultrasound doppler velocimetry), Chem. Eng. Sci. 56, 747. 

Figure 1. Axial liquid flow velocity profile behind circular obstruction with...

The overall operation is comprised of several phases. In the first phase, the adsorbent material is expanded and equilibrated by applying an upward liquid flow to the column. To allow for sufficient contact time and efficient binding of the target molecule, the expansion should be three times that of the sedimented bed ( expansion ratio ), to a height of approximately 50 cm. A stable bed is formed when the adsorbent particles achieve equilibrium between particle sedimentation velocity and upward liquid flow velocity. In the second phase, the sample is applied to the expanded adsorbent. The crude, unclarified protein solution of intact or disrupted biomass is pumped upward on the column. In a well-defined process, the expanded adsorbent will remain stable and will not change its expansion ratio. However, if the... 

Although percolation reactors have been in use extensively over several decades, it was not until 1983 that the first theoretical model of this type of reactor was introduced [5]. The model was developed for sequential first-order reactions in order to assess the performance in hydrolysis of hemicellulose. As an unsteady reactor, the model involves a partial differential equation with the following parameters kinetic parameter a = k2/kj operational parameter (3 = kiL/u, T = ut/L, where L is the bed length and u is the liquid flow velocity. 

The analysis in Subset II may point to the choice of countercurrent operation through a packed bed. The most commonly used regimes here are trickle flow and bubble flow. The possibility of flooding places an important constraint on the choice of the operating gas and liquid flow velocities. The pressure drop is significant for small catalyst particles this precludes countercurrent operation unless shaped catalyst particles are used. 

The hydrodynamic resistance of dispersion medium in the gap between particles against flowing out is one of the kinetic stability factors. The decrease in thickness of fluid layer between the particles during coagulation is related to viscous flow of liquid out of a narrow gap between the particles. For solid particles the liquid flow velocity is zero at the interface and highest in the center of a gap. The rate with which the gap between two circular plane-parallel plates of radius r (Fig. VII-7) shrinks, dh/dt, is related to the volume of liquid that flows per second across the side surface of cylindrical gap, dV/dt, via the following relationship ... 

The liquid flow velocity u and the velocity of motion of the bubble s boundary are not equal if phase transitions happen at the interface, since they cause the appearance of mass flux ... 

The craze tip growth velocity V can be limited by the liquid flow velocity within the craze. Figure 10.17 shows a craze containing a length L of liquid. The liquid pressure pi at the crack tip is atmospheric, but p2 at the liquid/air interface due to the capillary attraction. If the liquid moves inside the craze with the same velocity V as the advancing craze tip, and the pore area A of the craze cross section is constant, D Arcy s law for the flow of a liquid of viscosity tj through a porous medium... 

Now we consider the electrokinetic behavior of soft particles, i.e., colloidal particles covered with a polymer layer (Figure 2.2). A number of theoretical studies have been made [34-46] on the basis of the model of Debye and Bueche [47], which assumes that the polymer segments are regarded as resistance centers distributed in the polymer layer, exerting frictional forces y on the liquid flowing in the polymer layer, where u the liquid flow velocity and y a frictional coefficient. The Navier-Stokes equation for the liquid flow inside the polymer layer is thus given by... 

Estimate the pressure drop in upward gas-hquid flow in a circular capillary for air-water system as a function of gas flow velocity (range l-30mms ) for different liquid flow velocities of 30, 50, and 75 mm s . The hydraulic of the channel is 2 mm. 

When a suspension is stirred, fine particles may stick to the larger particles [310]. The sticking process can be rated quantitatively by means of the ratio where Kf and A ff are the respective quantities characterizing the sticking of fine particles to coarse particles and the sticking of fine particles to each other. As an example, we may note that a ratio KfjKff = (1.2-2.0) 10 has been found for fine particles with a diameter of 5.5 fxm and coarse particles with a diameter of 30 ixm. The ratio KfjKff was determined experimentally. At the same time, the adhesion of fine particles to a flat surface was studied, with a liquid flow velocity of 30 m/sec. The following results were obtained [310] ... 

Used widi steam or coofing. Liquid flow velocities are low and the flow is poorly distributed. Natural convection equations are suitable and cooling coefficients have low values. Conventional jackets are best applied to small vessels or high pressure applications, where flie vessel internal pressure is twice the jacket pressure as a minimum. The conventional jacket is the most common... 

We attribute these disturbances to the occurrence of slug flow just prior to cool-down. Much research has been done on two-phase flow, and several flow regime plots, similar to Fig. 2 [1, 2] are available in the literature. Since liquid flow velocity in the test system after cool-down was about 7-8 ft/sec, we would expect our system to pass through the slug-flow region just before cool-down. If slug flow is to be avoided, the system must be designed to have a liquid flow rate over 10 ft/sec. 

The flow pattern in a three-phase fluidized bed is usually much closer to complete backmixing than to a plug flow. Because of the higher liquid flow velocities, larger particles can be used than in bubble columns. 

The discrete distribution described by Eq. 7 is characterized by a minimum non zero value of the density of connection - it equals 1. The actual velocity distribution observed in a trickle-bed reactor has a similar characteristic. There exist a minimum liquid velocity u below which the liquid film trickling over a solid surface becomes unstable. The smaller this minimum liquid velocity, the better the ability to spread over the packing surface. This parameter gives a physical meaning to the concept of packing accessibility. Accounting for the proportionality between the liquid flow velocity and the density of connection, Eq. 7 may be transformed in an actual liquid velocity distribution (Eq. 8). is proportional... 

The mass-transfer resistances can be separated into external, in the MBL, and internal, in the matrix itself. The resistance in the MBL is proportional to its thickness, which depends mainly on the flow velocity of the liquid (Jorgensen and Des Marais 1990). The mass transport coefficient, k, and the thickness of the MBL, 6, can be calculated from the liquid flow velocity (u3). For example (Shaw and Hanratty 1977) ... 

Recent crash programs to improve the performance characteristics of guided missiles and high altitude aircraft have in some cases resulted in an increase of cavitation problems in their oxidizer and fuel systems. These problems are a result of attempts to obtain higher liquid flow velocities through these systems and the use of liquids having undesirable vapor pressure characteristics for such applications. 

Exan le 2 Liquid Flow. Next let us consider flow of an organic liquid. Thermowell has a 0.525-inch OD by 0.260-inch ID. The pencil-type thermocouple has a 0.250-inch OD. Let us look first at the effect of different liquid-flow velocities. 

In the above relations, Re is the Reynolds number, mo is the liquid flow velocity at the nozzle outlet, d i is the inner diameter of the nozzle, vl is the kinematic viscosity of liquid, Fr is the Froude number, g is the acceleration due to gravity, is the density of liquid. We is the Weber number, a is the surface tension of liquid, is the velocity ratio defined subsequently, and 2g is the gas flow rate. 

The dependence of the corrosion rate on liquid flow velocity decreases with increasing pH, as demonstrated in Figure 3.10 This is important for practical situations, where dissolved FeCOj can increase the pH significantly. 

Finally, in this section, a note about liquid flow. It was seen in section 4.5 that, when a liquid flows with a mean velocity less than the critical velocity, it does so in layers that, on the macroscopic scale, do not mix. Under these conditions, the behaviour of small elements of the liquid (liquid particles) can be specified in terms of streamlines. Streamlines are lines drawn in the liquid so that the tangent at any point is the direction of motion of the liquid particle at that point. Streamlines should not be confused with pathlines, which denote the actual paths of liquid particles through the bulk liquid. The components of the liquid flow velocity at any point may be functions of time as well as of position, in which case the streamlines vary with time. However, if the velocity components at any point do not vary with time the flow is said to be steady and the streamlines and pathlines coincide. 

As a very simple example of the use of the Navier-Stokes equation under creeping flow conditions, consider the flow of a Newtonian liquid in a parallel-sided, semi-infinite channel in the absence of body forces. Let the boundaries be planes located at y = /z, each lying in an xz plane and let the liquid flow be in the z direction. The motion is assumed to be so slow that a creeping solution is obtained, the liquid is assumed to be incompressible and r is treated as a constant. From the symmetry of the problem the liquid flow velocity is a function of y only, so that the three components of the Navier-Stokes equation are ... 

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