Liquid flow

A liquid possesses a definite volume at a given temperature and pressure, but no definite shape it takes up the shape of the containing vessel. This process may be accomplished very rapidly, as in the case of water under normal conditions, or it may take a considerably longer time, as with thick treacle. When a liquid undergoes a continuous deformation under the action of gravity or of an externally applied force, the process is called flow. As a flow process takes time to complete, the liquid must be offering some resistance to flow, which may be called, quite generally, a liquid friction. 

When the applied shear stress system is removed from an elastically deformed solid, the solid regains its original shape completely and the work of deformation is also recovered. No such recovery occurs in a liquid the work done in producing a given rate of shear is completely dissipated against the liquid friction forces. The resistance to flow offered by a liquid when it is subjected to a shear stress is called a viscous force and the liquid is said to possess viscosity. 

From a macroscopic viewpoint, a liquid may be treated as an isotropic, continuous medium and, to describe the flow behaviour, attention may be concentrated on a liquid particle , that is, an infinitesimal mass of liquid moving with the remainder of the liquid. 

The motion of an element of liquid, or liquid particle, may be specified in terms of the velocity of the liquid, which may be defined as follows. 

In the region of the liquid under consideration construct a plane surface of area a, and let the direction of the normal to the surface be denoted by a unit vector e. If, in a time 6r, a volume of liquid V crosses the surface from the negative side to the positive side, as given by the direction of e, the velocity u of the liquid is defined by  

---

In situations where a low concentration of suspended solids needs to be separated from a liquid, then cross-flow filtration can be used. The most common design uses a porous tube. The suspension is passed through the tube at high velocity and is concentrated as the liquid flows through the porous medium. The turbulent flow prevents the formation of a filter cake, and the solids are removed as a more concentrated slurry. 

The most common alternative to distillation for the separation of low-molecular-weight materials is absorption. In absorption, a gas mixture is contacted with a liquid solvent which preferentially dissolves one or more components of the gas. Absorption processes often require an extraneous material to be introduced into the process to act as liquid solvent. If it is possible to use the materials already in the process, this should be done in preference to introducing an extraneous material for reasons already discussed. Liquid flow rate, temperature, and pressure are important variables to be set. 

As with distillation, no attempt should be made to carry out any optimization of liquid flow rate, temperature, or pressure at this stage in the design. The separation in absorption is sometimes enhanced by adding a component to the liquid which reacts with the solute. 

The most common alternative to distillation for the separation of low-molecular-weight materials is absorption. Liquid flow rate, temperature, and pressure are important variables to be set, but no attempts should be made to carry out any optimization at this stage. 

V = vapor flow rate from the separator L = liquid flow rate from the separator Zi = mole fraction of component i in the feed y = mole fraction of component i in the vapor Xi = mole fraction of component i in the liquid... 

Component Vapor flow rate flunolh ) Liquid flow rate (kmolh" )... 

Surface sampling involves taking samples of the two phases (gas and liquid) flowing through the surface separators, and recombining the two fluids in an appropriate ratio such that the recombined sample is representative of the reservoir fluid. 

In such a plant the gas stream passes through a series of fractionating columns in which liquids are heated at the bottom and partly vaporised, and gases are cooled and condensed at the top of the column. Gas flows up the column and liquid flows down through the column, coming into close contact at trays in the column. Lighter components are stripped to the top and heavier products stripped to the bottom of the tower. 

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

Make a numerical estimate, with an explanation of the assumptions involved, of the specific surface area that would be found by (a) a rate of dissolving study, (b) Harkins and Jura, who find that at the adsorption of water vapor is 6.5 cm STP/g (and then proceed with a heat of immersion measurement), and (c) a measurement of the permeability to liquid flow through a compacted plug of the powder. 

Related phenomena are electro-osmosis, where a liquid flows past a surface under the influence of an electric field and the reverse effect, the streaming potential due to the flow of a liquid past a charged surface. 

Macroscopic properties often influence tlie perfoniiance of solid catalysts, which are used in reactors tliat may simply be tubes packed witli catalyst in tlie fonii of particles—chosen because gases or liquids flow tlirough a bed of tliem (usually continuously) witli little resistance (little pressure drop). Catalysts in tlie fonii of honeycombs (monolitlis) are used in automobile exliaust systems so tliat a stream of reactant gases flows witli little resistance tlirough tlie channels and heat from tlie exotlieniiic reactions (e.g., CO oxidation to CO,) is rapidly removed. 

When a gas or liquid flows over a surface, the pressure at the surface is reduced according to the formula shown in equation (1), in which d is the density and v is the linear flow velocity of the moving stream. 

The drop in pressure when a stream of gas or liquid flows over a surface can be estimated from the given approximate formula if viscosity effects are ignored. The example calculation reveals that, with the sorts of gas flows common in a concentric-tube nebulizer, the liquid (the sample solution) at the end of the innermost tube is subjected to a partial vacuum of about 0.3 atm. This vacuum causes the liquid to lift out of the capillary, where it meets the flowing gas stream and is broken into an aerosol. For cross-flow nebulizers, the vacuum created depends critically on the alignment of the gas and liquid flows but, as a maximum, it can be estimated from the given formula. 

Finally, in yet another variant, the sample liquid stream and the gas flow are brought together at a shaped nozzle into which the liquid flows (parallel-path nebulizer). Again, the intersection of liquid film and gas flow leads to the formation of an aerosol. Obstruction of the sample flow by formation of deposits is not a problem, and the devices are easily constructed from plastics, making them robust and cheap. 

The aim of breaking up a thin film of liquid into an aerosol by a cross flow of gas has been developed with frits, which are essentially a means of supporting a film of liquid on a porous surface. As the liquid flows onto one surface of the frit (frequently made from glass), argon gas is forced through from the undersurface (Figure 19.16). Where the gas meets the liquid film, the latter is dispersed into an aerosol and is carried as usual toward the plasma flame. There have been several designs of frit nebulizers, but all work in a similar fashion. Mean droplet diameters are approximately 100 nm, and over 90% of the liquid sample can be transported to the flame. 

To accommodate smaller liquid flows of about 10 pl/min, micro-ultrasonic nebulizers have been designed. Although basically similar in operation to standard ultrasonic nebulizers, in these micro varieties, the end of a very-small-diameter capillary, through which is pumped the sample solution, is in contact with the surface of the transducer. This arrangement produces a thin stream of solution that runs down and across the center of the face of the transducer. The stream of sample... 

A typical loop injector showing the sampling position with pressurized solvent flowing through one loop onto the column and the sample solution placed in the other loop at atmospheric pressure. Rotation of the loop carrier through 180° puts the sample into the liquid flow at high pressure with only momentary change in pressure in the system. 

In dynamic FAB, this solution is not stationary but flows steadily over the target area. Usually, the liquid flow is the eluant from a liquid chromatography column, but it need not be. 

On leaving the chromatographic column, the liquid flow passes along a narrow tube, into the FAB ion source, and then into the target zone of the fast atoms. 

In the gas/liquid spray form of nebulizer, a stream of gas interacts with a stream of liquid. Depending on the relative velocity of the two streams and their relative orientation, the liquid flow is broken down into a spray of droplets, as in the common hair sprays. 

The first of these problems involves relative motion between a rigid sphere and a liquid as analyzed by Stokes in 1850. The results apply equally to liquid flowing past a stationary sphere with a steady-state (subscript s) velocity v or to a sphere moving through a stationary liquid with a velocity -v the relative motion is the same in both cases. If the relative motion is in the vertical direction, we may visualize the slices of liquid described above as consisting of... 

Fig. 3. Comtrack 921 pipe prover. Liquid flow through the Comtrak s closed loop is created by the movement of a sealed piston. Flow meters being tested are installed in the loop upstream from the piston. As the piston advances, the caUbration fluid travels through the meters and returns to the back side of...

The hquid flow rate is adjusted to prevent resia from passiag through the openings ia either directioa. Liquid flow is stopped for a short period to allow resia to drop through openings to the chamber below. Liquid flow resumes before resia can drop through more than one chamber. 

Fig. 2. Liquid flow-through capiUary (Washburn equation). Time rate of penetration = dl/dt = l/4[7/ 7] x [r/l] x cos0, where 7 = surface tension and 77 = viscosity. A, contact angle 9 between Hquid and capiUary waU B, penetrating Hquid C, partiaUy fiUed capiUary, r = radius, and I = length already filled.

For weight flow, where W = liquid flow rate, 1000 kg/h,... 

Fig. 2. (a) Particle concentration profile of liquid flowing in a pipe, where YjD = the ratio of the distance along the diameter to the diameter ( ) (b)... 

---