Dead-water flow

Laboratory Microfiltration membranes have countless laboratory uses, such as recovering biomass, measuring particulates in water, clarifying and sterilizing protein solutions, and so on. There are countless examples for both general chemistry and biology, especially for analytical proc ures. Most of these apphcations are run in dead-end flow, with the membrane replacing a more conventional medium such as filter paper. 

Fic. 7. Properties of the F, C, I, E curves for particular patterns of flow (dead-water regions and bjrpassing flow absent) in closed vessels (L13). 

Lateral overflow, as in water reaching a filled tub. The water that fills the tub blocks the downflow direction of the added water (two-dimensional degrees of hydraulic freedom), and the latter overflows, that is, it flows laterally toward the bases of drainage (Fig. 2.11b). The observation that the water flows laterally indicates its surface (water table) is slightly tilted by the critical angle of flow. The latter is defined by the water viscosity. The water present in the deeper part of the tub does not flow—it is stagnant, bounded in a dead volume situated under... 

Fig. 2.12 A basic experiment in water flow an aquarium exposed to rain. The vessel fills up and the additional rainwater overflows. At a steady state, all the arriving rainwater flows laterally toward the bases of drainage, and the water at the bottom of the vessel is stagnant (dead volume).

Before discussing the characteristics of flow in the xylem, we will briefly review some of its anatomical features [see Chapter 1, Section 1.1C (e.g., Fig. 1-3) for an introduction to the xylem]. In general, the conducting xylem elements have thick, lignified secondary cell walls and contain no protoplasts. Indeed, the xylem cells serve their special function of providing the plant with a low-resistance conduit for water flow only when they are dead Because these conducting cells are essentially membraneless hollow pipes, water in... 

Water Flux The permeability of a UF membrane is determined by pore size, pore density, and the thickness of the membrane active layer. Water flux is measured in the absence of solute, generally on a newly made or freshly cleaned sample. The test is simple, and involves passing water through the membrane generally in dead-end flow under carefully controlled conditions. In a water flux test, the membrane behaves as a porous medium with the flow described by Darcy s law. Adjustments for viscosity and pressure are made to correct tne results to standard conditions, typically the viscosity of water at 25°C and the pressure to 50 psi (343 kPa). The water flux will be many multiples ofthe process flux when the membrane is being used for a separation. Virgin membrane has a standard water flux of over 1 mm/sec. By the time the membrane is incorporated into a device and used in an application, that flux drops to perhaps 100 pm/s. Process fluxes are much lower. 

Suppose we denote the liquid in dead-water regions as having compositon C, and liquid within the main bulk flow to have composition C. The liquid hold-up in the two regions would in general be different, but the sum of the two would be... 

A different type of river salinization in a dryland environment is represented by the Jordan River Basin along the border between Israel and Jordan. A 10-fold reduction of surface water flow in the Jordan River ((50-200) X 10 m today relative to —1,400 X 10 m in historical times) and intensification of shallow groundwater discharge resulted in the salinization of the Jordan River. During August 2001, the salinity of the southern end of the Jordan River, just before its confluence into the Dead Sea, reached 11 g L a quarter of the Mediterranean seawater salinity. Based on Na/Cl, Br/Cl, Sr/ Sr, S B, Ssuifate, and 5l Owater. ( B = [( B/ 1°B),ample/... 

The geometry of UV lamp arrangement, the water absorbance, the characteristics of the lamp, and the turbulence of water flow can influence the disinfection efficiency. Consequently, the elimination of dead area and the maintenance of uniform flow should be considered in the design. 

In hot climates, evaporation rates are high and ocean salinity ranges on the upper end of the scale. In the Red Sea and Persian Gulf, salinity may reach 42 percent. Salinity is also elevated in places where little or no new freshwater enters the system, or where water is trapped without a natural outlet. In the Dead Sea, water flows in from the Jordan River, but it has no path by which to leave the system. 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

Fig.4.3-3 demonstrates two perfectly-mixed reactors. Reactor 1 contains a "dead water" element of volume Vd [21, p.296] where the other part of volume Vi is perfectly mixed. The total volume of the reactor is Vi-i-Vd and the volume of the second reactor is V2. A tracer in a form of a pulse input is introduced into reactor 1 and is transferred by the flow Qi into reactor 2 where it is accumulating. 

Fig.4.4-2. Plug flow reactor with a "dead water" element...

Restrictions because of filtering and the accumulation of waterborne material (living and dead) may cause restrictions in water flow that might impair the operation of the whole system, including heat exchangers. 

In water and sediments, the time to chemical steady-states is controlled by the magnitude of transport mechanisms (diffusion, advection), transport distances, and reaction rates of chemical species. When advection (water flow, rate of sedimentation) is weak, diffusion controls the solute dispersal and, hence, the time to steady-state. Models of transient and stationary states include transport of conservative chemical species in two- and three-layer lakes, transport of salt between brine layers in the Dead Sea, oxygen and radium-226 in the oceanic water column, and reacting and conservative species in sediment. 

When one surface of an ion exchange membrane contacts a concentrated solution and the other a dilute one, a membrane potential is generated as explained in Chapter 2.4. For example, about 100 mV (unit pair)-1 of membrane potential is observed in seawater concentration to produce sodium chloride. Usage of the membrane potential as a battery has been studied in detail.281 Especially, detailed studies and analysis have been made by researchers in Israel due to the existence of salt lakes such as the Dead Sea.282 It was calculated that 1.08 X 106 m3/s of river water flows in seawater, which corresponds to about 2.43 X 1012 W of electricity if it is generated by a concentration cell using ion exchange membranes. This electric power is calculated to be larger than the electric power consumption of the world.283... 

Only chemical engineers have been active in the use of osmotic pressures—forward or reverse—dependent on the difference of concentration of two adjacent solutions of salts. At the point where the fresh water of a river flows into the salt water of the sea, the difference in osmotic pressure equals about 24 atm, which is equivalent to the pressure of 240 m (750 ft) of water behind a dam of that height. It has been calculated that theoretically for each cubic meter flowing from the river into the sea per second at least 2 MW of power are involved (12). The osmotic pressure difference is greater when fresh water flows into the Dead Sea (500 atm) with its high concentration also of divalent MgCl2 as well as NaCl. The relative theoretical power here would be more than 30 MW (13). 

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