Closed and Open Vessels

2 TYPES OF IDEAL FLOW, CLOSED AND OPEN VESSELS 13.2.1 Backmix Flow (BMF) 

Laminar flow (LF) is also a form of tubular flow, and is the flow model for an LFR. It is described in Section 2.5. LF occurs at low Reynolds numbers, and is characterized by a lack of mixing in both axial and radial directions. As a consequence, fluid properties vary in both directions. There is a distribution of residence times, since the fluid velocity varies as a parabolic function of radial position. 

The type of flow occurring at the inlet and outlet of a vessel leads to the following definitions  

The characterization of flow by statistical age-distribution functions applies whether the flow is ideal or nonideal. Thus, the discussion in this section applies both in Section 13.4 below for ideal flow, and in Chapter 19 for nonideal flow. 

Several age-distribution functions may be used (Danckwerts, 1953), but they are all interrelated. Some are residence-time distributions and some are not. In the discussion to follow in this section and in Section 13.4, we assume steady-flow of a Newtonian, single-phase fluid of constant density through a vessel without chemical reaction. Ultimately, we are interested in the effect of a spread of residence times on the performance of a chemical reactor, but we concentrate on the characterization of flow here. 

---

Fortunately, for small extents of dispersion numerous simplifications and approximations in the analysis of tracer curves are possible. First, the shape of the tracer curve is insensitive to the boundary condition imposed on the vessel, whether closed or open (see above Eq. 11.1). So for both closed and open vessels... 

Bernstein, "Determination of Moisture Content of Lead Azide", PicArsnGenLab Rept 51-H1-2331 (1951) (Comparison of closed and open vessel techniques) 9)US Rubber Co, Kankakee Ordnance Works, Joliet,... 

CA 40, 2764(1946) (Polaro-graphic detn of azide ion in general and in LA in particular) 5)D.F. Vasil ev, Trudy-KomissiiAnalKhim, OtdelKhimNauk, 2, [5], 90-5(1949) CA 44, 9300-1(1950) (Polarogra-phic detn of Pb content of LA) 6)US Military Specification MIL-L 3055(1949) and Amendment 1 (1952) (Requirements for crystalline LA intended for use in manuf of detonators, fuzes and priming compns) 7)W.H. Rinkenbach A. J.Clear, "Standard Laboratory Procedures for Sensitivity, Brisance and Stability of Explosives , PicArsnTech Rept 1401 (1944), Revised in 1950 8)J. Bernstein, "Determination of Moisture Content of Lead Azide , PicArsnGenLab Rept 51-H1-2331 (1951) (Comparison of closed and open vessel techniques) 9)US Rubber Co, Kankakee Ordnance Works, Joliet,... 

Food CRMs(BCR, NIES, NIST, NRCCRM, CGC) Cd Cu Pb Se Closed and open vessel micro-wave digestion with HNO3 [WDM] Inject with modifier into transverse-heated GEA [EAAS] [WDM-EAAS] Gawalko et al. (1997)... 

FIGURE 6. Typical behavior of temperature when mixtures of sorbent with nitric acid are heated in closed and open vessels. The relations are referred to a unified... 

Let us consider two types of boundary conditions either the flow is undisturbed as it passes the entrance and exit boundaries (we call this the open b.c.), or you have plug flow outside the vessel up to the boundaries (we call this the closed b.c.). This leads to four combinations of boundary conditions, closed-closed, open-open, and mixed. Figure 13.7 illustrates the closed and open extremes, whose RTD curves are designated as E c and E. ... 

Generally, two set-ups for conducting MAE are applied in laboratories closed vessels systems allowing for temperature and pressure adjustment and control, and open vessel systems for procedures carried out under atmospheric pressure. In the open vessel systems, maximal temperature is determined by the temperature at which the extractant boils. In those systems, absorption of microwave radiation occurs in the whole sample therefore, heating is effective and homogeneous. The main disadvantage of open vessel systems is the possibility of volatile compound loss. This can be reduced by application of a reflux system fitted into the top of the extraction vessel. 

Boundary Conditions There are two cases that we need to consider boundary conditions for closed vessels and open vessels. In the case of closed-closed vessels we assume that there is no dispersion or radial variation in concentration either upstream (closed) or downstream (closed) of the reaction section, hence tliis is a closed-closed vessel. In an open vessel, dispersion occurs both upstream (open) and downstream (open) of the reaction section hence this is an open-open vessel. These two cases are shown in Figure 14-8, where fluctuations in concentration due to dispersion are superimposed on the plug-flow velocity profile. A closed-open vessel boundary condition is one in which there is no dispersion in the entrance section but there is dispersion in the reaction and exit sections. 

As stated in Section 5.3, there are two main types of microwave units, namely closed-vessel systems, which use pressurized containers, and open-vessel systems, which use focused microwaves at atmospheric pressure. Both types of system have been used to digest solid samples and each has its own advantages and disadvantages, so it is impossible to recommend either as the more suitable overall. 

The use of microwave ovens for the decomposition of both inorganic and organic samples, first proposed in the mid-1970s, is now an important method of sample preparation. Microwave digestions can be carried out in either closed or open vessels, but closed vessels are more popular because of the higher pressures and higher temperatures that can be achieved. 

The examples provided above from the recent literature on IMDA and IMHDA reactions, typically illustrate the significant advantages of the use of solvent and ionic liquids under microwave conditions in closed or open vessels compared with classical heating procedures. 

PrecapiUary sphincters Rings of smooth muscle surrounding the entrance to capillaries where they branch off from upstream metarterioles. Contraction and relaxation of these sphincters close and open the access to downstream blood vessels, thus controlling the irrigation of different capillary networks. 

---