Hydrodynamic equilibrium

DIVER METHOD- This is a modification of the hydrometer method. Variation in effective density i and hence concn, is measured by totally immersed divers. These are small glass vessels of approximately streamline shape, ballasted to be in stable equilibrium, with the axis vertical, and to have a known density slightly greater than that of the sedimentation liq. As the particles settle, the diver moves downwards in hydrodynamic equilibrium at the appropriate density level. The diver indicates the position of a weight concn equal to the density difference between the diver and the sedimentation liq. Several divers of various densities are required, since each gives only one point on the size distribution curve... 

Fouling. If die gel-polarization layer is not in hydrodynamic equilibrium with die fluid bulk, die membrane may be fouled. Fouling is caused either by adsorption of species on the membrane or on the surface of the pores, or by deposition of particles on die membrane or wiilini the... 

In all cases, countercurrent chromatography (CCC) utilizes a hydrodynamic behavior of two immiscible liquid phases through a tubular column space which is free of a solid support matrix. The most versatile form of CCC, called the hydrodynamic equilibrium system, applies a rotating coil in an acceleration field (either in the unit gravity or in the centrifuge force field). Two immiscible liquid phases confined in such a coil distribute themselves along the length of the coil to form various patterns of hydrodynamic equilibrium [1],... 

The basic hydrodynamic equilibrium (the two liquid phases are evenly distributed from one end of the coil, called the head, and any excess of either phase is accumulated at the other end, called the tail). Here, the tail-head relationship of the rotating coil is defined by the direction of the Archimedean screw force which drives all objects toward the head of the coil. 

The unilateral hydrodynamic equilibrium [the two solvent phases are unilaterally distributed along the length of the coil, one phase (head phase) entirely occupying the head side and the other phase (tail phase) the tail side of the coil]. The head phase can be the lighter or the heavier phase and also can be the aqueous or the non-aqueous phase, depending on the physical properties of the liquid system and the applied experimental conditions. This type of equilibrium may also be called bilateral, indicating the distribution of the one phase on the head side and the other phase on the tail side [3],... 

To illustrate the process of estabfishing the hydrodynamic equilibrium, it is worthwhile to begin with the dis-... 

From this, the basic equation of the stationary-phase retention process can be derived, a number of assumptions and complex theoretical treatments being required. Taking as example the planetary centrifuge of Type J, the average cross-sectional area of a stationary-phase layer has been estimated for hydrophobic liquid systems, which are characterized by high values of interfacial tension y, low values of viscosity r], and low hydrodynamic equilibrium settling times ... 

Countercurrent chromatography (CCC) is a support-free liquid-liquid partition system in which solutes are partitioned between the mobile and stationary phases in an open-column space. The instrumentation, therefore, requires a unique approach for achieving both retention of the stationary phase and high partition efficiency in the absence of a solid support. A variety of existing CCC systems may be divided into two classes [1] (i.e., hydrostatic and hydrodynamic equilibrium systems). The principle of each system may be illustrated by a simple coil as shown in Fig. 1. 

The basic hydrodynamic equilibrium system (Fig. 1, right) uses a rotating coil which generates an Archimedean screw effect where all objects in different density present in the coil are driven toward one end, conventionally called the head. The mobile phase introduced through the head of the coil is mixed with the stationary phase to establish a hydrodynamic equilibrium, where a portion of the stationary phase is retained in each turn of the coil. This process continues until the mobile phase elutes from the tail of the coil. After the hydrodynamic equilibrium is established throughout the coil, the mobile phase displaces only the same phase, leaving the other phase stationary in the coil. Consequently, solutes introduced locally at the head of the coil is subjected to an efficient partition process between the two phases and separated according their partition coefficients. 

All these flow types appear more or less in a series one after the other during the evaporation of a liquid in a vertical tube, as Fig. 4.30 illustrates. The structure of a non-adiabatic vapour-liquid flow normally differs from that of an adiabatic two-phase flow, even when the local flow parameters, like the mass flux, quality, etc. agree with each other. The cause of this are the deviations from thermodynamic equilibrium created by the radial temperature differences, as well as the deviations from hydrodynamic equilibrium. Processes that lead to a change in the flow pattern, such as bubbles coalescing, the dragging of liquid drops in fast flowing vapour, the collapse of drops, and the like, all take time. Therefore, the quicker the evaporation takes place, the further the flow is away from hydrodynamic equilibrium. This means that certain flow patterns are more pronounced in heated than in unheated tubes, and in contrast to this some may possibly not appear at all. 

The instrument consists of a motor and an off-axis column that rotates in a particular mode of planetary motion. In this mode, the two liquid phases establish a hydrodynamic equilibrium wherein the stationary phase dominates the total volume of the coil, often exceeding 80% of the total column volume. Under this equilibrium, the introduced mobile phase moves with relatively high speed through the column. 

Figure 11-2 is a diagram of the component parts needed for an analysis. There are two main instrument systems in countercurrent extraction (1) the hydrostatic equilibrium system and (2) the hydrodynamic equilibrium system. In the hydrostatic equilibrium system (HSES), a stationary coil is placed in a horizontal position. In the hydrodynamic equilibrium system (HDES), the coil rotates around its own axis These will be discussed individually in more detail, but first, what happens when two immiscible liquids are placed in a tube and the tube rotated slowly will be examined. 

Now refer to Figures 11 -8 and 11-9, p. 121. "In 11 -8 the coil is first filled with the heavier stationary phase or the lighter stationary phase (11-9) and the mobile phase is introduced at the head of the coil while the coil is slowly rotated around its own axis top). As soon as the mobile phase meets the Figure 11-7. Motion of various objects in a rotating stationary phase in the coil, a hydrodynamic equilibrium is... 

As soon as the mobile phase reaches the first coil unit, the two phases interact to establish the hydrodynamic equilibrium where one phase with less wall surface affinity is split into multiple droplets which oscillate synchronously with the coil rotation. While continuous pumping of the mobile phase keeps breaking this equilibrium state at the head end of the coil, the two phases can quickly react to restore the equilibrium by readjusting their relative volumes in each coil unit. Thus the stationary phase pushes newly introduced excess amounts of the mobile phase toward the tail end of the coil. 

What is the difference be -. een the hydrostatic equilibrium system and the hydrodynamic equilibrium system What causes the mobile phase to break into droplets in the hydrostatic equilibrium system ... 

HDES Hydrodynamic equilibrium system SPE Solid phase extraction... 

The motion of the colunrn generates an Archimedian screw force. Independent of density, the contents of the column are driven towards one end called the head (the other end is referred to as the tail) [244]. The forces acting on the coiled column cause vigorous mixing of the two phases with formation of a succession of mixing and demixing zones in each successive turn of the coil. When hydrodynamic equilibrium is established, the phase ratio is constant, and only the mobile phase moves through the... 

Diffusion of any nonpolar component i does not depend on the electric field. The effect of other components, temperature and pressure shows up in a change of its chemical potential. If we disregard magnetic and gravity forces and assume the presence of hydrodynamical equilibrium, the only force, which compels nonpolar component to move, is gradient of its chemical potential. Relative to it the diffusions linear equation will assume the format... 

The shape of a suspended drop depends on the surface tension as well as on the gravitational force. The drop is photographed and the diameter at various positions is measured. A consistent shape factor can be evaluated when hydrodynamic equilibrium is reached. 

Figure 6 Mechanism of high-speed CCC (A) bilateral hydro-dynamic distribution of the two phases in the coil, where the white phase occupies the head side and the black phase the tail side (B) CCC operation utilizing the above hydrodynamic equilibrium condition and (C) mechanism of dual CCC, where the two phases literally undergo countercurrent movement.

Rgure 1 Archimedean screw effect in a rotating coil. (A) Motion of air bubbles and glass beads suspended in water (B) Motion of droplets of one phase of an equilibrated two-phase solvent system suspended in the other phase (C) Hydrodynamic equilibrium of two immiscible solvent phases in a slowly rotating coil. 

In Figure 1C, the coil is filled with nearly equal volumes of the two phases and rotated slowly about its axis. In this case, the lighter phase stays at the upper portion and the heavier phase at the lower portion of the coil, both competitively advancing toward the head of the coil. Sooner or later, the two phases establish a hydrodynamic equilibrium where each phase occupies about an equal space on the head side of the coil, and any excess of either phase remains at the tail end of the coil. Once this hydro-dynamic equilibrium is formed, continued rotation of the coil mixes the two solvent phases vigorously, while the overall distribution of the two phases remains unaltered. 

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