Flow trajectory

L Stratified wavy annular Minimum inclination angle to show bubble flow Trajectory of drops tom from liquid film Lift versus buoyant forces... 

It was demonstrated by research that the rectilinear form of electron flow trajectory is characteristic for macrostructures and the temperature doesn t considerably influence the overall process in this circumstances. At the same time changing of initial particle velocity (by varying the temperature or the potential) just leads to changing of accelerating area width and electron flow intensity near the anode. The influence... 

Detailed kinematic investigations of flow near the front of a stream were undertaken.284 A diagram of the experimental device is shown in Fig. 4.49. In the experimental procedure, a liquid was placed in a chamber with transparent walls above an aluminum piston, which was driven downwards by connection to a suitable drive. This resulted in the appearance of streams inside the liquid,and three different flow zones could be distinguished. The so-called "fountain effect discussed in Section 2.11 appeared near the free surface, while a reverse fountain flow was observed below the moving surface. It is interesting to note the movement of two liquids with different densities, when one liquid is used as a piston to push the other (analyzed experimentally and theoretically).285 If the boundary between the two liquids is stationary and the walls of the chamber move at constant velocity, then the pattern of flow is as shown in Fig. 4.50, where flow trajectories corresponding to front and reverse fountain effects are clearly shown. Two other flow patterns -developed flow inside the main part of the chamber and circulation near the surface of the aluminum piston - were also observed. 

Keywords Flow trajectory Homochirality Nonlinear autocatalysis Recycling Soai reaction... 

As the first step in analyzing flow trajectories in a phase space, we consider the simplest case when reactions such as spontaneous production (Eq. 1), linearly autocatalytic (Eq. 2), or quadratically autocatalytic (Eq. 4) reactions are active. Then the rate equations are simplified as ... 

The ratio r/s increases along the flow trajectory if it is initially larger than unity. Thus the r - s asymmetry increases, and the final value of the ee 0ool is larger than the initial value 0o. Figure 4b shows 0o - 4>oo for cases of positive 0. The enhancement is more evident when the initial ratio qo/c is smaller. These essential features are the same with the monomeric system, discussed in Sect. 2.3.3. 

In previous sections we have focused on the cases with X = it = 0. In these cases, the asymptotic value of a vanishes, ait = oo) = 0 so that A(t = oo) = Bit = oo) = 0, and the asymptotic value of the order parameter 4>i cannot be determined from Eq. 13. Another example with A = B = 0 happens for a special case with ko = k = //, = 0 and fe = k 2. In this case, we can calculate trajectories and Und a fixed line shifted from a = 0 to the one with a finite value of a(t = oo) [28] Flow trajectories are along lines passing through the origin, similar to those shown in Fig. lb, but terminating at a shifted fixed... 

The gradient is expressed in meters drop of height per kilometer of horizontal flow trajectory, as shown in Fig. 4.11. The drop in water table levels between adjacent wells is computed from their water table data, and the distance between the wells is commonly read from a map on which the wells have been accurately marked. The gradient may also be extracted from a water table map by reading the drop in water table altitude between selected points, as shown in Fig. 4.12. Water flows mainly along the maximum gradient, as shown in Fig. 4.4b. 

So far the method of solution is standard. With a great deal of effort the constants in Eqs. 7.24 and 7.25 can be evaluated from the initial and boundary conditions of the problem, and the flow trajectories of the aerosol particles determined. Phase analysis permits the bypassing of this laborious task, so that something can be learned from these equations without having to evaluate the constants. 

For a practical computation, these two last equations need (i) one procedure that gives the transition probabilities from e to k state at each j — a position (Pek(j (ii) some practical relations that express, for k= 1, k= 2, etc., the distributions of the step lengths (p (a)). It is not difScult to establish that the transition probabilities Pek(j — a) depend strongly on the totality of the previous trajectory. As a consequence, the fluid flowing trajectory is continuously updated step by step. 

Figure 11.7 Flow patterns associated with a rotating disk a) a three-dimensional representation of flow trajectories that lead to a net flow toward the disk and in the radial direction. The axial scale was expanded greatly in order to allow visualization of the flow trajectories, b) a projection of the flow trajectories onto a plane at a fixed axial position.

As well, a notch may do the same with regard to the diffusion from the points of view of the geometry and the stress effects on the transport phenomenon, if compared with the stress-unassisted diffusion in a smooth cylinder. In particular, the range of the disturbing effect of a notch on stress in assisted transport phenomena in solids can be estimated from fig. 4, where vanishing of the notch effect corresponds to fairly radial flow trajectories, or concentration contour bands parallel to the cylinder surface, the same as it occurs in smooth bars. 

It is usual in laminar mixing simulations to represent the flow using tracer trajectories. The computation of such flow trajectories in a coaxial mixer is more complex than in traditional stirred tank modelling due to the intrinsic unsteady nature of the problem (evolving topology, flow field known at a discrete number of time steps in a Lagrangian frame of reference). Since the flow solution is periodic, a node-by-node interpolation using a fast Fourier transform of the velocity field has been used, which allowed a time continuous representation of the flow to be obtained. In other words, the velocity at node i was approximated... 

Figure 18.3 shows a plot of the pressure and flow during a mandatory pressure-controlled ventilation. In this case, the respirator raises the airway pressure and maintains it at the desired level, Pj, which is set by the therapist, independent of the patient s respiratory mechanics. Although the ventilator maintains the same pressure trajectory for patients with different respiratory mechanics, the resulting flow trajectory, shown in Figure 18.3b, will depend on the respiratory mechanics of each patient. As in the case of mandatory volume-controlled ventilation, the total volume of delivered breaths is monitored to ensure that patients receive adequate ventilation. 

Respiration rate flow trajectory tidal volume %02 peak flow PEEP... 

The obstruction of the air under the weir flow determines the flow trajectory and flow regime, so to make a thin-plate rectangular measuring weir, ventilation hole must set on the weir wall between the weir plate and the water tongue under the weir, to make sure the weir flow is freedom, and to guarantee the flow rate calculate accuracy by empirical formula. The diameter of the ventilation hole can be calculated according to the following formula (Sun, J.S. et al. 2003) ... 

Huang, Z.-B., and Cheng, Z.-M. (2011), Determination of liquid multiscale circulation stmcture in a bubble column by tracing the liquid flowing trajectory, Industrial Engineering Chemistry Research, 50(21) 11843-11852. 

The axial dispersion in the liquid phase of a trickle-bed reactor results from transport processes occurring at the particle scale i.e., in each flow trajectory considered as independent, as well from the velocity distribution observed at the bed scale. If we assume that the axial dispersion at the particle scale may be represented by a diffusion-like process, the local mass balance in channel i is given by... 

To account easily for the velocity distribution influence, a very simple model is adopted. It consists in a set of parallel channels (see figure 12). Each channel corresponds to a flow trajectory. All the independent lengths of these trajectories i.e. the lengths between two intersection points are assumed to be equal to a mean channel length L. Using this model, Carbonell (198I) derived an approximate expression for the area and time-averaged value of the axial dispersion coefficient... 

The free path between two intersection points along the flow trajectories is assumed to be constant and equal to L. Actually in a trickle bed, the free path varies randomJy. This simplification will require to relate somewhat empirically L to the operating conditions (see Eq. 33). 

The mean length L corresponds to the mean free path along the flow trajectories of the percolation structures. In the absence of a detailed analysis of the frequency distribution of intersection points along these trajectories, we will assume the distribution to be a geometrical one. That means that the mean frequency should be proportional to the density of flow trajectories i.e. the irrigation rate. The mean length L (i.e. 

First, let us consider the kinematic definition of a streamline. A streamline is a flow trajectory across which fluid motion is absent fluid moves tangentially to it. Thus, its local slope must be equal to the ratio of the vertical to the horizontal velocities,... 

The tremor alarm systems mentioned previously are very simple and they lack the ability to locate tremor. Some observatories have exploited seismic data to track the location of tremor and map debris-flow trajectories, which could help mitigate hazards. 

Figure 5.18 Illustration of individual particle flow trajectories in (a) laminar and (b) turbulent flow.

---