Accelerated flow

Question. A reaction is carried out in an accelerated flow tube and observations are made spectrophotometrically. 

If the initial flow velocity is 400 cm s 1, calculate the time to reach an observation point 1 cm along the reaction tube. If the acceleration is such that the velocity increases progressively to 800, 1200 and 1600 cm s-1, calculate the reaction times corresponding to these flow rates. If the absorbances corresponding to these times are 0.124, 0.437, 0.655 and 0.812, draw a graph showing the progress of reaction. 

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In measuring the local velocity in ducts, the sensor will obstruct a part of the duct cross-section. This results in accelerated flow by the sensor and an error occurs. In a Pitot-static tube, this is called stem blockage. If the ratio of the tube diameter to the duct diameter is smaller than 0.02, stem blockage can be neglected. Otherwise a correction has to be applied. 

Proton inventory technique. 21.9-220 Pseudo-first-order kinetics, 16 Pulse-accelerated-flow method. 255 Pulse radiolysis, 266-268 Pump-probe technique. 266... 

A significant technical development is the pulsed-accelerated-flow (PAF) method, which is similar to the stopped-flow method but allows much more rapid reactions to be observed (1). Margerum s group has been the principal exponent of the method, and they have recently refined the technique to enable temperature-dependent studies. They have reported on the use of the method to obtain activation parameters for the outer-sphere electron transfer reaction between [Ti Clf ] and [W(CN)8]4. This reaction has a rate constant of 1x108M 1s 1 at 25°C, which is too fast for conventional stopped-flow methods. Since the reaction has a large driving force it is also unsuitable for observation by rapid relaxation methods. 

This method is similar to continuous flow method except that the rate of flow is continuously varied and the analysis is made at a fixed point along the observation tube. Since the rate of flow changes with time, the reaction mixtures arriving at observation point have different time. In the accelerated flow method the output from a photo electric colorimeter is fed to a cathode-ray oscilloscope, which sweeps out a complete time-concentration record which may be photographed. The method is useful for very rapid enzyme reactions and requires only small quantities of reactants. 

Fig. 3.2 The operation of flow methods. The distance x and the combined flow rate govern the time that elapses between mixing and when the combined solutions reach the observation, or quenching, point. In the stopped flow method, observation is made as near to the mixer as is feasible, and monitoring occurs after the solutions are stopped. In the pulsed accelerated flow method, observation is within the mixer.

The additives used for lacquer manufacture are composed of processing aids like hardening accelerators, flow agents, crosslinking agents and others like plasticisers, fillers and if necessary pigments. 

Pulsed continuous flow is a method in which continuous flow is established for a short time. This method can reduce reagent consumption to 5 ml, and fast jet mixers have lowered the accessible reaction half-time to the 10 ps range. Pulsed accelerated flow may be viewed as an adaptation of pulsed continuous flow in which the flow rate through the mixer and observation chamber is varied during the course of one kinetic run. This method can be used for reactions with half-times down to 10 ps. This method is limited to first-order reaction conditions. 

The flow profiles with H > 2.591, correspond to velocity distributions with inflection point and these are the decelerated flows or flows with adverse pressure gradient. On the contrary, the flow profiles with H < 2.591, correspond to - < 0 (the accelerated flows). The figure with = 0 and H = 2.59, corresponds to the Blasius profile. The profile with j3h = I and H = 2.22 corresponds to the stagnation point flow. The other two profiles in Fig. 2.7 are for flows with adverse pressure gradient and the crosses on the profile indicate the locations of the inflexion point. The profile for /3h = —0.1988 H = 4.032) corresponds to the case of incipient separation. 

Loyd et al. (L2) have found this inadequate for strongly accelerated flows beyond y+ = 5. Since the patching will take place at a much larger value of y+ (perhaps around 30-50), a better shear stress distribution is needed. Loyd et al. noted that for fully asymptotic flow, where U/U = f(y/S) throughout the entire layer (such flows can be realized with strong acceleration), the shear stress distribution is... 

Figure 2. Top and end views of a radial mixer/observation cell used in pulse-accelerated-flow spectrometer. W, windows, A and B, reactants. Reproduced with permission from S. A. Jacobs, M. T. Nemeth, G.W. Kramer, T. Y. Ridley, and D. W. Margerum, Anal. Chem. 1984, 56, 1058. Copyright 1984 American Chemical Society.

The pulsed-flow method evolved further into the pulsed-accelerated-flow method [7], Here, the solutions have a range of flow velocities owing to the constant flow... 

The limit for the measured rate constants is determined by the mixing rate and the instrument s dead time, defined as the time required for the solution to travel from the mixing chamber to the observation point. Nowadays, half-times in the millisecond range can be measured routinely. An extension of accessible rates up to 2000 s through algebraic corrections for mixing effects was discussed [11]. Under the assumption that the behavior of the solution at short times after mixing in the stopped-flow is described by the same equations that were found applicable for pulsed-accelerated flow, the precise rate constant can be obtained from a set of experiments carried out under pseudo-first-order conditions by use of Eq. 10. 

The cyclone, or inertial separation method, is a common industrial approach for segregating a dispersed phase from a continuous medium based upon the difference in density between the phases. The concept takes advantage of the velocity lag which occurs for dense particles with respect to a lower density medium when both phases are subject to an accelerating flow field, such as within a rotating vortex. The larger the acceleration, the smaller the particle which fails to follow the continuous phase streamlines and will migrate to the outer wall of the cyclone for collection. 

Magnaudet J., Rivero M., Fabre J. (1997) Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow. J. FluidMech. 284, 97-135. 

In the case where a gas flows over the front portion of a curved surface or a convex curve surface, the flow outside the boundary layer accelerates. The boundary layer over most of the front portion remains fairly thin and has a uniform streamline pattern over this portion. According to the Bernoulli equation [48], accelerated flow results in a pressure decrease in the vicinity of the front portion area. In this zone, the pressure gradient is positive, i.e. the direction of pressure gradient is the same as the flow direction. The positive pressure gradient is helpful to push the flow within the boundary layer forwards. The variations of velocity and pressure are expressed as... 

Flight of ideas—An accelerated flow of speech with thoughts that change rapidly from one topic to another. An almost continuous flow of pressured and rapid speech that abruptly changes from topic to topic. The associations between the topics are usually understandable. 

Problem 10-4. Boundary Layer on a Flat Plate in an Accelerating Flow, Uoo = Ax. Consider flow past a flat plate in the throat of a 2D channel as depicted in the figure. If the free-stream velocity is given by = ax, where x is the distance from the leading edge and X is a constant, show that the flow in the boundary layer on the plate is governed by an ODE. Solve for the streamfunction numerically. How does the boundary-layer thickness grow with x How does the shear stress vary with x ... 

Problem 10-5. Boundary-Layer on a Flat Plate in an Accelerating Flow, Uoo = Ax1/2. 

The shape of the flow passage that guides the air to the sensor element plays an important role in the function of an air-flow sensor (the bypass, Fig. 7.6.8). Cross section and length are the important factors. As an accelerated flow has the most stable boundary layers and therefore is less vulnerable to flow separation, it would be favorable to have a decreasing cross section (in the flow direction). To avoid a restriction of air flow in the bypass the cross section at the outlet should not be too small in relation to the inlet. Therefore a reduction of cross section for stable accelerated flow is only done in the vicinity of the sensor element and in curved parts of the bypass (Fig. 7.6.8). 

Zone with accelerated flow (reduction of cross section is also orthogonal lo the drawing plane)... 

B. Chance, The accelerated flow method for rapid reactions. Part II. Design, construction, and tests. I. Apparatus construction, J. Franklin Inst. 229 (1940) 737. 

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