Focus velocity

Suppose that the focusing velocity W= U = - ay originates as a relative displacement velocity U impelled by an external potential function of the following form having a minimum at y = 0... 

FIGURE 19.5 Nozzle shape channel geometry. Droplet breakup occurs at a fixed point due to the focused velocity gradient created by the nozzle shape geometry. The radius of the liquid thread decreases due to the perturbation caused by the extension of the thread. Initial balance of the pressure and shear forces at the interface of the thread determines the initial radius of the thread. The device also produces monodisperse submicron satellite drops. (Reprinted from Tan, Y.-C. et al. 2006. Sens. Actual. B 114 350-356. With permission.)... 

Let us focus our adention for the moment on a small volume in space, dr, and on particles in the volume with a given velocity v. Let us sit on such a particle and ask if it might collide in time t with another particle whose velocity is v, say. Taking the effective diameter of each particle to be a, as described above, we see... 

Figure Bl.7.17. (a) Schematic diagram of a single acceleration zone time-of-flight mass spectrometer, (b) Schematic diagram showing the time focusing of ions with different initial velocities (and hence initial kinetic energies) onto the detector by the use of a reflecting ion mirror, (c) Wiley-McLaren type two stage acceleration zone time-of-flight mass spectrometer.

This reduces many of the complications arising from the need for spatial focusing. Also, the initial velocity of ions generated are invariably in the TOP direction. 

In TOF-SARS [9], a low-keV, monoenergetic, mass-selected, pulsed noble gas ion beam is focused onto a sample surface. The velocity distributions of scattered and recoiled particles are measured by standard TOF methods. A chaimel electron multiplier is used to detect fast (>800 eV) neutrals and ions. This type of detector has a small acceptance solid angle. A fixed angle is used between the pulsed ion beam and detector directions with respect to the sample as shown in figure Bl.23.4. The sample has to be rotated to measure ion scattering... 

Double-focusing analyzer. A magnetic analyzer and an electrostatic analyzer combined in either sequence to effect direction and velocity focusing. 

Electrostatic analyzer. A velocity-focusing device for producing an electrostatic field perpendicular to the direction of ion travel (usually used in combination with a magnetic analyzer for mass analysis). The effect is to bring to a common focus all ions of a given kinetic energy. 

We begin the mathematical analysis of the model, by considering the forces acting on one of the beads. If the sample is subject to stress in only one direction, it is sufficient to set up a one-dimensional problem and examine the components of force, velocity, and displacement in the direction of the stress. We assume this to be the z direction. The subchains and their associated beads and springs are indexed from 1 to N we focus attention on the ith. The absolute coordinates of the beads do not concern us, only their displacements. 

Doppler Flow Meters. Doppler flow meters sense the shift in apparent frequency of an ultrasonic beam as it is reflected from air bubbles or other acoustically reflective particles that ate moving in a Hquid flow. It is essential for operation that at least some particles ate present, but the concentration can be low and the particles as small as ca 40 p.m. CaUbration tends to be influenced by particle concentration because higher concentrations result in mote reflections taking place neat the wall, in the low velocity portion of the flow profile. One method used to minimize this effect is to have separate transmitting and receiving transducers focused to receive reflections from an intercept zone neat the center of the pipe. 

The AeroSizer, manufactured by Amherst Process Instmments Inc. (Hadley, Massachusetts), is equipped with a special device called the AeroDisperser for ensuring efficient dispersal of the powders to be inspected. The disperser and the measurement instmment are shown schematically in Figure 13. The aerosol particles to be characterized are sucked into the inspection zone which operates at a partial vacuum. As the air leaves the nozzle at near sonic velocities, the particles in the stream are accelerated across an inspection zone where they cross two laser beams. The time of flight between the two laser beams is used to deduce the size of the particles. The instmment is caUbrated with latex particles of known size. A stream of clean air confines the aerosol stream to the measurement zone. This technique is known as hydrodynamic focusing. A computer correlation estabUshes which peak in the second laser inspection matches the initiation of action from the first laser beam. The equipment can measure particles at a rate of 10,000/s. The output from the AeroSizer can either be displayed as a number count or a volume percentage count. 

Two types of floater aozzles are curreafly ia use and they are based on two different principles. The Bernoulli principle is used ia the airfoil flotatioa aozzles, ia which the air flows from the aozzle parallel to the web and the high velocities create a reduced pressure, which attracts the web while keeping the web from touching the nozzles. The Coanda effect is used to create a flotation nozzle when the air is focused and thus a pressure pad is created to support the web as shown ia Figure 19. 

Theory of Electrophoretic Motion. The study of the mechanics of electrophoresis focuses on the basis of electric potential on the surface of an object, and the relation of the electric potential to the velocity of the particle. Whereas research has been generally limited to nonmolecular particles of weU-defined geometry and is not strictly apphcable to molecules such as proteins and DNA fragments, this work is useful for understanding the physics of electrophoretic motion. 

Isolated Droplet Breakup—in a Velocity Field Much effort has focused on defining the conditions under which an isolated drop will break in a velocity field. The criterion for the largest stable drop... 

Brenn-fieck, m. focus burned spot, -gas, n. combustible gas, fuel gas. -gerste, /. distilling barley, -geschwindigkeit, /. velocity of combustion or of burning or of distillation. 

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