Particle displacement

Figure 8.9 Phase separation in a mixed layer of protein + surfactant from Brownian dynamic simulation. In the picture are cross-linked protein-like particles (black) and surfactant-like displacer particles (grey). Reproduced from Wijmans and Dickinson (1999b) with permission.

Factors influencing properties of the cake during the cake filtration are particle shape, size, packing and dimensions of the cake in addition to the properties of the fluids, interfacial properties and the other factors such as temperature, pressure gradient and the rate of displacement. Particle shape may be an important factor in determining the drainage characteristics (1). 

Platelet transit to the vessel wall is also regulated by ted blood cells [49]. Under current lattrinar flow conditiorrs such as those taking place in cirxnilating blood, red blood cells displace particles of smaller size towards the boundary layer (subendothelium), hr an... 

Nevertheless, if one assumes a static, rather than a thermodynamic, equilibrium, one can attempt to estimate the dependence of the yield stress Oy and the modulus G on the shape and depth of the interparticle potential. Imagine that a gel is subjected to a shear strain Y that homogeneously displaces particles from their positions of static equilibrium. Pairs of particles are pulled apart by this strain, and separations between particle centers of mass should increase roughly by an amount yrQ, where ro = 2a + Dq is the separation between centers of mass in the absence of strain. Hence, the imposition of a strain y increases the gap between particle surfaces from Dq to... 

For systems whose particle-particle bonds are permanent (image (b) in Figure 23.1), the film tends to form a secondary layer of wrinkles. The displaced particles do not completely remove themselves from the interface, but remain coimected to the cross-linked network. Contrary to what happens with very breakable bonds, part of the interfacial stress is released — and the area fraction decreases significantly — once the collapse point is passed (see curve (b)). 

In flow FFF the particle is driven to the accumulation wall by the physical cross-flow of the carrier fluid. To implement this method, the walls of the channel must be permeable. A stream of carrier is then introduced through one wall and withdrawn from the opposite wall. The cross-flow fluid motion so generated is superimposed on the axial channel flow described earlier. This cross-flow displaces particles toward the accumulation wall as effectively as a sedimentation force. However, the driving force is density-independent specifically,... 

Displacement of particles along the near part is similar to displacement along the circumference so that inertia forces appear as centrifugal forces inhibiting deposition. The primary effect of inertia forces on the near part of the trajectory at St < St was determined by Dukhin (1983). A displacement of the particle trajectory with respect to stream-line 1 which is the grazing trajectory is shown in Fig. 10.14. After displacement, particles move along the stream-line 1 away from the bubble and do not touch its surface. 

Figure 8.1.2 Propagation of a traveling wave with density, normalized particle displacement, particle velocity and sound pressure as a function of normalized time or coordinate.

An oscillation in pressure, stress, particle displacement, particle velocity, etc., that is propagated in an elastic material, in a medium with internal forces (e.g., elastic, viscous), or the super-position of such propagated oscillations. Sound is also the sensation produced through the organs of hearing, usually by vibrations transmitted in a material medium, commonly air (Table S.3). See also Noise. 

In numerical simulations of systems of N polarizable dipolar particles the induced dipoles must be computed by solving a set of N linear equations depending on the positions and orientations of the N dipoles of the system. The solution of this set of equations requires of the order of operations and deteriorates considerably the efficiency of MC simulations since, in principle, for each MC elementary move involving, for instance, the displacement of one particle, the N linear equations have to be solved. The vaUdity of numerical procedures allowing us to overcome this problem is discussed in [94]. The procedures are based on the choice of an adequate cut-off of the interparticle distances such that the computation of the induced dipole of a displaced particle depends only on the positions and orientations of dipoles located at a distance of the trial particle position smaller than the cut-off. 

The simulations proceeds by first using a gas-phase equation of state to determine the pressure and the fugacity for the gas phase. The simulation then follows a series of trial moves which involve particle displacement, particle insertion and particle removal in order to establish equilibrium. The particles (molecules) in the simulation box are allowed to move, rotate or rearrange their configuration based upon the Boltzmann-weighted Metropolis sampling probability described earlier in Eq. (B12). In order to establish a constant volume, temperature and chemical potential, the number of molecules in the box can increase or decrease. In addition to the displacement moves described already, particle insertions and particle removals are also present. A new particle or molecule can be inserted into the system at a randomly chosen point based on the following probability ... 

Separation begins with the onset of flow down the channel. The flowing fluid displaces particles along the channel length. However, since the flow profile is parabolic (see Figure 2), particles held at different elevations will be displaced at different velocities f3 For steric FFF, larger particles, with centers held further from the wall, are displaced more rapidly toward the exit than smaller particles. The particles are separated and eluted through a detector at different times. The differential elution is recorded and converted to a PSD. 

As with shaken systems, this segregation by particle density has been commonly attributed to the Archimedean buoyancy force, essentially, the force on an object due to the difference between the weight of the object and the weight of the displaced particles. On the other hand, as detailed in the next section, mass, rather than density, is sometimes a better indicator of segregation trends. 

The top interface. Imagine the top interface to be subjected to a small disturbance, which displaces a particle some way into the clear fluid above (Figure 5.2). The displaced particle immediately encounters a reduced fluid velocity, and a consequential reduction in drag this results in a net downward force, which quickly returns the particle to its previous position. The top interface is therefore stable, a fact well confirmed by experiment. 

The bottom interface. Now consider the counterpart situation at the bottom interface. Here a displaced particle also experiences a net downward force, a result of the reduction in fluid velocity which it... 

Schurch S, Gehr P, Im Hof V, Geiser M, Green F. Surfactant displaces particles toward the epithelium in airways and alveoli. Respir Physiol 1990 80 17-32. 

Gehr P, Schurch S. Surface forces displace particles deposited in airways toward the epithelium. News in Physiological Sciences 1992 7 1-5. 

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