Thermal force particle motion

The control of sedimentation is required to ensure a sufficient and uniform dosage. Sedimentation behavior of a disperse system depends largely on the motion of the particles which may be thermally or gravitationally induced. If a suspended particle is sufficiently small in size, the thermal forces will dominate the gravitational forces and the particle will follow a random motion owing to molecular bombardment, called Brownian motion. The distance moved or displacement, Dt, is given by ... 

Thermal gradients either within particles or in the supporting medium can be responsible for motion of aerosol particles by creating forces which act on the individual particles. Here the discussion is not about convective motion of the medium set up by thermal gradients which carries particles with it, but with thermal forces which act directly on individual particles to cause motion. 

It was initially thought that Epstein s theory satisfactorily described the thermal motion of large aerosol particles (Rosenblatt and LaMer, 1946). The theory, however, predicted essentially no thermal force acting on particles of high thermal conductivity (since HE 0). Experiments by Schadt and Cadle (1957, 1961) and others showed that thermal forces do indeed act on highly conductive as well as poorly conducting particles. 

Motion in Thermal Gradient Fields. It has long been observed that particles in a medium move from hotter to colder regions. In a thermal gradient field and at atmospheric pressure, the thermal force acting on a particle is given by (7, 8)... 

Of these various forces, only the isothermal drag force and the thermal force will be discussed here. The isothermal drag force presents perhaps the simplest of the nonequilibrium, noncontinuum phenomena. Yet, as will be shown, the current state of knowledge of the drag force is inadequate. The thermal force provides an example of the complexity inherent in particle motion in nonequilibrium host gas. 

It will be assumed in the discussion which follows that Ma = 0 because the motion of a particle relative to the temperature gradient changes the measured thermal force as suggested by JACOBSEN and BROCK [2.98] and by PHILLIPS [2.107], whose analysis of this problem will be discussed later. The role of Br. in the thermal-force problem remains to be investigated. A central point is the separation between mean nonequilibrium and random forces as displayed in (2.45). 

In a discussion of thermal-force theories it is necessary to address the problem of experimental data for the following reason. It has been known for some time that experimental thermal-force data determined by the Millikan-cell method [2.97, 98,137-139] differed from the data obtained by measuring the velocity of particle motion due to the thermal force (thermophoretic velocity) in various flow systems with different configurations [2.121,140,141]. 

In general D q,t) has a nontrivial q -dependence, so it is equally generally incorrect to replace D q,t)t with a -independent F t), hence the closing inequality in the above equation. In a viscoelastic fluid, such as most polymer solutions, the elastic moduli are frequency-dependent. The fluctuation-dissipation theorem then substantially guarantees that the random thermal forces on probe particles have nonzero correlation times, so probe motions in polymer solutions are not described by Markoff processes. The mathematically correct discussion in Berne and Pecora on Brownian particles, including Eq. 9.5, therefore does not apply to probes in polymer solutions. 

Second, the dynamic equations for polymer motion and for colloid motion are qualitatively the same, namely they are generalized Langevin (e.g., Mori-Zwanzig) equations, including direct and hydrodynamic forces on each colloid particle or polymer segment, hydrodynamic drag forces, and random thermal forces due to solvent motion, all leading to coupled diffusive motion. 

What physical forces affect colloid dynamics Three forces acting on neutral colloids are readily identified, namely random thermal forces, hydrodynamic interactions, and direct interactions. The random thermal forces are created by fluctuations in the surrounding medium they cause polymers and colloids to perform Brownian motion. As shown by fluctuation-dissipation theorems, the random forces on different colloid particles are not independent they have cross-correlations. The cross-correlations are described by the hydrodynamic interaction tensors, which determine how the Brownian displacements of nearby colloidal particles are correlated. The hydrodynamic drag experienced by a moving particle, as modified by hydrodynamic interactions with other nearby particles, is also described by a hydrodynamic interaction tensor. 

The term hydrodynamic interactions describes the dynamic correlations between the particles, induced by diffusive momentum transport through the solvent. The physical picture is the same, whether the particle motion is Brownian (i.e., driven by thermal noise) or the result of an external force (e.g., sedimentation or electrophoresis). The motion of particle i perturbs the surrounding solvent, and generates a flow. This signal spreads out diffusively, at a rate governed by the kinematic viscosity of the fluid J]kin = tl/p (t] is the solvent shear viscosity and p is its mass density). On interesting (long) time scales, only the transverse hydrodynamic modes [14] remain, and the fluid may be considered as incompressible. The viscous momentum field around a particle diffuses much faster than the particle itself, so that the Schmidt number... 

The conservative force due to the potential(s) drives the particle motion even for particles of macroscopic size (for which the thermal Brownian force is negligible) and even in the absence of external flow. Thus, the stress tensor due to those particles has both viscoelastic and purely viscous components, the former reflecting the partide motion and the latter emerging only under flow. 

In contrast, the slow process in the ABS resin B is attributable to the motion of the aggregates of the B particles for which the stress can be expressed by eqn [11] with the conservative force/therein being related to the van der Waals and osmotic potentials. (The particle motion is driven by the thermal force as well as this conservative force.) This type of relaxation mechanism, not considered in the original emulsion model (eqns [75] and [77]) but incorporated in the modified emulsion modd that considers the interfacial stress, the Brownian stress, and the stress due to long-range potential between partides (domains), is noted also for similar parti-de/matrix blends.Obviously, a change in temperature results in chants in the magnitude of the potential as well as the viscodastic property of the matrix, which leads to the... 

The basic operations in dust collection by any device are (1) separation of the gas-borne particles from the gas stream by deposition on a collecting surface (2) retention of the deposit on the surface and (3) removal of the deposit from the surface for recovery or disposal. The separation step requires (1) application of a force that produces a differential motion of a particle relative to the gas and (2) a gas retention time sufficient for the particle to migrate to the coUecting surface. The principal mechanisms of aerosol deposition that are apphed in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. Thermal deposition is only a minor factor in practical dust-collectiou equipment because the thermophoretic force is small. Table 17-2 lists these six mechanisms and presents the characteristic... 

Diffusion filtration is another contributor to the process of sand filtration. Diffusion in this case is that of Brownian motion obtained by thermal agitation forces. This compliments the mechanism in sand filtration. Diffusion increases the contact probability between the particles themselves as well as between the latter and the filter mass. This effect occurs both in water in motion and in stagnant water, and is quite important in the mechanisms of agglomeration of particles (e.g., flocculation). 

The motion of particles of the film and substrate were calculated by standard molecular dynamics techniques. In the simulations discussed here, our purpose is to calculate equilibrium or metastable configurations of the system at zero Kelvin. For this purpose, we have applied random and dissipative forces to the particles. Finite random forces provide the thermal motion which allows the system to explore different configurations, and the dissipation serves to stabilize the system at a fixed temperature. The potential energy minima are populated by reducing the random forces to zero, thus permitting the dissipation to absorb the kinetic energy. 

According to the basic ideas concerning ionic atmospheres, the ions contained in them are in random thermal motion, uncoordinated with the displacements of the central ion. But at short distances between the central ion m and an oppositely charged ion j of the ionic atmosphere, electrostatic attraction forces will develop which are so strong that these two ions are no longer independent but start to move together in space like one particle (i.e., the ion pair). The total charge of the ion pair... 

The particles in a disperse system with a liquid or gas being the dispersion medium are thermally mobile and occasionally collide as a result of the Brownian motion. As the particles approach one another, both attractive and repulsive forces are operative. If the attractive forces prevail, agglomerates result indicating an instability of the system. If repulsive forces dominate, a homogeneously dispersed or stable dispersion remains. 

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