Brownian motion stability

In general, increasing the temperature within the stability range of a single crystal structure modification leads to a smooth change in all three parameters of vibration spectra frequency, half-width and intensity. The dependency of the frequency (wave number) on the temperature is usually related to variations in bond lengths and force constants [370] the half-width of the band represents parameters of the particles Brownian motion [371] and the intensity of the bands is related to characteristics of the chemical bonds [372]. 

Many precipitates, such as Fe(OH)3, form initially as colloidal suspensions. The tiny particles are kept from settling out by Brownian motion, the motion of small particles resulting from constant bombardment by solvent molecules. The sol is further stabilized by the adsorption of ions on the surfaces of the particles. The ions attract a layer of water molecules that prevents the particles from adhering to one another. 

Aerosols are solid or liquid particles, suspended in the liquid state, that have stability to gravitational separation over a period of observation. Slow coagulation by Brownian motion is implied. 

Chemical parameters determine the surface characteristics of the suspended colloids, the concentration of the coagulant and its effects upon the surface properties of the destabilized particles, and the influence of other constituents of the ionic medium upon the coagulant and the colloids. The extent of the chemical and physical interactions between the colloidal phase and the solution phase determines the relative stability of the suspended colloids. One speaks of stable suspensions when all collisions between the colloids induced by Brownian motion or by velocity gradients are completely elastic the colloidal particles continue their... 

In order to take particle-particle interactions into account, a stability ratio W is included which relates the collision kernel /So to the aggregation kernel /3agg. The stability ratio W depends on the interaction potential aggregation rate without to the rate with interactions additional to the omnipresent van der Waals forces. For Brownian motion as dominant reason for collisions, the stability ratio W can be calculated according to Eq. (6) taken from Fuchs [ 10]. In case of shear as aggregation mechanism, the force dip/dr relative to the friction force should rather be considered instead of the ratio of interaction energy relative to thermal energy. 

In this discussion of colloid stability we will explore the reasons why colloidal dispersions can have different degrees of kinetic stability and how these are influenced, and can therefore be modified, by solution and surface properties. Encounters between species in a dispersion can occur frequently due to any of Brownian motion, sedimentation, or stirring. The stability of the dispersion depends upon how the species interact when this happens. The main cause of repulsive forces is the electrostatic repulsion between like charged objects. The main cause of attractive forces is the van der Waals forces between objects. 

We first discuss atomic and molecular superlattices which are stabilized by interactions due to electronic screening in a two-dimensional (2D) electron gas of a surface state. In this case the perfect lattice distance represents a shallow minimum in total energy. Diffusion has to be activated to reach this minimum however, it also creates Brownian motion... 

Brownian motion, which is a result of random collisions between the particles in the suspension, might influence suspension stability especially for smaller particles (smaller than... 

First a coarse O/W emulsion is prepared and, on heating, phase inversion occurs. After cooling down through the microemulsion zone, the finely dispersed nature of the microemulsion is partially retained and emulsions with drop sizes of about 100 nm result [28-30]. They show considerable long-term stability as a consequence of the Brownian motion of the oil droplets [31] and pump sprayable deodorants are one of the cosmetic products based on this technology. 

Coagulation-Precipitation The nature of an industrial wastewater is often such that conventional physical treatment methods will not provide an adequate level of treatment. Particularly, ordinary settling or flotation processes will not remove ultrafine colloidal particles and metal ions. In these instances, natural stabilizing forces (such as electrostatic repulsion and physical separation) predominate over the natural aggregating forces and mechanisms, namely, van der Waals forces and Brownian motion, which tend to cause particle contact. Therefore, to adequately treat such particles in industrial wastewaters, coagulation-precipitation may be warranted. 

These are suspensions with a size range of 20 to 200 nm. Like suspensions, they are kinetically stable but, due to the small size of the particles, they have much longer physical stability (i) an absence of sedimentation, as the Brownian motion is sufficient to prevent separation by gravity and (ii) an absence of flocculation, as the repulsive forces (electrostatic and/or steric) are much larger than the weak van der Waals attraction. 

---