Brownian motion random

Colloids are particles with diameters of 1-500 nm. They are larger than molecules but too small to precipitate. They remain in solution indefinitely, suspended by the Brownian motion (random movement) of solvent molecules.2... 

Brownian motion random motion of small particles, such as dust or smoke particles, suspended in a gas or liquid it is caused by collisions of the particle with gas or solvent molecules that transfer momentum to the particle and cause it to move... 

Settling of particles less than 0.5 pm is slowed by Brownian motion (random motion of small particles from thermal effects) in the water. Conversely, large sand-sized particles are not affected by viscous forces and typically generate a frontal pressure or wake as they sink. Thus, Stokes law can only apply to particles with Reynolds numbers (Re) that are less than unity. The particle Reynolds number according to Allen (1985) is defined as follows ... 

Brownian motion random motion of small particles from thermal effects. 

Brownian Motion Random motion of small dispersed particles in a liquid caused by random fluctuations in density. 

Brownian Motion Random fluctuations in the density of molecules at any location in a liquid, due to thermal energy, cause other molecules and small dispersed particles to move along random pathways. The random particle motions are termed Brownian motion and are most noticeable for particles smaller than a few micrometers in diameter. 

Bronsted acid a substance that donates protons Bronsted base a substance that accepts protons Brownian motion random movement in suspensions caused by collisions with molecules... 

Brownian motion Random movement and motion of microorganisms when viewed in a wet mount under a microscope. 

As the radical diffuses by Brownian motion randomly through the solution it grows by homogeneous monomer addition. If it reaches its solubility limit before it collides with a particle, it will precipitate out and form a new primary particle. The distance travelled during this time we shall call L This process is represented schematically in Figure 11. The actual number of steps taken in such a "random walk" between successive additions of monomer units is very much greater than shown (ca 10 -10 ). 

Brownian motion Random directional motions of a particle or molecule resulting from collisions with the molecules that comprise the medium in which the particle is suspended. 

If the particles are small, shear rate and viscosity of the suspending fluid are low, so Brownian motion randomizes orientations completely and Pe = 0. With high viscosity and shear rates or with large particles, the disperse phase will orient with the flow as Pe 00. 

In the low Peclet limit (i.e., small particles and/or low shear rates). Brownian motion randomizes the orientation totally. For prolate spheroids the intrinsic viscosity becomes... 

Statistically, in a high-pressure region, an ion will be struck by neutral molecules randomly from all angles. The ion receives as many collisions from behind as in front and as many collisions from one side as from the other. Therefore, it can be expected that the overall forward motion of the ion will be maintained but that the trajectory will be chaotic and similar to Brownian motion (Figure 49.4b). Overall, the ion trajectory can be expected to be approximately along the line of its initial velocity direction, since it is still influenced by the applied potential difference V. 

The viscosity of a suspension of ellipsoids depends on the orientation of the particle with respect to the flow streamlines. The ellipsoidal particle causes more disruption of the flow when it is perpendicular to the streamlines than when it is aligned with them the viscosity in the former case is greater than in the latter. For small particles the randomizing effect of Brownian motion is assumed to override any tendency to assume a preferred orientation in the flow. 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

Other Factors Affecting the Viscosity of Dispersions. Factors other than concentration affect the viscosity of dispersions. A dispersion of nonspherical particles tends to be more viscous than predicted if the Brownian motion is great enough to maintain a random orientation of the particles. However, at low temperatures or high solvent viscosities, the Brownian motion is small and the particle alignment in flow (streamlining) results in unexpectedly lower viscosities. This is a form of shear thinning. 

In other words, the lower the mass of the particle, the higher its velocity, because the average energy of any particle at a given temperature is constant, kT. A dispersed particle is always in random thermal motion (Brownian motion) due to coUisions with other particles and with the walls of the container (4). If the particles coUide with enough energy and are not well dispersed, they will coagulate or flocculate. 

Brownian diffusion (Brownian motion) The diffusion of particles due to the erratic random movement of microscopic particles in a disperse phase, such as smoke particles in air. 

The irregular part of the motion comes from the apparently random bombardment of the particle by surrounding fluid molecules i.e. Brownian motion. The systematic part derives from the action of various external influences -mechanical, electrical and gravitational for example - the strength of which change in time and place. 

Perikinetic motion of small particles (known as colloids ) in a liquid is easily observed under the optical microscope or in a shaft of sunlight through a dusty room - the particles moving in a somewhat jerky and chaotic manner known as the random walk caused by particle bombardment by the fluid molecules reflecting their thermal energy. Einstein propounded the essential physics of perikinetic or Brownian motion (Furth, 1956). Brownian motion is stochastic in the sense that any earlier movements do not affect each successive displacement. This is thus a type of Markov process and the trajectory is an archetypal fractal object of dimension 2 (Mandlebroot, 1982). 

There would remain some very small residual motion of the pendulum due to the air molecules striking it at random (Brownian motion), but that does not count in the game of perpetual motion. In the condition of residual motion, the pendulum is just another (big) molecule sharing equally in the average kinetic energy of all the individual air molecules. In other words, the pendulum eventually comes to thermal equilibrium with the air. 

For particles smaller than O.lp the random Brownian motion is greater than the motion due to gravitational settling. Therefore the above relations based on Stokes Law will not hold. 

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