Forces on particles and molecules

A variety of external forces are of use in separation. Of course, the internal force of chemical potential gradient has great importance in chemical separations. We will begin, however, by treating external forces. Of these, the gravitational force due to the earth is perhaps the most familiar one and is therefore appropriate for consideration now. 

In vector notation, the vertically downward gravitational force per unit mass may be described as 

The vector gravitational driving force per unit mass of the particle due to the etcternal force field is simply the negative of the gradient of the scalar potential of that force field. Here increases with positive z nature, i.e. gravity, spontaneously drives the particle to a lower 

The movement of the particle of mass trip under the action of the gravitational force considered above, however, assumed free space. If this particle were instead immersed in a fluid of density p, a buoyancy force would act on the particle in the vertically upward direction. The net ejcternal driving force on the particle acting vertically downward would be 

A binary electrolyte A + Yf - when dissociated fully in a solvent will produce v+ ions of cation hf (whose electrochemical valence is Z. ) and v ions of anion Y -(whose electrochemical valence is Z ). For example, for Na2S04 in water, v+ = 2,Z+ = 1, v = 1,Z = -2 since the ions are Na and SO4 Thus Z, - s are positive for cations and negative for anions. If there is an electrical field in the solution, each species, positive and negative, will experience a force due to it according to (3.1.7). 

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