Forces tangential-detaching

Fig. 1.1 Possible cases of particle detachment (a) detachment of monolayer by normal force (b) detachment of layer by normal force (c) detachment of individual particle by tangential force.

The ratio between normal and tangential detachment forces may be related to the particle size and the particle contact area with the surface iirl. To arrive at such a relationship, the detachment force has been represented by Beams [13] in the form of a product of the force Fj per unit contact area and the particle-surface contact area, i.e., Fdet = TrrcFi orFi = At the same time,... 

Equations (1.44) and (1.45) were obtained from data with 180° > a > 0° for the adhesion of spherical glass particles to steel surfaces with these equations, we can use adhesion numbers for a normal or tangential detaching force to determine the adhesion numbers (ja/n and ya/t) the case in which the detaching force is directed at an angle a(pc 0 and a 90°) to the dust-covered surface [14]. 

Equations (1.18) and (1.19) are obtained with angles of 180° > O > 0° for the adhesion of spherical glass particles to steel surfaces [13] by using these equations and the adhesion numbers for the normal or tangential force of detachment, we may determine the adhesion numbers Ta/N Ta/T case in which the de-... 

By analogy with friction, we may distinguish static and kinetic adhesion. Static adhesion is measured by the force of resistance to the onset of detachment, and kinetic adhesion is measured by the interaction between particles and surface in the course of detachment. In order to detach particles, the force of static adhesion is the primary barrier that must be overcome since the kinetic adhesion is always smaller than the static. This situation attracted the attention of G. I. Fuks, who pointed out that static friction is measured by the force directed tangential to the substrate [12]. 

The detachment of dust particles (static adhesion) depends on the magnitude and direction of the force applied to the particle. If the force is applied in a direction normal to the dusty surface (Fig. I.l.a), then for the particles to be detached we must have F et >Fad. For a tangentially directed force (Fig. I.l. c), the moment of the forces is operative, i.e., Afdet = tan (where r is the particle radius). The first stage in the detachment process in this case will be rolling or sliding of the particle i.e., friction as well as adhesion must be overcome. 

Detachment of Particles. The force acting on an adherent particle in the direction perpendicular to the dust-covered surface determines the magnitude of adhesive interaction. If this force is directed tangential to the surface, we are measuring the static friction in the detachment of particles. Under real conditions, the detaching force may be directed at an angle to the dust-covered surface [30-32]. 

If the detaching force is directed perpendicular to the surface, 3 = 1 and Fdet ad the force is directed tangential to the surface, /3 = 0 and F et Fff. The friction of adherent particles in the absence of any external load is caused by adhesion Fg. = /xFgd (where [x is the coefficient of friction). Then, with p = 0,we find that F et Fad -... 

The relationship between adhesion numbers determined by tangential and normal detaching forces is expressed by empirical formulas obtained through treatment of experimental data [14] ... 

In an air medium, y > An analogous relationship was observed by G. I. Fuks [12] in the adhesion of quartz particles with diameters from 0.8 to 15 jum in water and in solutions of certain electrolytes. In this case, is equal to 1.2 to 2.0 times 7, depending on the electrolyte concentration. After detachment of particles by a force directed tangential to the dust-covered surface, they execute a complex movement rolling, sliding, and intermittent shifts. 

Particle detachment was accomplished by a force directed tangential to the surface. 

Thus, by the use of an inhomogeneous electric field and the consequent ponderomotive force directed tangential to the surface being cleaned, dust particles can be removed more thoroughly this has also been confirmed experimentally, in that the detachment of dust particles by the use of rod-type electrodes in more efficient than detachment by the use of continuous (plate-type) electrodes. 

Let us consider the forces acting on a dust particle being detached from a surface. First, we will make the assumption that we can ignore the forces directed tangential to the dust-covered surface this is equivalent to assuming that the electric field is uniform in the direction perpendicular to the surface. Then, after the particle is detached, it is affected only by electrical and gravitational forces. The height to which the particle z will rise can be determined from the equation of particle motion ... 

If the field is inhomogeneous in the transverse direction, the detached particles will experience not only the force, but also a force directed tangential to the dust-covered surface. By the use of the obvious relationships... 

Fig. I.l. Possible cases of the detachment of particles detachment of a monolayer (a) and a thicker layer (b) by a normal force, and of an individual particle by a tangential force (c).

The centrifugal method may be used for determining the adhesion of particles in a drop of water [67]. Dust is deposited on a carefully cleaned surface by means of a very thin, smooth, glass rod. Only a very small part of the surface (D 1.6 mm) need have the dust deposited on it. A drop of water from a calibrated capillary is placed on the dust-laden surface in such a way as to cover the whole of the dust with the drop. Plates are fixed in special holders and with the help of these the detaching forces acting on the drop and particles in directions tangential and perpendicular to the surface may be determined. 

The particles were detached by means of a force directed tangentially to the surface. 

Thus, the inhomogeneity or nonuniformity of the electric field, and the consequent ponderomotive force directed tangentially to the surface being cleaned, offer the best possibility of removing dust particles completely this is in fact confirmed by experiment in that the detachment of dust particles by rod electrodes is more effective than by continuous plates. 

If the field is nonuniform in the transverse direction, a force Fx directed tangentially to the dust-laden surface will act on the detached particles as well as the force Fz. 

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