Adhesive particle detachment

In conclusion, field-flow fractionation is a relatively simple technique for the study of adhesion and detachment of submicrometer or supramicrometer colloidal particles on and from solid surfaces. 

The rate of aggregation will depend essentially on probability of collision between particles, probability of attachment during such colhsions, and probability of their detachment from the aggregates snbsequently. While the probability of collision will depend on the Brownian motion determined essentially by the temperature of the system and on fluid flow motions determined by the viscosity of the fluid medium and external stirring, probabilities of adhesion and detachment are dependent on the type of physicochemical interactions between the particles and, to some extent, on velocity gradients in the medium. 

Adhesion can also be characterized by a number, ocp (in %), defined as the ratio between the number of particles detached under the influence of a certain force and the original number of particles ... 

Average Acceleration in Particle Detachment. The magnitude of adhesion would be better evaluated by means of a single index that would account for the distribution of adherent particles with respect to adhesive forces, i.e., the adhesion numbers and the equivalent adhesive forces. The evaluation of adhesion on the basis of the average adhesive force [18] is such a method. 

The average adhesive force can be determined if we know the average acceleration in particle detachment [19]... 

Thus, in determining the coefficient of removal, it is necessary to know the probabilities of particle detachment and removal. The detachment probability is in turn determined by the average adhesive force and the detaching force [23]. 

From this discussion, it can be seen that the efficiency of removal of adherent particles from different surfaces may be characterized not only by the adhesion number, but also by the coefficient of removal, which is a function of the probability of detachment and removal of the adherent particles. If we know the relationship between the average force of adhesion and the particle size, i.e., Fav - fid), and if the detachment force F et =/( ) is fixed, the method we have just examined can be used to determine the probability of particle detachment over a range of sizes from to c/max ... 

Sion of these particles. Under the action of an external force, particle detachment will take place if the force of detachment is equal to or greater than the force of adhesion (here we must emphasize that the force of detachment under these conditions is acting on adherent particles see Chapter III). With certain assumptions, we can write the following equality ... 

The force of adhesion is equal in magnitude and opposite in sign to the force required for particle detachment. The methods used to determine adhesive force can be divided into two groups on the basis of the specific features of action of the detaching force. 

In view of this situation, it is necessary to resort to indirect methods for the determination of adhesion of such particles, using the results obtained from experiments in particle detachment under identical conditions. The common features of all these indirect techniques is that the magnitude of the detaching force is not actually calculated, but is held constant. 

In apparatus of the second type, the adhesive forces are evaluated by reference to the elongation of a quartz spring at the instant of particle detachment, i.e.. 

A different principle can be used in determining adhesive interaction, i.e., the use of an electromagnet to pull away a fiber and thus detach the particles. The force of detachment is determined on the basis of the current in the electromagnet circuit [93]. The moment of particle detachment can be observed under a microscope. 

In determining adhesion by the particle detachment method, it is necessary to consider the possibility of a shift of the adherent particles as the fiber or sphere approaches. If such a shift does occur, it may distort the results that are obtained. 

Adhesion numbers were determined for the detachment of 30-jum diameter glass particles detached from a glass surface by a pulse method the following results were obtained ... 

First, let us examine the change in adhesion with increasing effective radius of curvature due to a difference in roughness of the substrate. The force of adhesion of gold particles (3-8-jLtm diameter) is affected by the method used in finishing glass surfaces, as follows (particles detached by centrifuging [157]) ... 

The adhesion of particles depends not only on the electrolyte concentration, but also on the cation valence, i.e., whether they are univalent, bivalent,or trivalent [77] this is particularly apparent for solutions with c = lO -lO mol/liter. With decreasing cation valence, particle detachment becomes easier. For example, with a detaching force of 2.7 10"" dyn, 56% of the particles remain when the detachment is performed in a 10" mol/liter solution of KCl, in comparison with 88% in a solution of AICI3 of the same concentration. 

When particles are detached by tilting the surface, the particle detachment depends on the position of these particles relative to the surface. Hence, a study has been made of the adhesion of elongated particles in contact with the surface through the longer and shorter sides of the particle base. The results obtained by detachment of these elongated particles are listed in Table VI.5 [185]. 

Conditions for Particle Detachment. Electrical forces can be used to prevent adhesive interaction or to detach particles already sticking to a surface. 

Estimation of Forces Causing Particle Detachment. Adherent particles may be detached if the forces of detachment are greater than the forces of adhesion and the particle weight. Let us assume that a detaching force acting on a dust particle represents a force of electrical interaction that can be defined by the equation... 

According to this formula, for conductive particles with a diameter of 10 jum and = 20 V/cm, we find that Fqi = 1.5 10 dyn and for particles with a diameter of 100 jum and the same field strength, the force is 1.5 10 dyn. In this case, the forces of electrical interaction exceed the forces of particle adhesion (see Section 19) as measured without the effect on the high-voltage field. Particle detachment, however, is opposed not only by the forces of adhesion ad but also by Coulomb forces (image forces), the forces governed by the electrical double layer Fq with allowance for the charge on the particles in the electric field, and the ponderomotive force Fpon. 

With increasing particle velocity, the force of elastic repulsion increases, making it easier to meet the condition for particle detachment and reducing the number of particles that adhere (Section I in Fig. IX. 1). This drop in number of adhering particles continues until the force of elastic repulsion arrives at equilibrium with the forces opposing particle detachment, i.e., the forces of adhesion. 

The deposition and adhesion of dust particles oii cyHndrical and spherical surfaces takes place in a nonuniform manner. The number of deposited particles of loess dust and the particle diameter are shown as functions of the angle of incidence on a cylindrical surface in Fig. IX.5, for various flow velocities [254]. The number and the maximum size of the deposited particles both fall off as the angle is increased from 0 to 90. For an angle near zero, the flow velocity will be minimal, and hence particle detachment due to aerodynamic drag will be negligible. With an angle p close to 90°, the number of adherent particles will drop off appreciably since the obUque impact gives a rotary motion to the particles. 

Forces Acting on Adherent Particles. When an air stream is flowing over a horizontal dust-covered surface, the particles are subjected to the action of the force of adhesion the particle weight P, the drag" F r, and the lift F f. The conditions for particle detachment can be expressed by the inequality [156]... 

When the relative humidity of the air is increased, we see an increase in the force of adhesion and since the flow velocity at which dust particle detachment occurs will depend on as indicated in Eq. (X.l), we find that as a consequence the velocity det Iso increases. For the detachment of spherical particles with a diameter of 20 fjim with an air relative humidity of 40%, the required flow velocity as determined in [17] was about 10 m/sec with 80% air humidity, the required velocity was 14 m/sec. 

From Eq. (X.51) it follows that the particle detachment depends on the properties of the medium (p, t ), the force of adhesion the particle size d, and the flow velocity v. Particle detachment, under otherwise equal conditions (P, ad> and d = const) will be determined by the flow velocity, which in turn depends on the conditions of flow around the objects or plates of different sizes. Hence, in order to create identical conditions of particle detachment from the model (small plate) and the object in nature (larger plate), the process of flow around the object must be modeled. Such modeling should bring about the establishemnt of an identical drag for the detachment of adherent particles under the model conditions and natural conditions in the case of laminar and turbulent boundary layers. 

In the turbulent flow regime, the thickness of the laminar sublayer represents the limit above which adhesion is impossible or difficult (see Fig. X.l). Hence, identical conditions or particle detachment can be expressed in the following manner ... 

In place of the adhesion number, the probability of detachment can be used for quantitative characterization of particle detachment by an air stream. If the probability of particle removal is equal to unity, i.e., if = 1, then, from Eq. (1.4) with due regard to the relationship between the removal coefficient and the adhesion number (Kjsr = I/tf) we obtain the relationship between the detachment probability and adhesion number = 1 - 7. When the adhesion number is zero, -Pd 1 when the adhesion number is unity, the detachment probability... 

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