Detachment forces

A method that has been rather widely used involves the determination of the force to detach a ring or loop of wire from the surface of a liquid. It is generally attributed to du Noiiy [42]. As with all detachment methods, one supposes that a first approximation to the detachment force is given by the surface tension multiplied by the periphery of the surface detached. Thus, for a ring, as illustrated in Fig. II-ll,... 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

Once it is recognized that particles adhere to a substrate so strongly that cohesive fracture often results upon application of a detachment force and that the contact region is better describable as an interphase [ 18J rather than a sharp demarcation or interface, the concept of treating a particle as an entity that is totally distinct from the substrate vanishes. Rather, one begins to see the substrate-particle structure somewhat as a composite material. To paraphrase this concept, one could, in many instances, treat surface roughness (a.k.a. asperities) as particles appended to the surface of a substrate. These asperities control the adhesion between two macroscopic bodies. 

As can be seen, the DMT detachment force is greater than that predicted by the JKR theory. 

As previously discussed, the JKR theory predicts that the detachment force is independent of the Young s modulus. Yet despite that, when Gady et al. [117] measured the detachment force of polystyrene particles from two elastomeric substrates having Young s moduli of 3.8 and 320 MPa, respectively, they found that the detachment force from only the more compliant substrate agreed with the predicted value. The force needed to separate the particle from the more rigid substrate was about a factor of 20 lower. Estimates of the penetration depth revealed that the particles would penetrate into the more compliant substrate more deeply than the heights of the asperities. Thus, in that case, the spherical particle approximation would be reasonable. On the other hand, the penetration depth... 

A similar analysis can be done for the curved surface of an essentially spherical particle that contains asperities. Let us assume that all the asperities are the same size. Initially, no more than three asperities on the particle can contact the presumably smooth surface. As the asperities compress under the applied load, more asperities, that are situated further away from the substrate due to the curvature of the particle s surface, come into contact. These are the first to separate from the substrate upon application of a detachment force. In essence, detachment occurs by breaking the contacts between the asperities and the contacting surface, one at a time. 

According to Duchene et al. [17], when tensiometry is used to measure the maximum detachment force as a function of the displacement of the upper support (function of the joint elongation), the work of bioadhesion can be defined as in Eq. (7). 

Targeting Hgands can be attached to the microbubble directly (Fig. 12 A) or via a flexible polymer spacer arm (e.g., polyoxyethylene. Fig. 12 C). Use of the spacer arm may allow for tighter binding in some situations. When the detachment force of the targeted microbubble removal from the receptor-coated surface was measured, microbubbles with spacer-ligand construct demonstrated superior retention as compared with the bubbles where the ligand was connected directly to the lipid anchor, without a spacer [92]. 

TWA, total work of adhesion MDF, maximum detachment force. 

The detachment force is related to the surface or interfacial tension by the expression... 

All presented forces are detaching forces. An increase in these forces will decrease the diameter of the droplets. On the contrary, the interfacial force caused by a uniform interfacial tension along the pore border is a holding force increasing this force will... 

The detachment force that realizes the detachment of the assembly microparticle-deposition element when the number of the... 

The detaching force, f, is the buoyancy of the bubble, which acts vertically upward (perpendicular to the surface under the conditions in consideration). 

Fig, 3 Dynamic strength spectra defined by most likely bond detachment force / vs. log floading rate = rp r°), where the loading rate scale = (fp/ti,)exp( — EJkgT) is set by thermal force/p = kpT/Xp, diffusive... 

The calculation of the term (Ttr /Vl-) is possible from knowing the detachment force AmaxT, the pin radius r, and the density of the liquid p according to the equation... 

It is a widely used detachment method, in which the force to detach a ring from the surface of the liquid is determined. In the first approximation, the detachment force is supposed to be equal to the surface tension multiplied by the periphery of the surface to be detached. For a ring we can thus write... 

The basis of this method is to measure the force required to detach a ring or loop of wire from the L/L interface [9]. As a first approximation, the detachment force is taken to be equal to the interfacial tension y, multiplied by the perimeter of the... 

The detachment of a ring or a plate (a Wilhelmy plate) from the surface of a liquid or solution is a static surface tension measurement method, which gives the detachment force of a film of the liquid and its extension from the liquid surface. These methods are less accurate than the capillary rise method, but they are normally employed in most surface laboratories because of their ease and rapidity. 

The force F required to detach a well-wetted thin ring of radius rr, from the liquid surface is measured in the duNotiy ring detachment method [6,26]. Within the first approximation one can assume that the equation relating the surface tension, a, to the detachment force, F, is analogous to that used in the Wilhelmy plate method, with the exception that the perimeter of the ring is used in place of the plate width, i.e. F = 4nrro. In reality, however, the curvature of the liquid surface at points of contact with a ring causes the surface tension vectors to be somewhat off the vertical (Fig. 1-19). 

When passing from Stokes field to the potential field of a bubble, hydrodynamic detachment forces grow / Up times. The radial velocity of the liquid flow at a distance of maximum... 

Hydrodynamic resistance, determining the rising velocity of bubbles, comprises the resistance of the shape, which depends on the position of the hydrodynamic flow separation line on the spherical bubble surface and the viscous resistance, which is a fimction of the degree of retardation of the whole surface. Since the contribution of viscous resistance is not small at Re < 40, the whole lower part of the bubble is strongly retarded. Otherwise the bubble velocity would strongly differ from the velocity of a solid sphere. It follows that at 1 < Re < 40 the detachment force increases insignificantly compared with the detachment force under the Stokes regime. 

Two techniques decrease the possibility of particle detachment. One consists of the use of reagents which decrease the non-electrostatic component of the disjoining pressure. The second technique consists of choosing bubble size and hydrodynamic regime so as to decrease detachment forces. 

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