Macroscopic particles

There are several distinctive features worth noting about the JKR equation. The first is in the limit of no adhesion (or, equivalently, large applied loads, as commonly occurs with macroscopic particles), Eq. 24 reduces to the Hertz equation... 

Macroscopic particles Microscopic particles Chemical grouting... 

The properties of the filter-cake formed by macroscopic particles can be significantly influenced by certain organic additives. The overall mechanism of water-soluble fluid loss additives has been studied by determining the electrophoretic mobility of filter-cake fines. Water-soluble fluid loss additives are... 

Classical mechanics which correctly describes the behaviour of macroscopic particles like bullets or space craft is not derived from more basic principles. It derives from the three laws of motion proposed by Newton. The only justification for this model is the fact that a logical mathematical development of a mechanical system, based on these laws, is fully consistent... 

Equation 6.1 is valid for a macroscopic particle moving in a continuous medium. In electrophoresis where the analyte ion moves in the media where particle size is comparable with that of the analyte size, this is definitely not the case. Also, analyte ions are not spherical and the term of the ionic radius, the value of which is difficult to estimate, becomes ambiguous. Thus, even in... 

The interaction between individual molecules obviously plays an important role in determining, for example, the nonideality of gas, as illustrated in Example 10.2. It is less clear how to apply this insight to dispersed particles in the colloidal size range. If atomic interactions are assumed to be additive, however, then the extension to macroscopic particles is not particularly difficult. Moreover, when dealing with objects larger than atomic dimensions, we also... 

Fig. 6.32. The decay in time of the macroscopic particle concentration for asymmetric (a) and symmetric (b) cases corresponding to >a = 0 and Da = Dr respectively. The initial concentration n(0) =0.1. Parameter rc/r 1(1) 2(2) 3(3). Full curves show many-particle effects, whereas dotted line shows results of their neglect.

You may, for example, see it written that aluminium is one of the most abundant elements in the Earth s crust . This, of course, does not mean that macroscopic particles of the light, silvery metallic substance from which jumbo jets and saucepans are largely fabricated are to be found in nature. Element has become a collective term, and encompasses all the atoms having a particular atomic number, regardless of their state of chemical combination. We must therefore be careful to refer to an elemental substance if that is what we mean. Thus when we say that lead occurs in sulphide minerals , we are referring to an element the statement that lead reacts only slowly with dilute hydrochloric acid obviously... 

Fig.2. Interaction forces acting in vacuum between a two atoms (f r 7) and b macroscopic particles (e.g., for surface-sphere interaction, F D 2). The tip position at D=0 corresponds to the tip-sample contact, while the range at D<0 corresponds to the sample indentation...

With these assumptions a common characteristic of all macroscopic particle systems can be expressed as qr = exp(e,) = exp(2jt + a) (assumptions 1 and 2). However, taking into consideration a diminution of er which is proportional to the maximum probability pe of place exchange (assumption 3), the value qr = exp(erpe) = exp[(a + 2Jt)/e] = eaf e27t/c = CI/ew becomes the specific relative density of interaction energy for a system where w = e2 and Cl/e = elx/e. 

Bentonite is a colloidal clay that is both hydrophilic and organophilic. It is waterswelling with some types of clay absorbing as much as 5 times their own weight in water. It is used in emulsions, adhesives, and sealants. It is a gritty, abrasive white particle filler. A macroscopic particle of bentonite is composed of many thousands of stacked and/or overlapped submicroscopic flakes. 

The DLVO theory [1,2], which describes the interaction in colloidal dispersions, is widely used now when studying behavior of colloidal systems. According to the theory, the pair interaction potential of a couple of macroscopic particles is calculated on the basis of additivity of the repulsive and attractive components. For truly electrostatic systems, a repulsive part is due to the electrostatic interaction of likely charged macroscopic objects. If colloidal particles are immersed into an electrolyte solution, this repulsive, Coulombic interaction is shielded by counterions, which are forming the diffuse layer around particles. A significant interaction occurs only when two double layers are sufficiently overlapping during approach of those particles. 

An attractive interaction arises due to the van der Waals forces between molecules of colloidal particles. Depending on the nature of dispersed particles, the Keesom forces (or the dipole-dipole interaction), the Debye forces (or dipole-induced dipole interaction), and the London forces (or induced dipole-induced dipole interaction) may contribute to the van der Waals interaction. First, the van der Waals interaction was theoretically computed using a method of the pairwise summation of interactions between different pairs of molecules of the two macroscopic particles. This method called the microscopic approximation neglects collective effects, and, as a consequence, misrepresents the Hamaker constant. For many problems of a practical use, however, specific features of the total interaction are determined by a repulsive part, and such an effective, gross description of the van der Waals interaction may often be accepted [3]. The collective effects in the van der Waals interaction have been taken into account in the calculations of Lifshitz et al. [4], and their method is known in the literature as the macroscopic approach. 

As was discussed in Section 3.33, Arrhenius29 assumed that, at a macroscopic temperature T, if a system has two states, namely (1) a ground state G with energy UG and a macroscopic particle occupation number Nc and (2) an upper or excited state U, with energy UE and occupation number NEr then the ratio of particles in the two states is given by... 

PROBLEM 5.2.5. Classical MB statistics. Same as in Problem 5.2.1, but now use macroscopic particles, which are distinguishable. Show that can we distribute these N boltzons in fB ways, where... 

All these methods have many features in common but at the same time they bear noticeable differences. For example, in foam flotation of macroscopic particles (suspensions),... 

Cross-linking the enzyme to itself or to other macroscopic particles (protein) with bifunctional coupling reagents to localize the immobilized enzyme as a thin layer over the electrode. 

If an oil-soluble monomer is dispersed in a continuous aqueous phase without the use of surfactants, suspension polymerization results. The viscosity of the resulting suspension will remain essentially constant over the course of the polymerization. Oil-soluble free radical initiators are used to effect polymerization. The monomer is dispersed into beads by the action of an agitator. Since little or no surfactant is used, no emulsification takes place, and, if the agitation is stopped, the monomer will form a separate bulk phase, usually above the aqueous phase. The monomer is polymerized by the initiator within the droplets, forming polymer beads of approximately the same size as the monomer droplets (0.1-10 mm diameter). The product can be readily separated from the aqueous phase (via filtration or decantation) in the form of macroscopic particles or beads, which can be easily packaged and/or transported. Heat transfer is facihtated by the presence of the continuous aqueous phase. Blocking agents such as clays or talcs are used to prevent particle ag-... 

Figure 6.4. Comparison of the surface area/volume ratio of macroscopic particles (marbles) and nanoscopic aluminum oxide particles. Since nanoparticules contain a proportionately large number of surface atoms, there are a significantly greater number of adsorption/reaction sites that are available to interact with the surrounding environment. Further, whereas bending of a bulk metal occurs via movement of grains in the >100nm size regime, metallic nanostructures will have extreme hardness, with significantly different malleability/ductility relative to the bulk material.

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