Deformable Particles

Limitations Some applications which seem ideal for MF, for example the clarification of apple juice, are done with UF instead. The reason is the presence of deformable solids which easily plug and blind an MF membrane. The pores of an ultrafiltration membrane are so small that this plugging does not occur, and high fluxes are maintained. UF can be used because there is no soluble macromolecule in the juice that is desired in the filtrate. There are a few other significant applications where MF seems obvious, but is not used because of deformable particle plugging. 

This assumption is based on the fact that PTFE agglomerates are soft and deformable particles in comparison to conventional (hard) fillers such as carbon black and silica for which (2) was originally derived. Morphological analysis (shown in Fig. 5) reveals that PTFE agglomerates can be considered as soft deformable particles. 

Figures 4A and 4B are the ultra-thin cross-sections of OsOi+-stained two-stage (styrene//styrene-butadiene) and (styrene-butadiene/ /styrene) latex particles at the stage ratio of 50/50 (LS-10 and LS-11), respectively. Latex samples were mixed with a polymerizable monomer mix of butyl and methyl methacrylates, cured, and microtomed for examination. Figure 4A shows particle cross-sections much smaller than the actual particle size of LS-10. It appears that since the embedding monomer solution was a solvent for polystyrene, the continuous polystyrene phase was dissolved and small S/B copolymer microdomains were left behind. This is further evidence that the second-stage S-B copolymers phase-separated as microdomains within the first-stage polystyrene phase, as shown in Figures 1A and 1A. Figure 4B shows somewhat swollen and deformed particle cross-sections, suggesting that the first-stage cross-linked S-B copolymers were a continuous phase. Indeed, the former (LS-10) behaved like a hard latex, but the latter (LS-11) behaved like a soft latex.

Deformation of a Sphere in Various Types of Flows A spherical liquid particle of radius 0.5 in is placed in a liquid medium of identical physical properties. Plot the shape of the particle (a) after 1 s and 2 s in simple shear flow with y 2s1 (b) after 1 s and 2 s in steady elongational flow with e = 1 s 1. (c) In each case, the ratio of the surface area of the deformed particle to the initial one can be calculated. What does this ratio represent ... 

Barker and Grimson (1991) modeled the flow of deformable particles after a free-draining floe whose shape, orientation, and internal structure ranged between the extremes of an extended chain and a folded globule. They interpreted the unhindered motions of free-flowing, deformable droplets to result from an unbalanced force imposed by the flow field, resulting in rotations around the particles center of mass this rotation is superimposed on the steady translational motion. 

Barker, G. C., and Grimson, M. J. (1991). Computer simulations of the flow of deformable particles. In Food Polymers, Cels and Colloids, Dickinson, E. (Ed.), pp. 262-271. Royal Chem. Soc., London. 

Now we consider the resistive force characterizing the movement of the particle along the streamline expressed as the product between tensor and its normal surface A (A = m/p.s j where Sj is the apparent height of the deformed particle)... 

Using the dimensionless velocity and streamline position, and completing these values with the dimensionless height of the deformable particle S(ja = S(j/1, Eq. (6.102) can be written as ... 

Materials analyzed by FFF range from high-density metals and low-density latex microspheres to deformable particles such as emulsions and biological cells. The particles need not be spherical since separation is based on effective particle mass. 

Emulsions, microemulsions, and liquid crystalline systems are suspensions of deformable particles, and many of the principles stated earlier for suspensions are valid to a similar extent. The effect of the phase volume, however, is less pronounced. ... 

The upper punch is withdrawn from the die, and so the force being applied to the tablet is removed. The effect of this might be to cause the deformed particles to return to their former shape, which would result in a decrease in interparticulate contact and hence tablet strength. It is essential that this does not occur. As the upper punch leaves the die, the lower punch moves upwards, pushing the tablet before it. During the compression stage, the particles are forced into intimate contact with the interior die wall. It follows that attempts to remove the tablet will be opposed by frictional forces and so successful ejection demands lack of adhesion between the tablet and the diewall. 

Particles remain deformed Particles return to former shape remain Cohesion maintained Cohesion lost fragmented... 

H.M. Princen, The Equilibrium Shape of Interfaces, Drops and Bubbles. Rigid and Deformable Particles at Interfaces, in Surface and Colloid Science, E. Matijevic, Ed., Wiley-Interscience (1969), 1. (Analysis of a variety of shapes, including those around floating fluid or solid objects.)... 

It can be assumed that molecular forces can be fully transmitted if the adsorption layer is thinner than 3 nm. Such forces are often high enough to deform particles at the contact points, causing larger contact areas and higher strength of the bond between adhering partners. The application of external forces may increase the contact area further. 

Fig. 4 Two deformable particles (i and j) compressed against each other and interacting elastically through their contacting facet...

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