Finger Formation

Suppose that the ribbon, in the process of spreading vei slowly [V oc I (kIiq), with 1 = f/t/], is iinmcrsed in a thermal gradient. Its free surface is the seat of astress (t,/d.T, creating a shear How of velocity t/v(z) = zih/ds and a material flow J = j v(z)dz = hoVo, when I o is gi -en by 

If Vq V5, a ridge forms at the line of contact and grows until the dynamical angle Ojj becoinos such that the advancing velocity Vs — V 6j equals V( At that point, the profile of the ridge becomes stationary in the frame of reference of the line of contact. It is then governed by equation (10.24) in which J = cVq and P  

Likewise, we can define a characteristic time tq by way of a dimensional analysis  

FIGURE 10.10. Dependence of the wavelength A and the characteristic time r of the periodic instability of the liquid front as functions of the initial thickness ho of the film. 

FIGURE 10.11. Festoon instability. Snapshot of a drop of low-volatlliiy. silicone oil (2-// volume. -liO-g molecular ma.ss). Optical interference can t e soon at the surface of the lrop. A liquid ridge forms around the i)erii)hery of the (Iroj) an l the line has a spatially inodulate l pattern. (From C- Re lon. F. Brocliard. and F. Rondelez, in Joimiaf. df- Physique II France, 2. 1671 (UM)2). EDP Sciences. Reproduced by pennission.) 

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Figure 15. Schematic diagram of finger formation at various times during precipitation.

Fig. 2.75 Belite particles with overlapping fingers formation in industrial clinker...

Fig. 6.10 Drying of a hemispherical suspension particle on a cooled glass sheet. Left to right Intrusion ofair fingers, formation of wet isles, migration of colored (dark) liquid towards the surface and deposition of the dissolved dark color at the outer rim of the particle.

Skin and Finger Formation. First attention is turned to the application of the model to the coagulation of a solution of 20% Nomex , an aromatic polyamide commercialized by DuPont, dissolved in Al-methylp5TTolidinone (NMP). An estimation of the range of veilues of the model pareuneters can be found in Reference 22. Figure 8 shows the calculated morphology obtained... 

R.J. Ray, W.B. Krantz, and R.L. Sani, Linear-stability theory model for finger formation in asymmetric membranes. Journal of Membrane Science 23 (1985) 155-182. 

Fig. 1. Formation of an ultrafUtration membrane A, unprecipitated polymer solution B, polymer solution separating into two phases C, pore fingers with...

The lack of zinc can also be a problem in biological systems and is responsible for disease states. For example, nitric oxide-dependent apoptosis can be induced in motor neurons by zinc-deficient SOD, and in some cases of amyotrophic lateral sclerosis, zinc-deficient SOD may participate in this type of oxidative mechanism involving nitric oxide.969 One form of hereditary human hair loss or alopecia was mapped to a specific gene and a mutation found in affected individuals. The gene encodes a single zinc finger transcription factor protein with restricted expression in the brain and skin.970 Zinc has been implicated in Alzheimer s via beta amyloid formation, and a role has been attributed for the cerebral zinc metabolism in the neuropathogenesis of Alzheimer s disease.971... 

Models of lipid bilayers have been employed widely to investigate diffusion properties across membranes through assisted and non-assisted mechanisms. Simple monovalent ions, e.g., Na+, K+, and Cl, have been shown to play a crucial role in intercellular communication. In order to enter the cell, the ion must preliminarily permeate the membrane that acts as an impervious wall towards the cytoplasm. Passive transport of Na+ and Cl ions across membranes has been investigated using a model lipid bilayer that undergoes severe deformations upon translocation of the ions across the aqueous interface [126]. This process is accompanied by thinning defects in the membrane and the formation of water fingers that ensure appropriate hydration of the ion as it permeates the hydrophobic environment. 

The traditional way of making these products is to mix the fat and the flour, a process known as rubbing in the fat. This name is understandable, deriving from the time when the fat was literally rubbed into the flour with the finger tips - this has the effect of water proofing the flour, which reduces gluten formation as the proteins need to absorb water for... 

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