Microscale gradients

Beyenal H, Babanta JT. Microscale gradients and their role in electron-transfer mechanisms in biofilms. Biochem Soc Trans 2012 40 1315-1318. 

Babauta JT, Nguyen HD, Istanbullu O, Beyenal H. Microscale gradients of oxygen, hydrogen peroxide, and pH in freshwater cathodic biofilms. ChemSusChem 2013 6(7) 1252-1261. 

Babanta JT et al. Microscale Gradients of Oxygen, Hydrogen Peroxide, and pH in Freshwater Cathodic Biofilms. Chemsuschem 2013 6(7) 1252-1261. 

Vacha M, Yokoyama N, Tokizaki T, Furuki M and Tani T 1999 Laser scanning microscope for low temperature single molecule and microscale spectroscopy based on gradient index optics Rev. Sc/. Instrum. 70 2041-5... 

J. M. Catchmark, S. Subramanian, and A. Sen, Directed rotational motion of microscale objects using interfacial tension gradients continually generated via catalytic reactions. Small 1,1—5 (2005). 

Instead of assuming that diffusive fluxes occur only vertically, following the macroscopic, measurable, large-scale concentration gradients, it seems reasonable to consider also lateral microscale concentration gradients within microniches (57-59). 

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Costin, C.D., Synovec, R.E., A microscale-molecular weight sensor probing molecular diffusion between adjacent laminar flows by refractive index gradient detection. Anal. Chem. 2002, 74, 4558 1565. 

Carbon-14 content is measured by specially designed gas proportional counters (7. Aerosol samples are first converted to CO2 by combustion in a macroscale version of the thermal evolution technique. A clam shell oven was used to heat the sample for sequential evolution of organic and elemental carbon under equivalent conditions. Due to the possibility of thermal gradients, conditions in the macroscale apparatus were adjusted to produce the same recoveries of total carbon (yg C per cm of filter area) as for the microscale apparatus. Carbon-14 data are reported as % contemporary carbon based on the 1978 1 C02 content in the atmosphere. Aldehyde data referred to in this paper were obtained by impinger sampling in dinitrophenylhydrazine/acetonitrile solution and analysis of the derivatives by HPLC with UV detection (12). Olefin measurements were made by a specially designed ozone-chemiluminescence apparatus (13) difficulties in calibration accuracy and background drift with temperature limit its use to inferences of relative reactive hydrocarbon levels. 

By introducing a time lag denoted as x (which may be related to the relaxation time of the PFPEs), the flux vector j, and the concentration (or proportional to film thickness, h) gradient V/i guarantee causality. Inspired by the microscale... 

This inaccuracy stems from their calculation of molecular transport effects, such as viscous dissipation and thermal conduction, from bulk flow quantities, such as mean flow velocity and temperature. This approximation of microscale phenomena with macroscale information fails as the characteristic length of the (gaseous) flow gradients approaches the average distance travelled by molecules between collisions - the mean path. The ratio of these quantities is referred to as Knudsen number. 

The collisions of drops or particles smaller than the microscale of turbulence are caused by two independent and essentially different mechanisms. These mechanisms differ depending upon whether the droplet has a density the same as or different from that of the surrounding fluid. Drops or particles that have essentially the same density as the surrounding fluid follow the motion of fluid completely. Thus, droplet velocity fluctuations can be described by the fluid velocity fluctuations. Under these conditions Saffman and Tbrner (S3) obtained the following expression by employing the gradient mechanism ... 

The boundary conditions are specified temperatures or zero slope at the walls and zero slope at any planes of symmetry. Compare Equations 8.20 and 8.24. The major difference is that is now a function of x and y rather than just r. Compare also Equations 8.50 and 8.51. Elows in the cross-channel directions that correspond to Vr have been ignored because cross-channel diffusion in microscale devices will largely eliminate the concentration and temperature gradients that drive these flows. 

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