Two-dimensional etching

Foam generated in porous media consists of a gas (or a liquid) dispersed in a second interconnected wetting liquid phase, usually an aqueous surfactant solution (1). Figure 1 shows a micrograph of foam flowing in a two-dimensional etched-glass porous medium micromodel (replicated from a Kuparuk sandstone, Prudhoe Bay, Alaska (2)). Observe that the dispersion microstructure is not that of bulk foam. Rather discontinuous... 

Figure 1. Micrograph of foam in a 1.1 pm, two dimensional etched-glass micromodel of a Kuparuk sandstone. Bright areas reflect the solid matrix while grey areas correspond to wetting aqueous surfactant solution next to the pore walls. Pore throats are about 30 to 70 /xm in size. Gas bubbles separated by lamellae (dark lines) are seen as the nonwetting "foam" phase.

Figure 5.18. Difference between (a) growth steps and (b) steps formed by two-dimensional etching.

Another attractive feature of two-dimensional network models is the fact that they can be carefully tested with laboratory experiments on well-defined porous media that closely replicate the media in the model. Thus, at this level the ambiguities that arise from the necessarily simplified description of a natural porous medium can be avoided. Experimental work on flow in two-dimensional etched media is represented by Chapter 12 by Shirley. Chapter 13, by Elsik... 

C. R. Tellier and A. Brahim-Bounab, Anisotropic etching of silicon crystals in KOH solution—Part II. Theoretical two-dimensional etched shapes Discussion of the adequation of the dissolution slowness surface, J. Mater. Sci. 29, 6354, 1994. 

Figure 12.7. Spiral step patterns observed on (a) 0001) and (b) 1011) faces of hematite. In (a), smooth growth steps are retarded two-dimensionally by etching, producing rough dissolution steps [3]-[6].

Parallel-plate radial flow CF4 etching Si Two-dimensional isothermal Navier-Stokes Ambipolar diffusion with assumed electron density and energy 84... 

Samalam [43] modeled the convective heat transfer in water flowing through microchannels etched in the back of silicon wafers. The problem was reduced to a quasi-two dimensional non-linear differential equation under certain reasonably simplified and physically justifiable conditions, and was solved exactly. The optimum channel dimensions (width and spacing) were obtained analytically for a low thermal resistance. The calculations show that optimizing the channel dimensions for low aspect ratio channels is much more important than for large aspect ratios. However, a crucial approximation that the fluid thermophysical properties are independent of temperature was made, which could be a source of considerable error, especially in microchannels with heat transfer. 

C. Spinella, V. Raineri, and S. U. Campisano, Selective etching of B-doped silicon Mechanisms and two-dimensional delineation of concentration profiles, J. Electrochem. Soc. 142, 1601, 1995. 

PS—alkyne probe, followed by a CC reaction to introduce a biotin tag with a tobacco etch virus (TEV) protease cleavage site. Tagged proteins were then enriched with streptavidin beads and subsequendy digested by trypsin. The supernatant contained peptide fragments of the enriched proteins and was, in contrast to the previous procedure, saved for subsequent analysis by multidimensional protein identification technology (MudPIT), a novel two-dimensional LC—MS/MS analysis method that will be discussed in more detail... 

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