Mushy layer

The boundary conditions at the bottom of the mushy layer at the cooled surface z = 0 are ... 

The model is used to predict the flow within the interstices of the mushy layer on the overall growth rate and on the distribution of solid within it. Further, the redistribution of solute is calculated indicating the level of macrosegregafion to be expected in a fully solidified system. 

From the solution of the above equations, Lu and Chen [108] showed that a liquid plume which carries a cooler and less concentrated fluid is released from the mushy region and penetrates into the fluid layer, forming plume convection. It was shown that two types of convection patterns form in the system. The first is a convection pattern circulating between the mushy layer and the fluid layer with a length scale of about the height of the mushy layer. This pattern is called the mushy layer mode (MLM). The second pattern forms above the melt/mush interface and is called BLM. 

Figure 10.7 shows the critical flow patterns obtained with the three models. It is shown that BLM is a convection cell sitting above the mush/melt interface and MLM consists of two separated cells, one in the mushy layer and one in the fluid layer. The critical flow patterns for the three models are similar except that the critical wavelength differs from one another. 

Studies employing the multi-domain method usually consider solidification problems cooled from the bottom. There are primarily three approaches for treating boundary conditions between the mush-melt and solid-mush interfaces in the multi-domain approach,. The first model to be considered is that used by Worster [2] and Chen et al. [97] in which the Darcy s equation is employed as the momentum equation in the mushy layer and the Navier-Stokes equation as the momentum equation in the fluid layer and no-slip boundary condition is prescribed at the melt-mushy interface. 

Consider a mushy layer that lies above a static solid region and below a semiinfinite fluid region in a binary solution of concentration Coo, and temperature Too, and unidirectional solidification from below. Both the melt/mushy and mushy/solid interfaces move upwards with a constant velocity V. The mushy layer extends form z = 0 to z = h x, y. t). The boundary conditions at the Z -> oo are. 

Worster [99] employed the non-slip condition based on the assumption that the characteristic length scale of the flow on the melt/mushy interface is much larger than the space between the arms of the dendrite. This in general sense may not be the case since the BLM convection prevails in the system for most of the cases considered in the experiments. An alternative (the second model) was proposed by Beavers and Joseph [105] who systematically developed an empirical relation between the horizontal velocities of the fluid and the porous layer (or a homogenous and isotropic mushy layer) based on a series of experiments. This condition primarily allows a slip between the velocities above and below the melt/mushy interface. This condition can be expressed as... 

Worster MG (1991) Natural convection in a mushy layer. J Fluid Mech 167 481-501... 

Anderson DM, Worster MG (1995) Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys. J Fluid Mech 302 307... 

Feltham, D. L. Worster, M. G. 1998 Flow-induced instability of a mushy layer J. Fluid Mech. (under consideration). 

The mushy residue is shaken with 250-300 ml. of water until the sodium acetate dissolves. The oily layer of lactone is separated, and the aqueous phase is extracted with two 100-ml. portions of ether. The combined oil and ether extracts are washed with 150 ml. of water and dried overnight over anhydrous sodium sulfate. The ether is removed under reduced pressure, and the product is distilled from a modified Claisen flask. The fraction boiling at 160—170°/11 mm. is collected refractionation yields 107-114 g. (61-64%) of product boiling at 164-168°/11 mm. or 151-156°/8 mm. 1.4815-1.4830 (Notes 6 and 7). 

Each generic foam type had a characteristic failure mode. Polyurethane foams exhibited fine hairline through cracks that grew in length and width polymethacrylimide foams exhibited arc-shaped surface cracks that grew in depth and length the polyisocyanurate foams became soft and mushy on the side bonded to the tank. Insulations poured or sprayed in layers failed at the interlayer boundaries. 

---