In the apparatus
pictured above the ammonium chloride solution flows in from the left,
through the narrows and over the test section. The fluid then
exits the flume through the exit. The copper base plate of the
test section is cooled via a brass manifold and an array of Peltier
devices pictured in the test section inlay. This cooling results
in a crystalline matrix growing from the base of the test section as
pictured at great magnification in the inlay entitled "mushy layer."
In the absence of a shear flow this mushy layer has a vertical porosity profile but is otherwise homogeneous on a scale much larger than the individual dendrites. However, as an external flow is applied we find that this matrix is unstable to tessellations of the phase fraction perpendicular to the flow as pictured below.
A tessellation movie shows both a planview image of the test section as well as a shadowgraph image of the convection initiated above the solidifying medium. The first segment of the movie shows uniform growth in the absence of a shear flow, then the external flow is initiated and convection is confined to a small boundary layer. In addition, the porosity of the mush becomes unstable to a series of tessellations of zero solid fraction which appear first as dark lines. These tessellations then coarsen into chimneys.
In the figure above we see that, in the absence of flow, this decrease in porosity (and hence permeability) due to the addition of CuSO4 (given in wt% within the figure) is manifest as a delay in convection within the mush. This convection locally dissolves the mush and leads to the formation of chimneys; regions of zero solid fraction.
Using our ability to control both the porosity of the mush via CuSO4 and the range of flow speads accessible with the laboratory flume we have explored the phase space as pictured below.
In the absence of a shear flow this mushy layer has a vertical porosity profile but is otherwise homogeneous on a scale much larger than the individual dendrites. However, as an external flow is applied we find that this matrix is unstable to tessellations of the phase fraction perpendicular to the flow as pictured below.
A tessellation movie shows both a planview image of the test section as well as a shadowgraph image of the convection initiated above the solidifying medium. The first segment of the movie shows uniform growth in the absence of a shear flow, then the external flow is initiated and convection is confined to a small boundary layer. In addition, the porosity of the mush becomes unstable to a series of tessellations of zero solid fraction which appear first as dark lines. These tessellations then coarsen into chimneys.
Phase Diagram
The stability of the mush to tessellations of the solid fraction is principally governed by the external flow velocity and the unperturbed permeability of the mushy layer. With the flume pictured above we are able to obtain flow rates up to 14 cm/s over the test section. We are also able to decrease the porosity of the mush by doping the NH4Cl solution with small quantities of copper sulfate (CuSO4).In the figure above we see that, in the absence of flow, this decrease in porosity (and hence permeability) due to the addition of CuSO4 (given in wt% within the figure) is manifest as a delay in convection within the mush. This convection locally dissolves the mush and leads to the formation of chimneys; regions of zero solid fraction.
Using our ability to control both the porosity of the mush via CuSO4 and the range of flow speads accessible with the laboratory flume we have explored the phase space as pictured below.
We find that above a
critical permeability and flow rate the mush becomes unstable to
variations in solid fraction evident as dark striations in the planform
images.