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Invited Article: Refractive index matched scanning of dense granular materials
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Image of FIG. 1.
FIG. 1.

(a) A schematic overview of a RIMS setup, with all the essential components indicated. (b) A typical cross section of a suspension, obtained with RIMS. Particles (diameter 5 mm) appear as dark spots in a bright background. (c) A stack of cross sections. Brightness is inverted for clarity. (d) From subsequent volume scans, one can obtain particle traces; a few examples are shown here as red/gray lines in the box. The flow is driven from the bottom by a rotating disk, hence the circular trajectories. The stochastic motion of the particles is clearly visible.

Image of FIG. 2.
FIG. 2.

The lengthscales encountered in a RIMS setup. The scan volume size is L, the particle diameter is d, the laser sheet to camera distance is r. The focal point of the laser is at distance f, the sheet thickness is e, and the focusing width (see text) is w.

Image of FIG. 3.
FIG. 3.

Top views of a cross section of a RIMS volume. The laser sheet shines from the right and intersects a layer in which only the dyed fluid is present. (a) With a high dye concentration, the gradient in the fluorescence is clearly visible. (b) Using a lower dye concentration, the contrast is decreased, and even deep in the box, far to the left, fluorescence is still observed.

Image of FIG. 4.
FIG. 4.

(a) A cross section of BK7 glass spheres in a fluid with varying index of refraction (see text). The number indicates the index mismatch n f − n B (see text) from the best matched sample (center). (b)–(d) Images of 3 mm glass beads at best index matching, ∼15 layers deep, for (b) soda-lime glass, (c) crystal glass, (d) BK7 glass.

Image of FIG. 5.
FIG. 5.

Ray-traced images of the visibility of a red cone and a red disk buried under seven layers of particles, in a box with about 25 particle layers between cone and camera. (a) The perspective; the arrow indicates from which direction the cone is observed. (b) The effect of index mismatch n f − n B by keeping the index of the fluid n f = 1.500 constant. (c) The effect of a spread with standard deviation of 0.001 in the index of refraction of the beads; the mean n B = n f = 1.500. (d) The effect of the number of layers N imaged, with an index difference of 0.001 between the fluid and the particles and no index spread in the particles.

Image of FIG. 6.
FIG. 6.

(a) The reference image for index mismatch measurements (see text). (b) Measurements of the image distortion at different fluid indices. Image (I) refers to worse matching and (II) refers to best matching.

Image of FIG. 7.
FIG. 7.

Various timescales encountered in RIMS setups. The strain rate is set by the type of experiment. Volume scan time should be small enough to image a whole volume before the strain becomes too large. The data rate is tied to the volume scan time and is limited by the camera system and other setup components, as discussed in the text.

Image of FIG. 8.
FIG. 8.

(a) Any ray in an optical system is described by its distance to the optical axis and angle. (b) A schematic diagram of the optical elements of a general RIMS.


Generic image for table
Table I.

Specifications of different kinds of transparent materials. The first five materials are all types of glass. BK7 glass is a borosilicate glass with well-defined properties. For more information on different glass types, see Refs. 49–51. Refractive indices as specified by manufacturers or commercial resellers. Price increase indicated is exponential, and given only for 3 mm spheres or closest available size. Besides size, the price also depends on supplier, sphericity, and optical quality (see Fig. 4).

Generic image for table
Table II.

Table with common high n D fluids; (aq) means if dissolved in an aqueous solution. Refractive index data obtained from various commercial resellers and from Ref. 69.

Generic image for table
Table III.

Table with fluorescent dyes used. λabs and λemi  are absorption peak and emission peak wavelengths; note that these wavelengths depend on the solvent the dyes are dissolved in. Only confirmed solvent compatibility is mentioned; compatibility with other solvents is not excluded. However, we found that Rhodamine 6G cannot be dissolved in NaI (aq) or in a mixture of Cyclohexyl bromide + Decalin. Unreferenced compatibilities we have tested ourselves. Dyes are available from, e.g., Exciton, American Dye Source, Radiant, Atto-tec.


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Scitation: Invited Article: Refractive index matched scanning of dense granular materials