Skip to main content
Engineering LibreTexts

11.7: Concentration Distributions

  1. Last updated
  2. Save as PDF
  • Page ID
    33154

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)

    13.7.1 Roco & Shook (1983)

    Figure 13.7-1: Roco & Shook (1983) d=0.165 mm, Dp=0.0515 m.

    Screen Shot 2020-08-13 at 11.19.56 AM.png

    Figure 13.7-2: Roco & Shook (1983) d=0.165 mm, Dp=0.2630 m.

    Screen Shot 2020-08-13 at 11.20.55 AM.png

    Figure 13.7-3: Roco & Shook (1983) d=0.165 mm, Dp=0.4950 m.

    Screen Shot 2020-08-13 at 11.21.55 AM.png

    Figure 13.7-4: Roco & Shook (1983) d=0.480 mm, Dp=0.0515 m.

    Screen Shot 2020-08-13 at 11.22.56 AM.png

    Figure 13.7-5: Roco & Shook (1983) d=0.520 mm, Dp=0.0507 m.

    Screen Shot 2020-08-13 at 11.23.48 AM.png

    Figure 13.7-6: Roco & Shook (1983) d=13.0 mm, Dp=0.2630 m.

    Screen Shot 2020-08-13 at 11.24.37 AM.png

    15.7.2 Gillies (1993)

    Figure 13.7-7: Gillies (1993) d=0.180 mm, Dp=0.0532 m, vls=1.8 m/s.

    Screen Shot 2020-08-13 at 11.25.40 AM.png

    Figure 13.7-8: Gillies (1993) d=0.180 mm, Dp=0.0532 m, vls=3.1 m/s.

    Screen Shot 2020-08-13 at 11.26.37 AM.png

    Figure 13.7-9: Gillies (1993) d=0.180 mm, Dp=0.4950 m, vls=3.1-3.8 m/s.

    Screen Shot 2020-08-13 at 11.27.33 AM.png

    Figure 13.7-10: Gillies (1993) d=0.190 mm, Dp=0.1590 m, vls=2.5-2.7 m/s.

    Screen Shot 2020-08-13 at 11.29.47 AM.png

    Figure 13.7-11: Gillies (1993) d=0.190 mm, Dp=0.1590 m, vls=3.7 m/s.

    Screen Shot 2020-08-13 at 11.30.50 AM.png

    Figure 13.7-12: Gillies (1993) d=0.290 mm, Dp=0.0532 m, vls=1.8 m/s.

    Screen Shot 2020-08-13 at 11.31.44 AM.png

    Figure 13.7-13: Gillies (1993) d=0.290 mm, Dp=0.0532 m, vls=3.1 m/s.

    Screen Shot 2020-08-13 at 11.36.20 AM.png

    Figure 13.7-14: Gillies (1993) d=0.290 mm, Dp=0.2630 m, vls=4.0-4.7 m/s.

    Screen Shot 2020-08-13 at 11.39.50 AM.png

    Figure 13.7-15: Gillies (1993) d=0.380 mm, Dp=0.2630 m, vls=4.1-4.8 m/s.

    Screen Shot 2020-08-13 at 11.47.12 AM.png

    Figure 13.7-16: Gillies (1993) d=0.550 mm, Dp=0.0532 m, vls=2.1 m/s.

    Screen Shot 2020-08-13 at 11.48.09 AM.png

    Figure 13.7-17: Gillies (1993) d=0.550 mm, Dp=0.0532 m, vls=3.1 m/s.

    Screen Shot 2020-08-13 at 11.49.08 AM.png

    Figure 13.7-18: Gillies (1993) d=0.550 mm, Dp=0.2630 m, vls=3.9-4.4 m/s.

    Screen Shot 2020-08-13 at 11.49.59 AM.png

    Figure 13.7-19: Gillies (1993) d=2.4 mm, Dp=0.0532 m, vls=1.8-3.1 m/s.

    Screen Shot 2020-08-13 at 11.50.52 AM.png

    Figure 13.7-20: Gillies (1993) d=2.4 mm, Dp=0.2630 m, vls=3.3-4.0 m/s.

    Screen Shot 2020-08-13 at 11.51.59 AM.png

    15.7.3 Gillies (2004)

    Figure 13.7-21: Gillies (2004) d=0.090 mm, Dp=0.1030 m, vls=3.0 m/s.

    Screen Shot 2020-08-13 at 11.53.23 AM.png

    Figure 13.7-22: Gillies (2004) d=0.270 mm, Dp=0.1030 m, vls=5.4 m/s.

    Screen Shot 2020-08-13 at 11.55.15 AM.png

    13.7.4 Kaushal & Tomita (2005)

    Figure 13.7-23: Kaushal & Tomita (2005) d=0.125 mm, Dp=0.0549 m, Cvs=0.10.

    Screen Shot 2020-08-13 at 1.31.23 PM.png

    Figure 13.7-24: Kaushal & Tomita (2005) d=0.125 mm, Dp=0.0549 m, Cvs=0.30.

    Screen Shot 2020-08-13 at 1.32.18 PM.png

    Figure 13.7-25: Kaushal & Tomita (2005) d=0.440 mm, Dp=0.0549 m, Cvs=0.10.

    Screen Shot 2020-08-13 at 1.33.11 PM.png

    Figure 13.7-26: Kaushal & Tomita (2005) d=0.440 mm, Dp=0.0549 m, Cvs=0.20.

    Screen Shot 2020-08-13 at 1.34.10 PM.png

    Figure 13.7-27: Kaushal & Tomita (2005) d=0.440 mm, Dp=0.0549 m, vls=4.0 m/s.

    Screen Shot 2020-08-13 at 1.38.53 PM.png

    15.7.5 Matousek et al. (2009) & (2014)

    Figure 13.7-28: Matousek et al. (2014) d=0.440 mm, Dp=0.1000 m, vls=3.0 m/s.

    Screen Shot 2020-08-13 at 1.41.37 PM.png

    Figure 13.7-29: Matousek et al. (2014) d=0.440 mm, Dp=0.1000 m, vls=3.5-4.0 m/s.

    Screen Shot 2020-08-13 at 1.45.21 PM.png

    Figure 13.7-30: Matousek et al. (2014) d=0.530 mm, Dp=0.1000 m, vls=3.0 m/s.

    Screen Shot 2020-08-13 at 1.46.17 PM.png

    Figure 13.7-31: Matousek et al. (2014) d=0.530 mm, Dp=0.1000 m, vls=3.5-4.0 m/s.

    Screen Shot 2020-08-13 at 1.49.41 PM.png

    Figure 13.7-32: Matousek et al. (2014) d=0.900 mm, Dp=0.1000 m, vls=3.5-4.0 m/s A.

    Screen Shot 2020-08-13 at 1.50.47 PM.png

    Figure 13.7-33: Matousek et al. (2014) d=0.900 mm, Dp=0.1000 m, vls=3.5-4.0 m/s B.

    Screen Shot 2020-08-13 at 1.52.18 PM.png

    Figure 13.7-34: Matousek et al. (2014) d=0.900 mm, Dp=0.1000 m, vls=3.5-4.0 m/s C.

    Screen Shot 2020-08-13 at 1.53.07 PM.png

    Figure 13.7-35: Matousek et al. (2014) d=0.120 mm, Dp=0.1500 m, vls=2.0-6.0 m/s.

    Screen Shot 2020-08-13 at 1.56.11 PM.png

    Figure 13.7-36: Matousek et al. (2014) d=0.370 mm, Dp=0.1500 m, vls=6.0 m/s.

    Screen Shot 2020-08-13 at 1.56.55 PM.png

    Figure 13.7-37: Matousek et al. (2009) d=0.370 mm, Dp=0.1500 m, vls=0.5-2.0 m/s.

    Screen Shot 2020-08-13 at 1.57.42 PM.png

    Figure 13.7-38: Matousek et al. (2009) d=0.370 mm, Dp=0.1500 m, vls=0.5-2.0 m/s.

    Screen Shot 2020-08-13 at 2.20.51 PM.png

    15.7.6 Vlasak et al. (2014)

    Figure 13.7-39: Vlasak et al. (2014) d=11.0 mm, Dp=0.1000 m, vls=1.8 m/s.

    Screen Shot 2020-08-13 at 2.23.27 PM.png

    Figure 13.7-40: Vlasak et al. (2014) d=11.0 mm, Dp=0.1000 m, vls=2.8 m/s.

    Screen Shot 2020-08-13 at 2.26.02 PM.png

    Figure 13.7-41: Vlasak et al. (2014) d=11.0 mm, Dp=0.1000 m, vls=4.1 m/s.

    Screen Shot 2020-08-13 at 2.27.05 PM.png

    This page titled 11.7: Concentration Distributions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Sape A. Miedema (TU Delft Open Textbooks) via source content that was edited to the style and standards of the LibreTexts platform.