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Analysis of Particle Recovery in Flotation Column Based on Information Entropy Theory

  • Ritesh Prakash
  • Subrata Kumar MajumderEmail author
Technical Paper

Abstract

Quality of mixedness in a flotation column has been analyzed by using information entropy theory. An empirical model with the consideration of geometric and dynamic variable, which affect the quality of mixedness, was developed by dimensional analysis. The efficiency of the particle separation in the floatation column has been enunciated based on the quality of mixedness. The present analysis on the quality of mixedness in flotation column may give insight into a further understanding and modeling of flotation device in industrial applications.

Keywords

Information entropy Mixedness Flotation column Recovery 

List of symbols

A1A2

Parameter used in Eq. (20)

C(t)

Tracer concentration (kg/m3)

dp

Particle diameter (m)

db

Bubble diameter (m)

dc

Column diameter (m)

dpmax

Maximum floatable particle size (m)

\(E_{a}\)

Particle–bubble attachment efficiency (−)

\(Ec\)

Particle–bubble collision efficiency (−)

Es

Particle–bubble stability efficiency (−)

F(x)

Cumulative distribution function of x

H(X)

Information entropy of discrete random variable X

i

Column sections 1, 2, 3,….. (−)

I (X)

Information content

I(wn)

Self information of x associated with outcome w n

k

Flotation rate constant (s−1)

M(t)

Mixedness factor (−)

P

Parameter used in Eq. (20)

P(t)

Probability of tracer appearance in every semi cylindrical shell (−)

R2

Correlation coefficient (−)

t

Time (s)

\(t_{i}\)

Induction time (s)

tc

Average contact time (s)

tm

Mean residence time (s)

u0

Velocity at column axis (m/s)

ub

Bubble rise velocity (mm/s)

ug

Gas velocity (mm/s)

ul

Liquid velocity (mm/s)

V

Volume of semi cylindrical shell (m3)

wn

Random variable

x

Real number

x0

Parameter

X

Real valued random variable

Z

Parameter used in Eq. (20)

Greek letters

εg

Fractional gas holdup (−)

μl

Viscosity of liquid (kg/m s)

ρl

Density of liquid (kg/m3)

ρg

Density of gas (kg/m3)

σ

Surface tension (N/m)

\(\theta\)

Contact angle (radian)

\(\theta_{A}\)

Maximum advancing contact angle (radian)

\(\theta_{R}\)

Minimum receding contact angle (radian)

\(\Delta \theta\)

Contact angle hysteresis (radian)

\(\Delta \rho\)

Difference in density between particle and liquid (kg/m3)

\(\varepsilon_{i}\)

Energy dissipation per unit mass (W/kg)

\(\gamma\)

Dynamic viscosity (Pa s)

β

Parameter

Dimensionless group

Rel

Liquid Reynolds number, \(\frac{{\rho_{l} u_{l} d_{c} }}{{\mu_{l} }}\) (−)

Reb

Bubble Reynolds number, \(\frac{{\rho_{l} u_{b} d_{b} }}{{\mu_{l} }}\) (−)

Pe

Peclet number (−)

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Copyright information

© The Indian Institute of Metals - IIM 2016

Authors and Affiliations

  1. 1.Department of Chemical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

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