Specific surface area of polydispersions as a function of size distribution sharpness

LOPES, PAULO FILIPE T.; LUZ, JOSÉ AURÉLIO M. DA; MILHOMEM, FELIPE O.

doi:10.1590/0001-3765202020191407

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ENGINEERING SCIENCES • An. Acad. Bras. Ciênc. 92 (3) • 2020 • https://doi.org/10.1590/0001-3765202020191407 copy

Specific surface area of polydispersions as a function of size distribution sharpness

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Knowledge of particulate system properties is very important in various industrial instances and the possibility of fast predicting the behavior of such systems is an important control tool. The specific surface area of simulated particulate systems was studied as a function of the sharpness parameter of the size distribution of the Gates–Gaudin-Schumann, Gaudin–Meloy and Rosin–Rammler equations. The results showed good statistical adherence, especially the Rosin–Rammler equation, in situations where it is the best descriptor of particle size distribution.

Key words
particle size distribution; sharpness index; statistical distribution; surface area

Tag	Accumulated passing (Y(x))	Parameters	Eq.
GGS	$Y (x) = {(\frac{x}{x_{\max}})}^{n}$	n — distribution exponent; x_max — top size.	(1)
GM	$Y (x) = 1 - {(1 - \frac{x}{x_{\max}})}^{n}$	n — distribution exponent; x_max — top size.	(2)
RR	$Y (x) = 1 - \exp [\ln (\frac{1}{2}) \times {(\frac{x}{x_{50}})}^{n}]$	n — sharpness (uniformity coefficient); x₅₀ — median diameter.	(3)

Granular system	x₅₀ [m]	Shape coefficient	Primary data source (apud Orr Jr. & DallaValle, 1959)
White sand	2.90 x 10^-3	k_s = 0.668	DallaValle (1938)
White sand	8.00 x 10^-4	k_s = 0.859	DallaValle (1938)
White sand	4.00 x 10^-4	k_s = 0.828	DallaValle (1938)
Filter sand	6.00 x 10^-4	k_s = 0.859	DallaValle (1938)
Filter sand	5.00 x 10^-4	k_s = 0.923	DallaValle (1938)
Crushed quartz	8.30 x 10^-3	k_s = 0.796	Martin (1927–8)
Crushed quartz	4.90 x 10^-3	k_s = 0.796	Martin (1927–8)
Crushed quartz	1.10 x 10^-3	k_s = 0.700	Martin (1927–8)
Crushed quartz	3.00 x 10^-4	k_s = 0.668	Martin (1927–8)
Crushed quartz	2.20 x 10^-3	k_v = 0.535	Martin (1927–8)
Crushed quartz	1.90 x 10^-3	k_v = 0.325	Goldman & DallaValle (1939)
Crushed quartz	8.90 x 10^-4	k_v = 0.286	Goldman & DallaValle (1939)
Crushed quartz	4.90 x 10^-4	k_v = 0.516	Martin (1927–8)
Crushed quartz	–	k_v = 0.267	Hatch & Choate (1929)
Calcite	–	k_v = 0.258	Hatch & Choate (1929)
Hornblende	5.00 x 10^-5	k_v = 0.038	Goldman & DallaValle (1939)
Dolomite	4.00 x 10^-5	k_v = 0.363	Goldman & DallaValle (1939)
Feldspar	4.00 x 10^-5	k_v = 0.497	Goldman & DallaValle (1939)

Distribution	Regression equations	Fitting parameters	Equation
GM	$s_{v} = a \times [1 - \exp (- b \times n^{c})]$	a = 1022.79 b = 0.0385428 c = 0.808936 Coefficient of determination: R² = 0.99991	(10)
GGS	$s_{v} = [a \times k \times b^{a} \times n^{\frac{(a - 1)}{{(n^{a} + b^{a})}^{2}}}] + c$	a = 1.9592 b = 0.38077 c = 6.4148 k = 144.129 Coefficient of determination: R² = 0.99905	(11)
RR	$s_{v} = a (n) \times d_{50}^{- b (n)}$ (12)	$a (n) = \frac{290.0568 \times n^{1.65813}}{(n^{1.65813} + {0.20708}^{1.65813})} + 6$ Coefficient of determination: R² = 0.99910	(12a)
		$b (n) = 1 - \exp (- {(\frac{n}{0.67235})}^{1.46902})$ Coefficient of determination: R² = 0.99970	(12b)

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[1] Correspondence to: José Aurélio Medeiros da Luz E-mail: jaurelio@ufop.edu.br