Fluid Dynamics Properties of Barium Hexaferrite Particle

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Perdamean Sebayang/Fluid Dynamics Properties of Particle Barium Hexaferite

Jurnal Fisika Indonesia No: 49, Vol XVII, Edisi April 2013

ISSN : 1410-2994

Perdamean Sebayang1),Muljadi1), Anggito Tetuko1), Priyo Sardjono1) 1)

Pusat Penelitian Fisika LIPI

Komplek Puspiptek Gedung 440, Tangerang Selatan, 15314 Telp : (021) 7560570, Fax : (021) 7560554

E-mail: [email protected]; [email protected]

Abstract - Particle size distribution of Barium Hexaferrite sample has been performed with commonly used

methods of mathematical models by Rosin-Rammler (RR model) distribution. By using sieving method from 20-400 mesh, the basis of network analysis distribution function F(d) and density function, f(d) were obtained. Particle size estimation was performed using sedimentation gravitation based on Stokes law to obtained Reynolds numbers and terminal velocity of flocs in medium value has been calculated. The results of Reynolds numbers shows that Barium hexaferrite flocs in ethanol medium in laminar flow, whereas terminal velocity increases as larger particle size and density, however, bulk density reduce due to contained highly porous in the sample which yields lower bulk density. The relationship of turbidity with the floc size has been evaluated. The results show that turbidity and bulk density increases as smaller particle size, meanwhile, terminal velocity reduced. Differences in turbidity for each sample (20-400 mesh) has been determined which shows two region instead, with first region from 150-850 µm yields larger differences compared to the second region: 37-105 µm.

Keywords: Rosin-Rammler model, terminal velocity, Reynolds numbers, turbidity, sedimentation

I. INTRODUCTION

Particle size is one of the most important physical properties of solids, which are used in many fields of human activity, such as construction, waste management, metallurgy, fuel fabrication, etc. The aggregation of ﬁne particles and colloids into larger assemblages is a process that resulting aggregates that form are known as ‘ﬂocculation’ which are described as being highly porous, irregularly structured and loosely connected aggregates composed of smaller primary particles

[1]. Once the solid particles are produced, they may be separated from water using sedimentation,

flotation, filtration and thickening techniques [2]. The physical characteristics of floc are therefore fundamental in determining their removal efficiency. For example, large compact flocs have a high settling rate that results in a treated water of low turbidity during settlement [3], whilst large and porous flocs aid filtration due to high permeability

[4]. A number of methods aimed at determining Particle Size Distribution (PSD) (i.e., sieving, cycloning, microscopy, etc.), where sieving are the known as the most common method due to its simplicity, which have been described in the literature [5]. There are several analysis techniques, both mathematical models GGS and RR

distribution has widely used to study the PSD of solids, which have been applied to a cork granulate sample. However, based on literature [6-9], RR model were used to provide excellent results when applied to the sample of agglomerate cork studied, which leads to a more accurate separation of the different particle sizes to a better industrial profit of the material. Hence, with analysis technique were used will depend on the ultimate goal of the characterization. The aim of this study is to obtain the distribution F(d) (mass fraction) and density f(d) functions (number of particles binned between two given mesh sizes) of a Barium Hexaferrite particles by applying the RR distribution of mathematical models to the PSD data obtained by sieving through different size meshes [10]. The results of PSD analysis can be expressed according to the particle diameter indicating the nominal mesh sizes, or by particle size distribution, in grams, in percentage by weight of each fraction (differential distribution, as the cumulative percentage of sizes below a given value, undersize, and as the cumulative percentage of size above a given value, oversize) [11]. In this experiment, settling techniques was used to perform the gravity sedimentation. This technique is one of sedimentation method to determine ﬂoc structural

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ISSN : 0853-0823

characteristics, which takes on an extra relevance because the settling behavior of aggregates is an important parameter for optimizing the sedimentation process. Floc settling behavior is dependent upon size, eﬀective density and porosity

[11]. Settling velocity has several advantages such as measuring fractals of compact ﬂocs, cheap and simple method, and also good for aggregates particles which made from a number of diﬀerent primary particles [12]. Turbidity measurement was conducted and to observed the sedimentation as theoretically with larger particle size will yields a lower turbidity value.

II. METHODOLOGY

Bulk green-body barium hexaferrite from PT. Neomax, Cilegon were used as in the form of powder. A 100 gram of bulk barium hexaferrite was which was firstly grinded by using mortar and sieves using standard sieves of known apertures with different mesh size from 20, 30, 40, 50, 100, 150, 200, and 400 meshes. To determine the particle distribution of barium hexaferrite by using mathematical RR model distribution. The function F(d) is particularly suited to represent powders made by grinding, milling, and crushing operations

[13]. The general expression of the RR model is given by:

(1)

Where, F(d) is a distribution function, d particle size (diameter of spherical particles) in µm, l is mean particle size (µm), and m is the measured of the spread of particle sizes. Parameters l and m are adjustable parameters characteristic for the distribution. Eq. (1) can be rewritten as:

(2)

By using the RR mathematical model for particle size distribution, a plot of the first term of Eq. 2, indicating the applicability of RR model for particle size distribution curve. For the regression analysis method of least squares is also frequently used to estimate the data point between two mesh sieves size. The correlation coefficient is used as a parameter indicating the relevance of the measured data set. The density function in RR mathematics model will be:

(3)

Particle size distribution analysis was done by plotting the graph of cumulative % passing,

distribution function and density function against particle size using equation (1) and (3), whereas for the fitting to RR model by using equation (2). From the grinded powder Barium Hexaferrite and filtered using mesh sieves and each of which passing powder (undersize) through sieves were then weight to calculate the density of the powder using pycnometer with ethanol (medium) and the others mixed in the toluene (medium) as dispersant to calculate bulk density of powder and settling velocity as well as particle flow through the medium, respectively. To determine the behavior of particle settling velocity in a medium were used sedimentation method (gravity sedimentation). A mathematical model was used to explain the phenomena of gravity sedimentation by using Stokes law and also Reynolds number can be obtained. Settling velocity can be applicable for spherical particles (assumed) falling through a medium not particle that could react to the medium.

To estimate the true value of terminal velocity, VT, thus drag force must be taken account.

For spherical particle under streamline condition (also known as laminar or Newtonian conditions), Stokes has determined drag force, FD = 6πrµVT.

The ratio of inertia force divided by viscous force is known as Reynolds number (Re). The streamline condition can be determined when the fluid flowing past the streamline (laminar), Re<2100, transitional stage with Re between 2100 and 4000 but when the flow is turbulent Re is greater than 4000. During settling of a particle under streamline condition, force acting on the particle due to gravitational acceleration is given by: mg=V(ρs-ρf)g, where V is

the volume of spherical particles. In practice it is difficult to ascertain whether the flow past a falling particle is streamline or turbulent. Considering projected area, A, of a particle falling freely as FD

as total drag force on particle, where constant k is a function of the shape of the particle and ρs is the

density of the Barium hexaferrite powder, shown as:

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Next, by dividing both sides of the equation by term ρFV2 and multiplying by Re2, yields to

below Eq. (6):

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Perdam

and b the eq

fluid p under

mean Sebayang/Fl

by substituting quation,

The right h properties onl r any conditio value of left ha

garithmic form m literature [1 where the lo )= log [(FD/ρfA

nal velocity ca µ/dpρf (unit m/

idity measure dity meter TU NTU as sample ch undersize 00 mesh, we um. Turbidity val 10 s for eac

RESULTS AN

The sampl of grinded B sieves was % passing as bution analysi hown in the F

st particle si cle value deno

3 from Eq. (2 ed equal to ured data of ssion equatio ned and were ion of particle le using the g

l, equal to 460

re 1. Plot log ng of cumulati

luid Dynamics Pr

Jur

g Re = dpVρF

hand side of ly and diamete on can be com and side Eq. ( m. Thus, from 3] as the corr ogarithmic fu AVT2)Re2] an

an be calculat /s).

ement has be U-2016 (calib e references)

particle pass eight and mix

data was take ch data point.

ND DISCUSS

le powder fro Barium Hexaf weigh to ob s shown in Ta is of barium Fig. 1, cumu ze which sho ote as m, the 2) in logarithm 0.9143. Fro Fig. 1, show on, the slope

used to calcu e size Barium given Eq. (1) 0 µm.

arithmic PSD ive % passing

roperties of Partic

rnal Fisika Indo

F/µ and simpl

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Eq. (5) deals er of particle f mputed by eq

(6) to determi m Table 1 and rection value f unction writte d log Re. Sim ted from equa

een done by brated using

with sample c through the xed in tolue en for 400 dat

SIONS

om different p ferrite pass th btained cumu able 1. Particl hexaferrite p ulative passin ows the spre

slope of the mic equation w om the fittin ws the logar e of the grap ulate the distrib m Hexaferrite

with mean p

D curve obtain (undersize).

cle Barium Hexaf

onesia No: 49, Vo

ISSN : 1410-2

lifying

s with falling quating ine Re Table for the en as: milarly,

tion V

using 0 and consist

sieves ene as

ta with

particle hrough ulative le size ithmic ph, m

bution in the particle

ned by

ol XVII, Edisi A

2994

Rosin-hown in Fig. action by volu flocs) with R2 hat the point w

he value of t action of th olume) that is

Thus, th zes (i.e., d1

articles (expr whose diameter

abel 1.Size a t of tested mat

d, µm

Cum. Mass % passing

600 1.00

850 0.78

600 0.56

425 0.43

300 0.34

150 0.14

105 0.07

74 0.03 37 0.02

Pan 0.00

Where: d=apertu y= ln{–l

The i depending on ach point in which is define

his function which correspo

certain size. F istribution fun sing Eq. (2) t y plotting both ig. 3a. From xperimental d

-squaredequa orrelation coe n d. The appl SD curve allo urpose). There

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-Rammler dis 2a. This func ume, mass, or equal to 0.99 was perfectly f the function a he number o below a given

he area under and d2) ind

essed as part rs are compris

analysis with terial to RR m ure mesh size ln[1–F(d)]}

inclination of the diamete ndicates the d

ed by Eq. 3 represents t onds to the pr From the Tabe nction, F(d), t o calculate ln h value to the the graph s data to Rosin-al to 1, thus th

fficient betwe lication of th

ws one to ext efore from Fig

stribution func ction may rep r by number o 994, this value fit the logarith at a given po of particles

n size.

the curve bet dicates the n ticle mass or sed in this inte

cumulative m model.

f(d) (x10-3) y

0.058 0.33 0.114 0.16 0.164 0.07 0.232 -0.02 0.327 -0.11 0.632 -0.30 0.877 -0.39 1.204 -0.49 2.386 -0.69

- - e,

f distribution er of particles

density funct and shown in the logarithm roportion of p

el 1, shows th thus it was po n{-ln[1-F(d)]} e graph as sho shows perfect -Rammler mo he correspond een ln{-ln[1-F hese expressio trapolate (for e g. 3a, has been

ction, F(d), present the of particles e represent hmic curve.

oint is the

masses and

ln(d)

35 0.058 65 0.114 71 0.164

21 0.232

15 0.327

01 0.632

96 0.877

90 1.204

99 2.386

-

n function s, f(d), at ion f(d), n Fig. 2b. mic curve,

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the li

inear regressi e used to esti mple for parti

re 2. Plot ibution funct st particle size

re 3. Plot of fi R model.

Bulk de ferrite passed determined by um. From the cle size in Fig

een particle si ty of Barium to 0.9664.

Jur

on equation, mate the distr icle size range

of the R tion and (b) e.

itting curve ex

ensity of through each y using pycno e graph of bu

. 4, shows the ize with incre m Hexaferrite Therefore, lin

y=0.2683x-1 ribution of pa e within 37 –

Rosin-Rammle Density fu

xperimental m

grinded B

h sieves (unde ometer with e

ulk density a e linear relatio

asing value o , where R-sq near equation

ISSN : 0853-0

.6449, articles – 1600

er (a) unction

method

Barium ersize) ethanol against onship of bulk

0823

6481x + 5722 or bulk dens stimation from

m.

able 2. Based elocity and Re Aperture

size, d ighly porous w sing Eq. (6), erminal veloc

ravitation sed Hexaferrite pa Whereas, sphe

ssumed as the hrough the siev

Data f e value range ze between xplained that B oluene medium ow (theoretic aminar flow). elocity increa with fitting lin ased on Sto ncreasing in t alue of Bariu ompacts flocs, uring the fre medium as prov Measu sing turbidity article in whic s the sieves ap esults of turbid nterval 10 s ea xplained that f

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2.4 obtained fr sity of Bariu m certain part

d on Stokes law eynold numbe

Bulk density, ρp (kg/m3)

5204.98

5265.56

5481.75 5504.65

5651.03 5667.58

5673.44

5683.70

ionally, larger which yields l to determine ity of particl dimentation article shape

rical diamete e aperture size ves (undersize from Table 2, e within 0.05

37 – 850 µ Barium Hexaf m in streamlin cally Re va From Fig. 6 asing as the p near line R-sq okes law. It

terminal velo um Hexaferrite

, and also the ee fall of p ved in Eq. (6) urement of t y meter TU ch the particle

perture size. F dity measurem ach data poin for smaller pa

from Fig. 4, ca um Hexaferri ticle size with

w to determin ers.

r particle size lower bulk de e Reynold nu les (flocs) du

by assuming e factor wit er of particles e from passing e).

with Reynold – 247.70 wit µm, respectiv ferrite particle ne condition o alue below

6, shows that particle size g quared equal t also expla ocity thus bul e reduced du

effect of drag article in th .

turbidity has U-2016 for e diameter wa

From Fig. 5, ment for 400 s nt. This graph article size sho

an be used ite as an hin 37-850

e terminal

erminal ocity, Vt

contained ensity. By

g particles

d numbers, th particle vely. This

e mixed in or laminar 2100 are t terminal get bigger, to 0.9957 ained that

lk density ue to large g force, FD,

he toluene

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Perdam

mean Sebayang/Fl

dity compared µm.

re 4. Relation termina Thus, fro ve the sedim h of difference mum (Tmin) tu

ch particle size

re 5. Turbidity for 400s From Fig een Δ Turbidi get larger and

47 up to 238 cle size, can ded region sho ge in Δ Turbid region from p µm yields Δ , respectively

imental data nd region show

µm and Δ

ctively, with ed equal to 0 explain the sed ly in first reg

luid Dynamics Pr

Jur

d to larger par

nship between al velocity tow om Fig. 5 it mentation tim es between m urbidity (ΔTur e as shown in

y (NTU) depe .

g. 6 shows ity with partic d Δ Turbidity NTU. Graph

be divided ow in the dot dity occurred f particle size r Turbidity fro y, with line a R-squared

ws particle siz Turbidity f

fitting line 0.9984. These dimentation e gion compare

roperties of Partic

rticle size fro

n bulk densit wards particle t was possib me by plottin maximum (Tma

rbidity = Tmax

Fig. 6.

ends on partic

s the relatio cle size, as p y increase in

Δ Turbidity a into two re line) due to r from 150 to 10 range within om 137 up t ar fitting lin

equal to 0 ze range with from 47-66 ar line valu e phenomena

ffect occurred d to second r

cle Barium Hexaf

ISSN : 1410-2

om

37-onship article value against egions rapidly 05 µm. region

w

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with difference espectively. T was approxim model for termi article size ran r sedimentati elocity from 1 Turbidity occ 50 µm.

Thus egions can edimentation

ifferent region 50 µm and egression eq

=0.28x+36.84 tting linear lin

Additi alue of bulk urbidity, whi arger particle esults in low tu

igure 6. Re den

V. CONCLUS

article Size d mathematical

erformed wit quared equal t ensity functio Hexaferrite sam Re<2100) in

elocity value owever, bulk ighly porous ulk density. erformed, as l f turbidity, me or each sample ossibly occurr

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in Δ Turbidit This argument mately agreed

inal velocity u nge within 30 on occurred 1.28 up to 30 curred within

in Fig. 8, w be used a based on si ns. For particl 37 – 105 µm quation, y= 41, respective

ne.

ionally, in Fig density yiel ch shows tha size) have a urbidity durin

elationship Δ nsity against p

SSIONS

istribution by model dis th perfectly to 1, where di on. Reynold mple was sho

ethanol medi increases a k density red

in the samp Turbidity m arger particle eanwhile the e size divided red due to hig

ty value are 10 t of experim d with mat using stokes la 00–850 µm th

rapidly with .79 (x10-3 m/s particle size r

which divided s the estim ize range w le size range m can be us =0.1425x+118

ely, due to

g. 6 shows th lds lower va at large com a high settling ng settlement.

Turbidity w particle size (f

y using Rosin stribution h fitting linear istribution fun numbers fo own to be lam

ium, whereas as larger part duce due to ple which yie measurement

size yields lo differences in d into two reg

gher particle

01 and 19, ental data thematical aw, where he free fall h terminal

s) whereas range

150-into two mation of within two

from 150-sed linear

.54 and perfectly

hat higher alue of Δ mpact ﬂocs

g rate that

with bulk flocs).

n-Rammler has been

r line R-nction and or Barium minar flow

s terminal ticle size, contained elds lower

has been ower value

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results the sedimentation time is faster compared to the smaller particle size (flocs).

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