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Predicting the Angle of Internal Friction from Simple Dynamic Consolidation Using Lactose Grades as Model

  • Žofie Trpělková
  • Hana Hurychová
  • Pavel Ondrejček
  • Tomáš Svěrák
  • Martin Kuentz
  • Zdenka ŠklubalováEmail author
Original Article
  • 51 Downloads

Abstract

Purpose

Powder flow and packing behavior are among other factors determined by particle friction, which is traditionally measured in shear cells as the angle of internal friction (AIF). Considering that an AIF at a normal stress should be comparable to friction during tapping consolidation, this work aims at whether dynamic consolidation under gravity can be used to estimate an AIF.

Methods

Powder consolidation by controlled tapping was studied for seven commercially available types of lactose. A porosity factor was determined, and values were compared with the AIF obtained from Jenike shear cell measurements.

Results

Plotting porosity factor vs. number of applied taps provided an estimated angle of internal friction (AIFE) that was obtained from the slope of a linear relationship. A significant linear correlation (r = 0.825; p = 0.0223) was evidenced between AIFE and those AIFJ estimated from linearized yield locus measurements of using the Jenike shear cell.

Conclusions

The good linear correlation between the angle of internal friction estimated from dynamic powder consolidation and the internal friction obtained by a shear cell is of high practical relevance. The latter shear cell behavior is only occasionally studied in the pharmaceutical industry, whereas dynamic powder tapping is a standard analysis.

Keywords

Powders Consolidation Angle of internal friction Jenike shear tester Tapping 

Abbreviations

Symbols

Variables units

AIF

Angle of internal friction (°)

AIFJ

Angle of internal friction (°), measured

AIFE

Angle of internal friction (°), estimated

τ

Shear stress (Pa)

σ

Normal stress (Pa)

K

Porosity factor (−)

ε

Porosity of powder bed (−)

N

Number of applied taps

x10

Size of 10% of cumulative size (μm)

x50

Mean particle size (μm)

x90

Size of 90% of cumulative size (μm)

db

Bulk density (g/mL)

dN

Tapped density (g/mL) related to N

dt

Final tapped density for 1250 taps (g/mL)

VN

Volume (mL) related to N

ds

True density (g/mL)

σpre

Preshear normal stress (kPa)

σsh

Reduced normal stress (kPa)

n

Number of replicas

εN

Powder porosity related to N

Vred

Volume reduction (−)

HR

Hausner ratio (−)

CI

Compressibility index (%)

V0

Bulk volume before tapping (mL)

V

Final tapped volume (mL)

r

Correlation coefficient

p

Probability

span

Width of the particle size distribution

RSD

Relative standard deviation

YL

Yield locus

Notes

Acknowledgements

This study was supported by the Funding Agency of Charles University under Grant No. 1286218/2018 and the Funding Agency of Charles University under Grant No. SVV 260 401.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Pharmacy, Department of Pharmaceutical TechnologyCharles UniversityHradec KrálovéCzech Republic
  2. 2.Faculty of Chemistry, Institute of Materials ScienceUniversity of TechnologyBrnoCzech Republic
  3. 3.School of Life Sciences, Institute of Pharma TechnologyUniversity of Applied Sciences and Arts Northwestern SwitzerlandMuttenzSwitzerland

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