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



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.


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.


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.


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.


Powders Consolidation Angle of internal friction Jenike shear tester Tapping 



Variables units


Angle of internal friction (°)


Angle of internal friction (°), measured


Angle of internal friction (°), estimated


Shear stress (Pa)


Normal stress (Pa)


Porosity factor (−)


Porosity of powder bed (−)


Number of applied taps


Size of 10% of cumulative size (μm)


Mean particle size (μm)


Size of 90% of cumulative size (μm)


Bulk density (g/mL)


Tapped density (g/mL) related to N


Final tapped density for 1250 taps (g/mL)


Volume (mL) related to N


True density (g/mL)


Preshear normal stress (kPa)


Reduced normal stress (kPa)


Number of replicas


Powder porosity related to N


Volume reduction (−)


Hausner ratio (−)


Compressibility index (%)


Bulk volume before tapping (mL)


Final tapped volume (mL)


Correlation coefficient




Width of the particle size distribution


Relative standard deviation


Yield locus



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

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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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