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Computational Fluid Dynamics Simulation of Hydrodynamics in USP Apparatus 3—The Influence of Dip Rate

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Abstract

Purpose

This study investigated the influence of dip rate on USP Apparatus 3 hydrodynamics in the presence of a solid dosage form (e.g. tablet) using Computational Fluid Dynamics (CFD) simulations. The primary variables of interest were the liquid phase velocity in the computational domain and wall shear stresses on the tablet surfaces.

Methods

Geometry building and model setup were based on a number of simplifying assumptions. Computational grid-independent solutions were achieved for dip rates ranging from 5 to 10 dips per minute (dpm).

Results

For all cases studied, the hydrodynamics exhibited a periodicity dictated by the dip rate. Cycle-to-cycle variations were found to be negligible. Higher velocities were predicted in the wake of the tablet and they peaked at midway positions both during the up- and downstrokes of the cylinder. Three sub-regions of velocity were identified inside the reciprocating cylinder. Results also showed localized vortices/recirculations specific to the up- and downstroke, in addition to local stagnation zones. The wall shear stresses and velocity magnitudes scaled proportionately with increasing dip rates while exhibiting qualitatively similar behavior in their spatial and temporal distributions.

Conclusions

Based on the predictions of the 2D axisymmetric CFD model, the hydrodynamics in USP Apparatus 3 is characterized by complex and periodic flow structures.

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Notes

  1. Hereafter the terms ‘mesh screen’, ‘porous surface’ and ‘porous jump’ are used in relation to the top and/or bottom mesh screens.

Abbreviations

C 2 :

Pressure jump coefficient (m−1)

C v :

Total liquid volume (m3)

d :

Tablet thickness (m)

d*:

Dimensionless axial coordinate of a point on the tablet side surface

h :

Computational domain height (m)

h c :

Cylinder height (m)

h l :

Liquid level with submerged tablet (m)

N :

Dip rate or rate of reciprocation (dpm)

OA:

Open surface area of mesh screens

R:

Tablet radius (m)

r :

radial position/coordinate (m)

r*:

Dimensionless radial coordinate of a point on the tablet bottom and top surfaces

Re:

Reynolds number

t :

Physical time elapsed from start of process defined as cylinder position at the beginning of the upstroke (s)

t*:

Dimensionless time defined as ratio of time t, and time required for completion of two cycles of operation

U n :

Surface-normal fluid velocity (m/s)

U z :

Axial velocity of moving solid parts (m/s)

V :

Tablet volume (m3)

z :

Axial position/coordinate (m)

z 0 :

Initial axial position of a point on the bottom mesh screen (m)

α :

Porous surface permeability (m2)

Δh bottom :

Distance between the bottom surfaces of the cylinder and vessel (m)

Δh top :

Distance between the top surfaces of the computational domain and the cylinder at the end of up stroke (m)

Δm :

Porous surface thickness (m)

ΔP :

Pressure drop across a porous surface (N/m2)

μ :

Liquid dynamic viscosity (kg/m-s)

ρ :

Liquid density (kg/m3)

τ bot τ side , τ top :

Wall shear stresses on the tablet bottom, side and top surfaces respectively (N/m2)

Φ c :

Cylinder diameter (m)

Φ v :

Vessel diameter (m)

ω :

Frequency of oscillation of moving solid parts (rad/s)

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Acknowledgments and Disclosures

The authors thank Drs. Narayana Rayapati, Luke Munholand, Genong Li, and Brian Bell from ANSYS, Inc., Lebanon, NH, for their technical support in the development of models. The authors would also like to thank Drs. Stefan Schuber and James Austgen for editorial assistance.

Disclaimer

Certain software and hardware are identified in this paper to specify adequately the modeling effort involved. Such identification does not imply approval, endorsement, or certification by USP of the particular brand or product, nor does it imply that the software or hardware is necessarily the best available for the purpose or that any other brand or product was judged to be unsatisfactory or inadequate.

Author information

Authors and Affiliations

  1. US Pharmacopeial Convention, 12601 Twinbrook Parkway, Rockville, Maryland, 20852-1790, USA

    Satish Perivilli & Erika Stippler

  2. Food and Drug Administration, Office of Testing and Research, 10903 New Hampshire Ave., Silver Spring, Maryland, 20993, USA

    Maziar Kakhi

Authors
  1. Satish Perivilli
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  2. Maziar Kakhi
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  3. Erika Stippler
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Corresponding author

Correspondence to Satish Perivilli.

Additional information

Maziar Kakhi’s Disclaimer: The views expressed in this paper are those of the authors and do not reflect the opinion nor the policy of the FDA.

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Perivilli, S., Kakhi, M. & Stippler, E. Computational Fluid Dynamics Simulation of Hydrodynamics in USP Apparatus 3—The Influence of Dip Rate. Pharm Res 32, 1304–1315 (2015). https://doi.org/10.1007/s11095-014-1534-9

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  • DOI: https://doi.org/10.1007/s11095-014-1534-9

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