How To Calculate Parenteral Product Viscosity Using The Rotational Rheometer Method
What is viscosity?
Viscosity is the amount of internal friction (or internal resistance) between components in a fluid. Honey is an everyday example of a highly viscous product. Products with high viscosity are considered “thick” and flow slowly. In contrast, water is an example of a fluid with low viscosity. Products with low viscosity are considered “thin” and flow quickly and easily. A fluid’s flow speed depends on how fast the molecules in a fluid can rearrange and move past each other. Thus, liquids with small molecules tend to have low viscosity. Liquids with long-chain molecules (such as hyaluronic acid) have higher viscosity. Also, liquids with molecules that can form bonds with each other are more viscous. The bonding of glucose and fructose in honey is why honey is so viscous.
What types of injectable products are viscous?
Viscous injectable formulations often have high concentrations of large molecules or non-aqueous solvents. Highly viscous formulations contain both. Examples of large molecules include monoclonal antibodies, proteoglycans, and high molecular weight polymers. Proteoglycans like hyaluronic acid are included in many cosmetic or parenteral products. Additionally, controlled release versions of parenteral formulations often include high molecular weight polymers. When it comes to non-aqueous solvents, oil-based product formulations tend to be the most viscous.
How is parenteral product viscosity calculated?
The United States Pharmacopeia offers three methods for viscosity determination. The first method is the viscosity-capillary viscometer approach (USP 911), which is the focus of this article. The second method is a rotational rheometer technique (USP 912). The rolling ball viscometer method (USP 913) is the third option for calculating viscosity.
How is viscosity calculated using the rolling ball viscometer method?
The rolling ball method is used to determine the viscosity of a Newtonian fluid (a liquid with a viscosity independent of the shearing stress or rate of shear). The rolling ball method uses a rolling ball viscometer.
A rolling ball viscometer consists of a tube that contains the test sample liquid and a ball. The ball size is chosen so that it will require a minimum rolling time of twenty seconds at the measuring angle of the sample liquid. The rolling ball viscosity measurement is based on Stokes’s Law and determined using the calculation below.
Newtonian viscosity calculation, η, in millipascals x seconds (mPa x s):
η = [(ρ1 − ρ2) x g x r2 x sinθ]/v∞
Where:
ρ1 = density of the ball used in grams per milliliter (g/mL)
ρ2 = density of the sample liquid (g/mL)
g = gravitational constant in millimeter per second squared (mm/s2)
r = radius of the ball (mm)
θ = angle of inclination of the tube (or capillary)
v∞ = terminal velocity of the ball (mm/s)
In the calculation above, the tube of the rolling ball viscometer is considered a capillary. A liquid’s viscosity can be determined by measuring a ball’s rolling time within an inclined cylindrical tube filled with the fluid under assessment. The ball’s velocity is determined by measuring the time the ball takes to travel a fixed distance (i.e., the distance between two ring marks or measuring sensors). For each measured velocity (rolling time), the resulting viscosity can be expressed as dynamic viscosity (mPa x s) and kinematic viscosity (mm2/s) for a sample of known density.
To perform the rolling ball technique, select a tube and ball combination are chosen based on the anticipated viscosity range of the parenteral product liquid. A measuring angle (the angle of inclination) is selected based on an anticipated ball rolling time of at least twenty seconds. Then the selected tube is carefully filled with the sample liquid to avoid bubbles forming within the tube. Next, the tube is inserted into the rolling ball viscometer. The rolling ball viscometer will equilibrate at its specified temperature. If the testing tubing is large, the temperature equilibration process will take at least fifteen minutes. After temperature equilibration, the viscometer will release the ball and record the time required for the ball to roll a fixed distance. For accurate results, the test will need to be run at least four times for each parenteral product tested to obtain a viscosity reading with not more than a two percent relative standard deviation between readings. The final viscosity reading will be the mean of the four or more consecutive viscosity determinations with a maximum relative standard deviation between readings of two percent.
Newtonian viscosity calculation of, η, in (mPa x s) using calibration constant “k”:
η = k x (ρ1 − ρ2) x t
Where:
k = calibration constant of the instrument (mm2/s2) at a specified measuring angle and temperature
ρ1 = density of the ball used (g/mL)
ρ2 = density of the sample liquid (g/mL)
t = rolling time of the ball (s)
As part of calibration, fluids of known viscosities (and densities) are evaluated with different sizes of tubes and balls within the rolling ball viscometer. Evaluation of fluids of known viscosities and densities enables calculation of the measuring system constant, k. Some automated viscometers use a polynomial function to calibrate different angles of inclination and temperatures. Since calibrations are dependent on the ball radius, ball density, temperature, and test angle, recalibration is required if any of these parameters is modified. If the materials of the ball and tube are not the same, corrections calculated using the linear thermal expansion coefficients of the materials are to be applied to the calibrations.
Summary
Overall, viscous injectable formulations often have high concentrations of large molecules or non-aqueous solvents. With large protein biologics popularizing the drug therapy market, viscosity calculations for viscous products are essential for determining delivery mechanisms and accurately filling parenteral products. The rolling ball method is one of three methods described in the United States Pharmacopeia for determining viscosity. All in all, when filling a thick parenteral or cosmetic product, ensure you choose a contract manufacturing organization to support your sterile filling needs.
MycoScience is a contract manufacturing organization specializing in sterile syringe and vial filling. MycoScience also offers Preservative Efficacy Testing, Sterilization Validations, Bioburden Testing, Cleaning Validations, Microbial Aerosol Challenge Testing, Accelerated Aging, Microbiology Testing, Cytotoxicity Testing, Bacterial Endotoxin Testing, EO Residual Testing, Package Integrity Testing & Environmental Monitoring services medical devices and allied industries. MycoScience is an ISO 13485 certified facility.
References
Michael J. Akers. Sterile Drug Products Formulation, Packaging, Manufacture, and Quality. Drugs and the Pharmaceutical Sciences. Informa Healthcare. 2010.
Andrew Donnelly. Injecting High Viscosity Drugs: Challenges and Solutions. Bespak.com
Andy Fry. Injecting Highly Viscous Drugs. Pharmaceutical Technology. 2021.
United States Pharmacopeial Convention. <913>. Viscosity- Rolling Ball Method. Rockville, MD, USA. 2021. (USPC <913>)
