Pharmaceutical suspensions : Theory of Sedimentation

Pharmaceutical suspensions are crucial formulations that involve the dispersion of solid particles within a liquid medium. The stability of these suspensions is paramount for ensuring consistent dosing, efficacy, and safety of the administered medication. One critical aspect of stability revolves around maintaining the uniform distribution of particles throughout the dispersion. In this article, we delve into the theory and factors influencing the sedimentation velocity of particles within pharmaceutical suspensions, exploring Stokes's law and its modifications, and the implications for suspension stability.

The Quest for Stability: Sedimentation in Suspensions

Sedimentation, the process by which particles settle under the influence of gravity, poses a challenge to the stability of pharmaceutical suspensions. While complete prevention of settling over time is often impractical, understanding the factors affecting sedimentation velocity is essential.

Stokes's Law: Foundation of Sedimentation Analysis

At the core of sedimentation analysis lies Stokes's law, which mathematically expresses the velocity of sedimentation. The law is defined as follows:

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Where:

• v is the terminal velocity in cm/sec.
• d is the diameter of the particle in cm.
• ρs​ and ρo​ are the densities of the dispersed phase and dispersion medium, respectively.
• g is the acceleration due to gravity.
• ηo​ is the viscosity of the dispersion medium in poise.

Stokes's law primarily applies to dilute pharmaceutical suspensions, typically containing less than about 2 g of solids per 100 mL of liquid. In such dilute systems, particles do not significantly interfere with one another during sedimentation, allowing for free settling.

Delayed Settling: Beyond Stokes's Law

However, in suspensions with higher particle concentrations (e.g., 5%, 10%, or higher percentages), delayed settling occurs. Here, particles impede each other's movement as they settle, rendering Stokes's law insufficient for accurate analysis.

Addressing Delayed Settling: Dilution and Its Caveats

To approximate physical stability in suspensions exhibiting delayed settling, dilution is sometimes employed. By reducing the concentration of dispersed phase to about 0.5% to 2.0% w/v, some estimation of stability can be obtained. However, dilution may alter the suspension's properties, including flocculation or deflocculation, thereby potentially skewing the stability assessment.

Beyond Ideal Conditions: Modifications to Stokes's Law

Real-world pharmaceutical suspensions rarely conform to ideal conditions, often exhibiting nonuniform particle size and shape distributions. To accommodate such complexities, modifications to Stokes's law have been proposed. One notable modification introduces the concept of initial porosity (ε) and a hindering factor (n):

Where:

• ′v′ is the rate of fall at the interface in cm/sec.
• v is the velocity of sedimentation according to Stokes's law.
• ε represents the initial porosity of the system, ranging from zero to unity.
• n is a constant reflecting the hindering effect specific to each system.

Implications and Considerations

Understanding sedimentation behavior and its implications on suspension stability is vital for pharmaceutical formulation scientists. While Stokes's law provides a foundational understanding, real-world suspensions often necessitate adjustments and considerations for factors such as particle concentration, shape, and size distribution.

Conclusion

Pharmaceutical suspensions play a crucial role in drug delivery, and their stability is a fundamental concern for formulation scientists. Sedimentation, influenced by factors such as particle concentration and interactions, poses challenges to stability assessment. While Stokes's law serves as a cornerstone in understanding sedimentation velocity, real-world suspensions require nuanced considerations and potential modifications to accurately assess stability. By delving into the intricacies of sedimentation theory, pharmaceutical researchers can better design suspensions that maintain uniform particle distribution and enhance therapeutic efficacy.

• Understanding the Role of Brownian Motion

  • Counteracting Sedimentation: Brownian motion plays a crucial role in suspensions, especially for particles ranging from 2 to 5 μm in diameter. Depending on particle and medium characteristics, Brownian movement acts against sedimentation, maintaining dispersed material in random motion, particularly evident at room temperature.

  • Critical Radius Determination: Burton proposed the concept of a critical radius ($r$) below which particles remain suspended due to kinetic bombardment by molecules of the suspending medium, driven by Brownian motion.

  • Microscopic Observations: Observation under a microscope reveals that the smallest particles in a pharmaceutical suspension experience reduced Brownian motion when dispersed in a 50% glycerin solution with a viscosity of approximately 5 centipoise. Consequently, ordinary pharmaceutical suspensions with suspending agents may not exhibit vigorous Brownian motion.

 Sedimentation of Flocculated Particles

• Distinct Sedimentation Behavior in Flocculated Systems

  • In flocculated systems, particles tend to aggregate into flocs, falling together during sedimentation.
  • This aggregation creates a clear boundary between the sediment and the supernatant liquid.
  • Even small particles in the system associate with the flocs, resulting in clarity in the liquid above the sediment.

• Comparison with Deflocculated Suspensions

  • Deflocculated suspensions contain particles of various sizes, and according to Stokes's law, larger particles settle faster than smaller ones.
  • Unlike flocculated systems, deflocculated suspensions lack a clear boundary between sediment and supernatant.
  • The supernatant in deflocculated suspensions remains turbid for an extended period, indicating a lack of particle aggregation.
  • Initial clarity or turbidity of the supernatant during settling stages serves as an indicator of flocculated or deflocculated state respectively.

• Factors Influencing Sedimentation Rate in Flocculated Systems

  • According to Hiestand, the initial settling rate in flocculated particles depends on floc size and the porosity of the aggregated mass.
  • Subsequent sedimentation rate is influenced by compaction and rearrangement processes within the sediment.
  • The term "subsidence" is often used to describe settling in flocculated systems, emphasizing the gradual settling process driven by floc characteristics and internal rearrangement.

Understanding the distinct sedimentation behavior of flocculated particles provides valuable insights for pharmaceutical suspension formulation and stability assessment. By recognizing the indicators and factors influencing sedimentation in flocculated systems, formulation scientists can optimize suspension designs to achieve desired stability and performance characteristics.