The other important issue is the settling of the dispersed material in the suspension (Swarbrick et al. 2005). The particle diameter and densities of the particle and medium can be used to predict the particle sedimentation rate using the Stoke’s equation:

dX /dt = d2 (ρp -ρM )g / 18η,

where dX/dt is the rate of sedimentation, d is the particle diameter,

rp is the particle density,

rM is the density of the medium, g is the gravitational constant, h is the viscosity of the medium.

Assumptions for the applicability of Stoke’s equation include (a) particles are spherical, (b) suspension is very dilute, (c) particles do not cause turbulence during settling,

(d) particles do not collide with each other, and (e) particles do not interact physically or chemically with the suspending medium. Although these assumptions may not hold true for many pharmaceutical suspensions, Stoke’s equation provides a basis for adjusting important formulation variables including particle size, density of the medium/ particles, and viscosity of the medium in order to decrease particle sedimentation rate.

Another key stability issue that should be addressed for suspensions is Ostwald ripening (Welin-Berger and Bergenstahl 2000). Since pharmaceutical suspensions contain a wide distribution of particle sizes, this phenomenon is relevant. In Ostwald ripening, particles of smaller size dissolve or release surface molecules, which in turn can re-grow on bigger particles. The rate at which particles undergo Ostwald ripening depends on diffusion or reaction of molecules on the particle surface. The diameter of the particles typically increases in a manner proportional to cube root of time (diffusion or dissolution-limited ripening) or square root (reaction or surface detachment-limited ripening) of time. In case of diffusion-controlled growth kinetics, which is more common for pharmaceutical suspensions, smaller particle size and high solubility results in faster ripening. By maintaining a narrow particle size, by coating the particle surfaces with a polymer or excipients that minimizes the energy of molecules on the particle surface, or by including excipients with low solubility that minimize drug dissolution from the particle surface can minimize Ostwald ripening to a significant extent during particle storage.

18.3.1.2  Formulation Methodology

To develop a suitable formulation with ideal properties, several methodologies utilizing the physical pharmacy principles are available (Swarbrick et al. 2005). Suspensions can be stabilized by (a) using a structured vehicle to keep particles deflocculated, (b) engineering controlled flocculation as a means to prevent cake formation, and (c) employing both structured vehicle and controlled flocculation.

After drug particles of suitable size are milled, the powder is wetted by an aqueous vehicle with or without wetting agents that are usually surfactants, as needed. In addition, structured vehicles can be employed to stabilize the formulation. Structured vehicles include aqueous solutions of usually negatively charged polymeric and hydrocolloid materials. Suitable excipients for this purpose by the oral route include methylcellulose, carboxymethylcellulose, bentonite, and carbomer. The concentration of these materials in a formulation will depend on the desired viscosity and consistency of the final preparation. These agents serve as suspending agents by virtue of their ability to alter viscosity and hence particle sedimentation rates.

The second approach for suspension stabilization incorporates flocculating agents, which are typically electrolytes, polymers, or surfactants that participate in the formation of floccules with particles. The addition of flocculating agents is optimized so as to obtain the maximum sedimentation volume in order to prevent caking and to allow easy resuspension. In general, flocculation of suspensions requires a careful optimization since flocculation by itself might lead to particle sedimentation and growth. If the floccules are porous networks, they may settle less rapidly and result in high volume sediments. Controlled flocculation was used in the design of ophthalmic suspensions intended for the back of the eye (Kabra and Sarkar 2009).

Sedimentation volume fraction and degree of flocculation can be assessed quantitatively during formulation development. The sedimentation volume fraction (FSV) can be estimated using the following equation.

FSV =VS / VT .

Where VS is the equilibrium volume of the sediment and VT is the total volume of the suspension. The value for FSV ranges between 0 and 1. When FSV = 1, no sediment is apparent since the system is well flocculated. Under these conditions, the suspension is esthetically pleasing with no supernatant layer and also it will not result in caking. High values of FSV suggest that the suspension is largely occupied by loose, porous flocs forming the sediment.

Degree of flocculation (D) is measured as the ratio of sedimentation volume fractions between flocculated and deflocculated suspensions.

D = (FSV )flocculated/ (FSV )deflocculated.

The degree of flocculation indicates the increased sediment volume resulting from flocculation. If D has a value of 4.0, this indicates that the volume of sediment in the flocculated system is four times than that in the deflocculated state. If a second flocculated formulation has a higher D value, the second formulation is preferred for greater stability. When flocculation in the system decreases, D approaches unity, its theoretical minimum.