**2. Standard methods and instrumentations of surface tension measurement**

Surface tension is a very complicated property of a liquid and it depends upon many variables such as temperature, composition of the solution, measurement time, materials of the apparatus and viscosity of the liquid. When a new surface is being formed, surface active chemicals diffuse to the surface and align. During this process, the surface tension is changing rapidly and continuously. Dynamic surface tension measurements allows track of these changes. When the process reaches equilibrium, static surface tension is obtained by measuring the maximum force at a liquid/gas interface on a sample where the net forces on the line is zero during the test time. Pure fluids and solvents have a single surface tension value and are measured with these devices (Drelich et al. 2002, Thiessen and Man, 1999).

There are a number of commonly available methods for measuring surface tension of liquids. Each has its advantages and limitations. The choice of a method depends on the nature of system to be studied and its stability, the degree of accuracy required, the condition under which its tension is to be measured and possibly on the ability of the instrument to automate the measurements. Realistically the surface tension values of a liquid will vary depending upon the method used (Thiessen and Man, 1999). The following section describes the most used methods for measuring static and dynamic surface and interfacial tension of liquid mixtures as well as semi solids and solids (a summary of the methods is shown in Table 1).

#### **2.1 Wilhelmy plate method**

The Wilhelmy plate consists of a thin glass, platinum plate or pre-wetted paper, usually on the order of a few centimeters square, attached to an electrobalance via thin metal wire and is used to measure equilibrium interfacial tension at an air-liquid or liquid-liquid interface (Figure 1). The metal plate must be cleaned from organic contaminants or test solutions, therefore the plate is flamed before the experiment to avoid contamination and to help maintain good wetting of the plate by the test liquid. The plate is then immersed and retracted into and out of the test solution contained in a beaker on a mechanical stage. During these cycles the force acting on the plate vs. depth of immersion are recorded. The meniscus formed at the solid–liquid interface is characterized by the contact angle. Two contact angles are measured, an advancing contact angle and a receding contact angle and the surface tension is calculated from the resulting force. The wetting force is monitored with time and this method is specially suited to check static surface tension value which in some cases is more than 4 h, hence the measurements are assumed to represent equilibrium. The main drawback of this method is that the surface age (time taken from surface formation till measurement) is not taken into account. When working with viscous liquids it takes time for a viscous material to flow from the dipped portion of the plate. Thus the surface tension will decrease initially till it reaches a pleatue once the excess liquid has flowed from the plate, therefore this method is not suited for highly viscous solutions (Avranas and Taspoulos, 2000; Krishnan et al., 2005; Santos and Castanho, 2004). The static wetting force on the plate is used to calculate the static surface tension (γ) using the Wilhelmy equation:

$$\gamma = \frac{F}{l.\cos\theta} \tag{1}$$

where *F* is the difference in wetting force upon immersion and withdrawal in mN/m, *l* is the wetted perimeter of the Wilhelmy plate and is the advancing or receding contact angle between the liquid phase and the plate. The contact angle of most liquids against platinum plate or clean glass is often assumed to be zero. This method does not require other correction factors such as fluid density. This method can be used to measure the contact angle and wetting properties of solid surfaces, where the platinum ring plate is replaced by the test surface (Avranas and Tasopoulos, 2000; Krishnan et al., 2005; Santos and Castanho, 2004; Sipahi, 2001; Tan et al., 2005).

The static contact angle, , is an important parameter in many industries including pharmaceutics. Contact angle measurements span every pharmaceutical field, from fluid dynamic to powder and tablet (Muster and Prestidge, 2002), adhesion and spray-drying of various drug delivery systems (Millqvist-Fureby et al., 1999) to the detection of impurities in the solutions of surface active compounds (Al-Maaieh and Aburub, 2007). It is of particular interest in powders, because the formulations are dependent on the contact angle. Contact angle measurements can be performed using various methods including Wilhelmy plate method, capillary rise method, goniometer and sessile drop method (Dingles and Harris, 2005). Among the interfacial tensiometry methods, the Wilhelmy plate method has been extensively developed and used by scientists in the pharmaceutical industry. The equipment used in this method is commercially available at several companies. With this technique it is possible to measure and control interfacial properties in granulation and tabletting, (Dreu et al., 2005) polymeric surfactants, emulsions and foams, protein-phospholipid interaction (Oritz et al., 2003), interfacial tension of topical skin formulations (Vejnovic et al., 2010), bioadhesive forces between mucosal tissue and microsphere drug delivery system (Vasir et al., 2003).

#### **2.2 Du Noüy ring method**

48 Toxicity and Drug Testing

plasma protein binding. By applying special surface treatments such as contact angle and surface tension measurements to pharmaceutical compounds, drug distribution, dissolution behavior and release pattern in various body fluids can be improved

Surface tension can influence the development, prediction and performance of pharmaceutical products and help to solve industrial problems and improve products quality. Due to the importance of this phenomenon in drug formulations, there is a growing need for specific interfacial consideration that can be used routinely to solve pharmaceutical problems and improve product quality and stability. In order to meet challenges and develop new and better performing pharmaceutical products, knowledge of surface tension and its measurements techniques is of utmost importance. Amongst many techniques used for characterizing the surface energies of pharmaceuticals are the surface tension measurements, contact angle and wettability tests (Buckton, 1988; Chamarthy et al., 2009; Puri et al., 2010). The objective of this chapter is to introduce experimental and computational methods of surface tension measurment in the

**2. Standard methods and instrumentations of surface tension measurement**  Surface tension is a very complicated property of a liquid and it depends upon many variables such as temperature, composition of the solution, measurement time, materials of the apparatus and viscosity of the liquid. When a new surface is being formed, surface active chemicals diffuse to the surface and align. During this process, the surface tension is changing rapidly and continuously. Dynamic surface tension measurements allows track of these changes. When the process reaches equilibrium, static surface tension is obtained by measuring the maximum force at a liquid/gas interface on a sample where the net forces on the line is zero during the test time. Pure fluids and solvents have a single surface tension value and are measured with these devices (Drelich et al. 2002, Thiessen and Man, 1999). There are a number of commonly available methods for measuring surface tension of liquids. Each has its advantages and limitations. The choice of a method depends on the nature of system to be studied and its stability, the degree of accuracy required, the condition under which its tension is to be measured and possibly on the ability of the instrument to automate the measurements. Realistically the surface tension values of a liquid will vary depending upon the method used (Thiessen and Man, 1999). The following section describes the most used methods for measuring static and dynamic surface and interfacial tension of liquid mixtures as well as semi solids and solids (a summary of the

The Wilhelmy plate consists of a thin glass, platinum plate or pre-wetted paper, usually on the order of a few centimeters square, attached to an electrobalance via thin metal wire and is used to measure equilibrium interfacial tension at an air-liquid or liquid-liquid interface (Figure 1). The metal plate must be cleaned from organic contaminants or test solutions, therefore the plate is flamed before the experiment to avoid contamination and to help maintain good wetting of the plate by the test liquid. The plate is then immersed and retracted into and out of the test solution contained in a beaker on a mechanical stage. During these cycles the force acting on the plate vs. depth of immersion are recorded. The

(Hancock et al., 1997; Ho et al., 2010).

pharmaceutical industry.

methods is shown in Table 1).

**2.1 Wilhelmy plate method** 

Du Noüy ring method is a traditional method used to measure static surface or interfacial tension. The measurement simply requires the ring to be wetted by the liquid and then pulled through the interface while measuring the force exerted on the ring (see Figure 1). Wetting properties of the surface or interface have little influence on this measuring technique. As in the case of Wilhelmy plate, the ring, with a diameter of 2-3 cm, is usually

Experimental and Computational Methods Pertaining to Surface Tension of Pharmaceuticals 51

techniques to measure the dynamic surface tension of various surfactants around and above their CMC value where adsorption is rapid (Christov et al., 2006). In the maximum bubble pressure method, a single interfacial tension value is drawn from each bubble formed. This device is the only available method capable of measuring surface tension in milliseconds time range. This method is particularly useful in measuring surface tension of highly concentrated

Among the conventional methods of surface tension measurement, drop shape techniques have proven to be reliable and easy to handle. This method weighs the mass of the liquid drop or the volume of the drop that falls off a capillary tip of known diameter when pumped very slowly. The weight of the drop falling off the capillary correlates with the interfacial tension and is measured by balancing it against a known gravitational force

> *W V g rf* 2

gravitational constant (*g*=9.81652 m/s2), *r* is the radius of the capillary tip and *f* denotes the empirical drop correction factor introduced by Harkins and Brown. The correction factor is required because only a portion of the drop falls from the capillary tip during detachment and this corrects the deviation of the drop volume from its ideal value (Drelich et al., 2002; Gunde et al., 2001). Impurity of active pharmaceutical solutions (Al-Maaieh and Aburub 2007), emulsion stability (Rangsansarid and Fukada, 2007), potency of local anesthetics (Matsuki et al., 1998), stability of biphasic aqueous systems (Mishima et al., 1998) and surface active properties of drugs (Deo et al., 2004) have been evaluated using this

Most of surface tension measurement techniques have limitations and only a few are suitable for protein solutions and high viscous solutions such as polymers blends. As discussed earlier, the Wilhelmy plate technique requires the establishment of a zero contact angle of the liquid at the plate which is difficult to guarantee with systems involving protein solutions and polymeric solutions with high viscosity. Du Noüy ring method, the drop volume technique or the maximum bubble method also lack dynamic control (Chen et al., 1999). In general, the equilibrium static methods such as sessile drop, spinning drop or a pendant drop method are most commonly used for measuring surface tension of molten

The pendent drop technique is capable of producing highly accurate static as well as dynamic interfacial tensions and contact angle measurements. This method is mostly used for the surface tension measurements of metals, alloys and polymers. In this method geometry of the drop is analyzed optically. The increased accuracy and simplicity of this ground based method allow ultra low surface tension, temperature and time dependence of interfacial tension as well as surface tension measurements at elevated pressures (Chen et

metals and viscous solutions (Arashiro and Demarquette, 1999).

is the difference in the density of the heavy phase and the light phase, *g* is the

(4)

surfactant solutions (Mischuk et al., 2000) and molten metals (Drelich et al., 2002).

**2.4 Drop volume/weight method** 

through the following equation:

where

technique.

al., 1999).

**2.5 Pendant drop method** 

made up of platinum or iridium is submerged into liquid and then pulled through the liquid-air interface. Maximum pull exerted on the ring by the surface is measured which is directly proportional to the surface tension value at equilibrium (Bodour and Miller-Maier, 1998). The ring is submerged into the solution and then slowly pulled through the liquid-air interface to detach from the interface with a force that is correlated to the surface tension. With this method, it is possible to measure the interfacial tension at both liquid-air and liquid-liquid interfaces. Surface tension can be calculated using the equation below:

$$\gamma = \frac{F}{p \cos \theta} f \tag{2}$$

where *p* is the perimeter of the three-phase contact line, *f* is the correction factor (because additional volume of liquid is lifted during the detachment of the ring from the interface) between each measurement. The platinum wire ring was rinsed three times with water, later with acetone as was blow dried (Drelich et al., 2002).

One major difference between the Du Noüy ring method and Wilhelmy's plate is the way in which the surface tension measurement is carried out. The ring moves through the interface whereas the plate is static at the interface, therefore there is no disturbance at the interface and this method is the recommended geometry for studying time dependent characteristics. Both ring and plate geometries can be used with the force balance type of tensiometer. A single instrument is normally capable of performing either Wilherlmy plate or du Noüy ring measurements (Thiessen and Man, 1999).

The surface tension measured by du Noüy method has been utilized in pharmaceutical research, for example, in the measurement of emulsion stability (Ishii et al., 1988; Takamura et al., 1984) and development of a dissolution media to simulate the physiological environment of the gastric region (Luner et al., 2001). This method can be used for characterization of pharmaceutical formulations such as plasticizer and polymer coating and surface tension calculation of various surfactant solutions and their CMC values (Palma et al., 2002) at the point of intersection of the interfacial tension value versus surfactant concentration plot (de la Maza, 1998; Korhonen et al., 2004; Zelkó et al., 2002).

#### **2.3 Maximum bubble pressure method**

The maximum bubble pressure method involves flow of a gas bubble (typically air or nitrogen) at a constant rate and blows them through a capillary with a known diameter which is submerged in the sample liquid. The pressure inside of the gas bubble increases until the bubble becomes hemispherical and its radius corresponds to the radius of the capillary. Beyond this the bubble is unstable and grows explosively until it detaches itself from the capillary and a new bubble is formed. The method is based on the continuous measurement of the applied pressure versus bubble rate formed at the end of the capillary. Figure 1 shows each step of bubble formation and corresponding change of bubble radius. The dynamic surface tension can be directly calculated by Young-LaPlace equation:

$$\gamma = \frac{\Delta P\_{\text{max}} R}{2} \tag{3}$$

where Δ*P*max is the maximum pressure difference and *R* is the capillary radius (Drelich et al., 2002; Hallowell and Hirt, 1994; Fainerman et al., 2006). This method is one of the most popular their CMC value where adsorption is rapid (Christov et al., 2006). In the maximum bubble pressure method, a single interfacial tension value is drawn from each bubble formed. This device is the only available method capable of measuring surface tension in milliseconds time range. This method is particularly useful in measuring surface tension of highly concentrated surfactant solutions (Mischuk et al., 2000) and molten metals (Drelich et al., 2002).
