Medical Physics: Fluids PDF

Medical Physics: Fluids Department of Pharmacy First Year Fluids In this topic we will discuss the behavior of liquids and gases, both of which play an important role in the life sciences. The differences in the physical properties...

Medical Physics: Fluids Department of Pharmacy First Year Fluids In this topic we will discuss the behavior of liquids and gases, both of which play an important role in the life sciences. The differences in the physical properties of solids, liquids, and gases are explained in terms of the forces that bind the molecules. In a solid, the molecules are rigidly bound; a solid therefore has a definite shape and volume. The molecules constituting a liquid are not bound together with sufficient force to maintain a definite shape, but the binding is sufficiently strong to maintain a definite volume. A liquid adapts its shape to the vessel in which it is contained. In a gas, the molecules are not bound to each other. Therefore a gas has neither a definite shape nor a definite volume—it completely fills the vessel in which it is contained. Both gases and liquids are free to flow and are called fluids. Fluids and solids are governed by the same laws of mechanics, but, because of their ability to flow, fluids exhibit some phenomena not found in solid matter. FORCE AND PRESSURE IN A FLUID Solids and fluids transmit forces differently. When a force is applied to one section of a solid, this force is transmitted to the other parts of the solid with its direction unchanged. Because of a fluid's ability to flow, it transmits a force uniformly in all directions. Therefore, the pressure at any point in a fluid at rest is the same in all directions. The force exerted by a fluid at rest on any area is perpendicular to the area. A fluid in a container exerts a force on all parts of the container in contact with the fluid. A fluid also exerts a force on any object immersed in it. The pressure in a fluid increases with depth because of the weight of the fluid above. In a fluid of constant density ρ (the greek letter rho ‫)روو‬, the difference in pressure, P2 − P1, between two points separated by a vertical distance h is 1  Medical Physics: Fluids Department of Pharmacy First Year Fluid pressure is often measured in millimeters of mercury, or torr [after Evangelista Torricelli (1608–1674), the first person to understand the nature of atmospheric pressure]. One torr is the pressure exerted by a column of mercury that is 1mm high. Pascal, abbreviated as Pa is another commonly used unit of pressure. The relationship between the torr and several of the other units used to measure pressure follows: PASCAL’S PRINCIPLE When a force F1 is applied on a surface of a liquid that has an area A1, the pressure in the liquid increases by an amount P (see Fig. 1), given by In an incompressible liquid, the increase in the pressure at any point is transmitted undiminished to all other points in the liquid. This is known as Pascal’s principle. Because the pressure throughout the fluid is the same, the force F2 acting on the area A2 in Fig.. FIGURE 1 2  Medical Physics: Fluids Department of Pharmacy First Year FIGURE 2 Surface tension SURFACE TENSION The molecules constituting a liquid exert attractive forces on each other. A molecule in the interior of the liquid is surrounded by an equal number of neighboring molecules in all directions. Therefore, the net resultant intermolecular force on an interior molecule is zero. The situation is different, however, near the surface of the liquid. Because there are no molecules above the surface, a molecule here is pulled predominantly in one direction, toward the interior of the surface. This causes the surface of a liquid to contract and behave somewhat like a stretched membrane. This contracting tendency results in a surface tension that resists an increase in the free surface of the liquid. It can be shown that surface tension is a force acting tangential to the surface, normal to a line of unit length on the surface (Fig. 2). The surface tension T of water at 25°C is 72.8 dyn/cm. The total force FT produced by surface tension tangential to a liquid surface of boundary length L is When a liquid is contained in a vessel, the surface molecules near the wall are attracted to the wall. This attractive force is called adhesion. At the same time, however, these molecules are also subject to the attractive cohesive force exerted by the liquid, which pulls the molecules in the opposite direction. If the adhesive force is greater than the cohesive force, the liquid wets the container wall, and the liquid surface near the wall is curved upward. If the opposite is the case, the liquid surface is curved downward (see Fig. 3). The angle θ in Fig. 3 is the angle between the wall and the tangent to the liquid surface at the point of contact with the wall. For a given liquid and surface material, θ is a well-defined constant. For example, the contact angle between glass and water is 25°. If the adhesion is greater than the cohesion, a liquid in a narrow tube will rise to a specific height h (see Fig. 4A), which can be calculated 3  Medical Physics: Fluids Department of Pharmacy First Year FIGURE 3 Angle of contact when (A) liquid wets the wall and (B) liquid does not wet the wall. If the adhesion is smaller than the cohesion, the angle θ is greater than 90°. In this case, the height of the fluid in the tube is depressed (Fig. 4B). Eq. 9 still applies, yielding a negative number for h. These effects are called capillary action. FIGURE 4 (A) Capillary rise. (B) Capillary depression. Another consequence of surface tension is the tendency of liquid to assume a spherical shape. This tendency is most clearly observed in a liquid outside a container. Such an uncontained liquid forms into a sphere that can be noted in the shape of raindrops. The pressure inside the spherical liquid drop is higher than the pressure outside. The excess pressure ΔP in a liquid sphere of radius R is This is also the expression for the excess pressure inside an air bubble in a liquid. In other words, to create a gas bubble of radius R in a liquid with surface tension T, the 4  Medical Physics: Fluids Department of Pharmacy First Year pressure of the gas injected into the liquid must be greater than the pressure of the surrounding liquid by ΔP as given in Eq. 10. SURFACTANTS Surfactants are molecules that lower surface tension of liquids. (The word is an abbreviation of surface active agent.) The most common surfactant molecules have one end that is water-soluble (hydrophilic) and the other end water insoluble (hydrophobic) (see Fig. 5). As the word implies, the hydrophilic end is strongly attracted to water while the hydrophobic has very little attraction to water but is attracted and is readily soluble in oily liquids. Many different types of surfactant molecules are found in nature or as products of laboratory synthesis. FIGURE 5 Schematic of a surfactant molecule. When surfactant molecules are placed in water, they align on the surface with the hydrophobic end pushed out of the water as shown in Fig. 6. Such an alignment disrupts the surface structure of water, reducing the surface tension. A small concentration of surfactant molecules can typically reduce surface tension of water from 73 dyn/cm to 30 dyn/cm. In oily liquids, surfactants are aligned with the hydrophilic end squeezed out of the liquid. In this case the surface tension of the oil is reduced. The most familiar use of surfactants is as soaps and detergents to wash away oily substances. Here the hydrophobic end of the surfactants dissolves into the oil surface while the hydrophilic end remains exposed to the surrounding water as shown in Fig. 7. The aligned surfactant molecules reduce the surface tension of the oil. As a result, the oil breaks up into small droplets surrounded by the hydrophilic end of the surfactants. The small oil droplets are solubilized (that is suspended or dissolved) in the water and can now be washed away. 5  Medical Physics: Fluids Department of Pharmacy First Year FIGURE 7 Action of detergents. (A) Oil drop FIGURE 6 Surface layer of on a wet spot. (B) The hydrophobic end of surfactant molecules. surfactant molecules enter the oil spot. (C) The oil spot breaks up into smaller sections surrounded by hydrophilic ends. Importance of Surface Tension in Pharmaceutical Sciences In the life sciences, surface area is gaining importance in the characterization of materials during their development, formulation and manufacturing. The chemical activity, adsorption, dissolution, and bioavailability of a drug may depend on the surface of the molecule. In order to meet manufacturing challenges and develop new and better performing products with improved qualities, knowledge of surface tension is of utmost importance. Dosage Forms Tablets are the most popular and widely used dosage forms because of the advantages they offer both to the manufacturer and the patient. The formation of tablets requires knowledge of the surface tension for the different materials used in the process but here we will talk briefly about the tablet coating. Coatings on tablets are typically used to improve the appearance, mask the taste and odor or control the rate of drug release. Polymers are typically used as coating and therefore the surface tension of the polymer solutions affects the successfulness of the coating. Surface active molecules are routinely added to 6  Medical Physics: Fluids Department of Pharmacy First Year polymer coating solutions to lower their surface tension. Thus, knowledge of critical micelle concentration of surfactants is highly important also in the pharmaceutical industry. Example 1. pH Calculation What is the pH of 0.1 M acetic acid solution, pKa = 4.76? What is the pH after enough sodium acetate has been added to make the solution 0.1 M with respect to this salt? Answer:...................................... 7