- Email: [email protected]
Friction
Chapter 2
Friction If we examine the surface of any object, we observe that it is irregular. It has protrusions and valleys. Even surfaces that appear smooth to the eye show such irregularities under microscopic examination. When two surfaces are in contact, their irregularities intermesh, and as a result there is a resistance to the sliding or moving of one surface on the other. This resistance is called friction. If one surface is to be moved with respect to another, a force has to be applied to overcome friction. Consider a block resting on a surface as shown in Fig. 2.1. If we apply a force F to the block, it will tend to move. But the intermeshing of surfaces produces a frictional reaction force Ff that opposes motion. In order to move the object along the surface, the applied force must overcome the frictional force. The magnitude of the frictional force depends on the nature of the surfaces; clearly, the rougher the surfaces, the greater is the frictional force. The frictional property of surfaces is represented by the coefficient of friction μ. The magnitude of the frictional force depends also on the force Fn perpendicular to the surfaces that presses the surfaces together. The force Fn includes the weight W of the block (W ¼ mg; see Appendix A.7) plus any other force perpendicular to the surface. The magnitude of the force that presses the surfaces together determines to what extent the irregularities are intermeshed. The frictional force Ff is given by Ff ¼ μFn
(2.1)
Distinction has to be made between the frictional force that acts on moving object (called the kinetic frictional force) and the frictional force that acts on the object when it is stationary. The kinetic frictional force opposing motion of the object is obtained from Eq. 2.1 using the kinetic coefficient of friction μk : In general, it takes a larger force to get the object moving against a frictional force than to keep it in motion. This is not surprising because in the stationary case the irregularities of the two surfaces can settle more deeply into each other. The force that must be applied to an object to get it moving is again obtained from Eq. 2.1 but this time using the static coefficient of friction μs . This is the magnitude of the maximum static frictional force. The magnitude of the frictional force does not depend on the size of the contact area. If the surface contact area is increased, the force per unit area Physics in Biology and Medicine. https://doi.org/10.1016/B978-0-12-813716-1.00002-1 © 2019 Elsevier Inc. All rights reserved.
21
22 Physics in Biology and Medicine
Fn
Applied Force Ff
Frictional Force
F
FIGURE 2.1 Friction. For simplicity the reaction force that is equal and opposite to Fn is not shown.
(pressure) is decreased, and this reduces the interpenetration of the irregularities. However, at the same time, the number of irregularities is proportionately increased. As a result, the total frictional force is unchanged. Coefficients of static and kinetic friction between some surfaces are shown in Table 2.1. As is evident, the coefficient of static friction for two given surfaces is somewhat larger than the coefficient of kinetic friction. We have illustrated the concept of friction with surfaces sliding along each other, but frictional forces are encountered also in rolling (rolling friction) and in fluid flows (viscous friction). Rolling motion is not encountered in living systems, but viscous friction plays an important role in the flow of blood and other biological fluids. Whereas sliding friction is independent of velocity, fluid friction has a strong velocity dependence. We will discuss this in Chapter 3. Friction is everywhere around us. It is both a nuisance and an indispensable factor in the ability of animals to move. Without friction an object that is pushed into motion would continue to move forever (Newton’s first law, Appendix A). The slightest force would send us into eternal motion. It is the frictional force
TABLE 2.1 Coefficients of Friction, Static (μs) and Kinetic (μk) Surfaces
μs
Leather on oak
0.6
0.5
Rubber on dry concrete
0.9
0.7
Steel on ice
0.02
0.01
Dry bone on bone Bone on joint, lubricated
μk
0.3 0.01
0.003
Friction Chapter
2
23
that dissipates kinetic energy into heat and eventually stops the object (see Exercise 2-1). Without friction we could not walk; nor could we balance on an inclined plane (see Exercise 2-2). In both cases, friction provides the necessary reaction force. Friction also produces undesirable wear and tear and destructive heating of contact surfaces. Both nature and engineers attempt to maximize friction where it is necessary and minimize it where it is destructive. Friction is greatly reduced by introducing a fluid such as oil at the interface of two surfaces. The fluid fills the irregularities and therefore smooths out the surfaces. A natural example of such lubrication occurs in the joints of animals, which are lubricated by a fluid called the synovial fluid. This lubricant reduces the coefficient of friction by about a factor of 100. As is evident from Table 2.1, nature provides very efficient joint lubrication. The coefficient of friction here is significantly lower than for steel on ice. We will illustrate the effects of friction with a few examples.
2.1 STANDING AT AN INCLINE Referring to Fig. 2.2, let us calculate the angle of incline θ of an oak board on which a person of weight W can stand without sliding down. Assume that she is wearing leather-soled shoes and that she is standing in a vertical position as shown in the figure. The force Fn normal to the inclined surface is Fn ¼ Wcos θ
(2.2)
Ff ¼ μFn ¼ μs Wcos θ ¼ 0:6Wcos θ
(2.3)
The static frictional force Ff is
The force parallel to the surface Fp , which tends to cause the sliding, is Fp ¼ Wsin θ
Ff
FIGURE 2.2 Standing on an incline.
Fp
(2.4)
24 Physics in Biology and Medicine
The person will slide when the force Fp is greater than the frictional force Ff ; that is, Fp > F f
(2.5)
At the onset of sliding, these two forces are just equal; therefore, Ff ¼ Fp 0:6Wcos θ ¼ Wsin θ
(2.6)
or sin θ ¼ tan θ ¼ 0:6 cos θ Therefore θ ¼ 31°.
2.2 FRICTION AT THE HIP JOINT We have shown in Chapter 1 that the forces acting on the joints are very large. When the joints are in motion, these large forces produce frictional wear, which could be damaging unless the joints are well lubricated. Frictional wear at the joints is greatly reduced by a smooth cartilage coating at the contact ends of the bone and by synovial fluid which lubricates the contact areas. We will now examine the effect of lubrication on the hip joint in a person. When a person walks, the full weight of the body rests on one leg through most of each step. Because the center of gravity is not directly above the joint, the force on the joint is greater than the weight. Depending on the speed of walking, this force is about 2.4 times the weight (see Chapter 1). In each step, the joint rotates through about 60°. Since the radius of the joint is about 3 cm, the joint slides about 3 cm inside the socket during each step. The frictional force on the joint is Ff ¼ 2:4Wμ
(2.7)
The work expended in sliding the joint against this friction is the product of the frictional force and the distance over which the force acts (see Appendix A). Thus, the work expended during each step is Work ¼ Ff distance ¼ 2:4Wμð3cmÞ ¼ 7:2μW erg
(2.8)
If the joint were not lubricated, the coefficient of friction ðμÞ would be about 0.3. Under these conditions, the work expended would be Work ¼ 2:16 W erg
(2.9)
This is a large amount of work to expend on each step. It is equivalent to lifting the full weight of the person 2.16 cm. Furthermore, this work would be dissipated into heat energy, which would destroy the joint. As it is, the joint is well lubricated, and the coefficient of friction is only 0.003. Therefore, the work expended in counteracting friction and the resultant heating of the joint are negligible. However, as we age, the joint cartilage begins
Friction Chapter
2
25
to wear, efficiency of lubrication decreases, and the joints may become seriously damaged. Studies indicate that by the age of 70 about two-thirds of people have knee joint problems and about one-third have hip problems.
2.3 SPINE FIN OF A CATFISH Although in most cases good lubrication of bone-contact surfaces is essential, there are a few cases in nature where bone contacts are purposely unlubricated to increase friction. The catfish has such a joint connecting its dorsal spine fin to the rest of its skeleton (Fig. 2.3). Normally the fin is folded flat against the body, but when the fish is attacked, the appropriate muscles pull the bone of the fin into a space provided in the underlying skeleton. Since the coefficient of friction between the fin bone and the skeleton is high, the frictional force tends to lock the fin in the up position. In order to remove the fin, a force must be applied in a predominantly vertical direction with respect to the underlying skeleton. The erect sharp fin discourages predators from eating the catfish. Figure 2.3b is a simplified representation of the spine and the protruding fin. The shaded block represents the movable fin bone, and the horizontal block is the spine holding the fin. Assume that a force F at an angle θ is applied at point A to dislodge the bone. The force is shown to act at point A, 2.5 cm above point B. Dorsal spine
(A) A θ
2.5 cm
Fin bone
1/2 cm
Spine B
C
(B)
1 cm
FIGURE 2.3 (A) Catfish. (B) Simplified representation of the spine in the catfish.
26 Physics in Biology and Medicine
The dimensions shown in the figure are to be used in the calculations required for Exercise 2-3. The applied force tips the bone, and as a result reaction forces are set up at points B and C. The components of these forces normal to the fin-bone surface produce frictional forces that resist removal of the bone. Calculation of some of the properties of the locking mechanism is left as an exercise.
2.4 BIOTRIBOLOGY Tribology is a field of engineering and physics that studies friction. Traditionally, most of the studies in this field focused on reducing friction in industrial equipment such as electric motors, generators, gears, and internal combustion engines. More recently, during the past 20 years or so, the field has expanded to study friction in as it pertains to biology and medicine. This new subarea of tribology has been named “biotribology.” We have already touched on this subject in the preceding two sections where we described the effect of friction at the hip joint and the role of friction in the defensive positioning of the spine in the catfish. Here we examine briefly some of the other areas of this field. Experiments in biotribology present problems of reproducibility and control principally, because the properties of a given biological material, such as skin or mucus for example, change as a function of many variables such as the prevailing temperature, humidity, and time of day. The relevant materials also show wide variability from person to person. The properties of human skin that covers 1.5 to 2 m2 of the body are significantly different at the various regions on the body and depend significantly on the age of the individual. For example, depending on the location, the roughness of human skin (the distance between the lowest and highest point at a given location) varies from 10 to 200 μm. In spite of these challenges, relevant issues in biotribology have been identified and progress has been made in this important field. We will briefly discuss three active areas of biotribology.
2.4.1 Oral Biotribology The principal components of the oral cavity (mouth) are teeth, tongue, and saliva. The composition of saliva and its role in the chemistry and tribology of the mouth are now well understood. Most of the saliva is produced by three pairs of salivary glands. Two of the glands are located at either side of the mouth below the jaw bone. The third pair of glands is located between the ear and the jaw. In addition, several smaller glands, distributed throughout the mouth, contribute to the flow of saliva. Human saliva consists of about 99% water and a highly complex mixture of proteins and ions that give the saliva its remarkable properties necessary for the proper functioning of the oral system. Some of the proteins in saliva adhere strongly both to teeth and to soft tissue in the oral cavity. These adhered molecules form a substrate for the formation of a coating of saliva on oral surfaces that provides an excellent lubricant for these
Friction Chapter
2
27
surfaces. The coefficient of friction of such a coated surface is about 0.02, similar to that of synovial fluid. The coefficient of friction of the surface coated saliva is about two orders of magnitude lower than the uncoated surface or the surface coated with clear water. The low friction coating protects the teeth from excessive wear and also protects soft tissue from being bruised and damaged by hard foods. Another role of saliva is in the processing of food. In the process of chewing, the saliva is mixed with the food making the mixture more slippery promoting easy sliding down the esophagus into the stomach. A simple calculation shows that the thickness of the saliva layer on the oral surfaces is approximately 0.1 mm. (See Exercise 2-4.) In addition to its tribological properties, saliva is also a mild antiseptic containing a range of compounds that have antibacterial and antiviral properties. Some fraction of these molecules also promotes blood clotting. This protective and healing nature of saliva is probably why wounded animals, including humans, respond instinctively to an injury by licking the wound. These attributes of saliva are likely the reason for the observation that in most cases wounds in the mouth heal faster than wounds on other parts of the body. The process of licking of course also clears the wound of debris that is likely to retard healing. As is pointed out in the literature, licking of wounds is not universally recommended. Licking may introduce into the wound bacteria and viruses that are immune to the disinfectant properties of the saliva. Such complications, however, seem to be rare. Further saliva is somewhat basic and functions as a buffer that keeps the acidity of the mouth near the neutral point (pH 7). This is important because acid tends to leach out calcium and other minerals out of teeth making them susceptible to cavities and other structural damage. The normal wear of teeth is due to mastication (chewing). During normal wear, only about 40 μm of the tooth is worn off per year. A greater destructive effect on teeth is the increase in the consumption of soft drinks and sugar that have contributed to an increase in cavities and tooth decay worldwide. Soft drinks are mostly acidic and therefore have a direct deleterious effect on teeth. The effect of sugar is indirect. The oral cavity contains a variety of bacteria that feed on sugar. Some of the bacteria are helpful in maintaining oral health. They control the population of other bacteria that cause oral diseases such as oral candida, for example. However, some bacteria feed on sugar and produce acids as a byproducts that, as mentioned earlier, leach out the minerals that compose teeth. Here again saliva has a significant role in repairing the damage. The inorganic ions in the saliva can remineralize, at least partially, the eroded tooth material. However, saliva cannot fully compensate for the deleterious effects of a damaging diet.
2.4.2 Hair Biotribology Frictional forces act between hair fibers and between hair and objects in contact with hair such as a comb. In large measure, hair friction determines the esthetic
28 Physics in Biology and Medicine
properties of hair. Too much friction and the hair fibers stick together giving the hair a stringy appearance. Not enough friction makes styling difficult giving hair an unruly appearance. Millions of dollars annually are spent by the hairproducts industry to study frictional properties of hair, and how it is affected by products such as shampoo, hair conditioner, and hair spray. Measurement of hair friction coefficient is difficult but techniques have been developed to perform such measurements. The effect on hair friction of environmental conditions such as natural hair oil, sweat, dirt, hair dyes has been measured. These factors all tend to increase friction. Shampoos and hair conditioners are formulated to yield optimum hair properties as envisioned by the manufacturer. Shampoo is designed to clean the hair and is essentially a soap. (See also Chapter 7.) The main cleaning agents in shampoos are surfactants. These are molecules that have a hydrophilic (water-attracting) and a hydrophobic (water-repelling) components. The hydrophobic component attaches itself to hair oil, sweat, and other foreign components. The hydrophilic component attaches to the rinsing water and washes away the dirt. This is essentially the way all soaps work. Hair conditioners contain positive ion surfactants and large fatty alcohol molecules that replace the natural washed-away oils that make the hair soft and adequately lubricated. Both shampoos and conditioners contain a variety of inactive ingredients among them perfumes, foaming agents, preservatives, and coloring, designed to enhance the appeal of the products.
2.4.3 Biotribology of Textiles Friction is obviously present in areas of contact between skin and textiles. Under most conditions, such frictional contact does not cause problems. However, in some cases, repeated relative motion subject to friction can damage the skin. Most people have experienced an occasional blister, often on the heel or sole of the foot caused by motion between the skin and an ill-fitting shoe-sock combination. The coefficient of friction increases when the skin and textile are wet, making skin damage more likely. A simple blister is relatively easy to treat by improving the shoe-sock fit and cushioning the blister with padding. Bedsores (also called decubitus) are a much more serious condition found mostly in patients who require long periods of bed rest. They are caused by the pressure and friction at the areas of contact between the skin and the resting surface. Even though the patient appears to be at rest, everpresent tiny movements tend to frictionally abrade the skin. Pressure due to body weight reduces blood flow to the contact area, increasing the risk of serious ulceration and infection. Decubitus may also be a problem for people confined to wheel chairs who like wise remain in a fixed pressure bearing position for prolonged periods of time. Several research groups are working on the development of new textiles for bedsheets and other applications involving skin contact that would reduce the
Friction Chapter
2
29
friction on the skin of patients at risk of decubitus. Initially five qualities are sought. 1. The material should readily wick away moisture so that the area of contact be kept as dry as possible. 2. While covering the same overall area the material should present a smaller microscopic contact area. This can be achieved by increasing the free interfacial volume. 3. Reducing the penetration of the textile surface into the skin. 4. Making the fibers of the material more elastic resulting in reduced abrasiveness. 5. Reducing pressure on specific areas of the body. In trial tests, several new materials have yielded promising improvements.
EXERCISES 2-1. (a) Assume that a 50-kg skater, on level ice, has built up her speed to 30 km/h. How far will she coast before the sliding friction dissipates her energy? (Kinetic energy ¼ 12 mv2 ; see Appendix A.) (b) How does the distance of coasting depend on the mass of the skater? 2-2. Referring to Fig. 1.5, compute the coefficient of friction at which the tendency of the body to slide and the tendency to topple due to the applied force are equal. 2-3. (a) Referring to Fig. 2.3, assume that a dislodging force of 0.1 N is applied at θ ¼ 20° and the angle between the fin bone and the spine is 45°. Calculate the minimum value for the coefficient of friction between the bones to prevent dislodging of the bone. (b) Assuming that the coefficient of friction is 1.0, what is the value of the angle θ at which a force of 0.2 N will just dislodge the bone? What would this angle be if the bones were lubricated ðμ ¼ 0:01Þ? 2-4. Calculate the thickness of the saliva layer on the inside of the oral cavity and the tongue using the following measured values. (These are approximate values obtained by measuring the parameters for several people.): Volume of oral cavity 40 cm3, Volume of tongue 30 cm3. In your calculation, assume the shape of both the oral cavity and the tongue is spherical. Volume of residual saliva after swallowing all excess saliva 0.8 mL ¼ 0.8 cm3. Assume that this amount of saliva coats evenly the tongue and the inside of the oral cavity. Neglect the saliva coating the teeth.
Friction If we examine the surface of any object, we observe that it is irregular. It has protrusions and valleys. Even surfaces that appear smooth to the eye show such irregularities under microscopic examination. When two surfaces are in contact, their irregularities intermesh, and as a result there is a resistance to the sliding or moving of one surface on the other. This resistance is called friction. If one surface is to be moved with respect to another, a force has to be applied to overcome friction. Consider a block resting on a surface as shown in Fig. 2.1. If we apply a force F to the block, it will tend to move. But the intermeshing of surfaces produces a frictional reaction force Ff that opposes motion. In order to move the object along the surface, the applied force must overcome the frictional force. The magnitude of the frictional force depends on the nature of the surfaces; clearly, the rougher the surfaces, the greater is the frictional force. The frictional property of surfaces is represented by the coefficient of friction μ. The magnitude of the frictional force depends also on the force Fn perpendicular to the surfaces that presses the surfaces together. The force Fn includes the weight W of the block (W ¼ mg; see Appendix A.7) plus any other force perpendicular to the surface. The magnitude of the force that presses the surfaces together determines to what extent the irregularities are intermeshed. The frictional force Ff is given by Ff ¼ μFn
(2.1)
Distinction has to be made between the frictional force that acts on moving object (called the kinetic frictional force) and the frictional force that acts on the object when it is stationary. The kinetic frictional force opposing motion of the object is obtained from Eq. 2.1 using the kinetic coefficient of friction μk : In general, it takes a larger force to get the object moving against a frictional force than to keep it in motion. This is not surprising because in the stationary case the irregularities of the two surfaces can settle more deeply into each other. The force that must be applied to an object to get it moving is again obtained from Eq. 2.1 but this time using the static coefficient of friction μs . This is the magnitude of the maximum static frictional force. The magnitude of the frictional force does not depend on the size of the contact area. If the surface contact area is increased, the force per unit area Physics in Biology and Medicine. https://doi.org/10.1016/B978-0-12-813716-1.00002-1 © 2019 Elsevier Inc. All rights reserved.
21
22 Physics in Biology and Medicine
Fn
Applied Force Ff
Frictional Force
F
FIGURE 2.1 Friction. For simplicity the reaction force that is equal and opposite to Fn is not shown.
(pressure) is decreased, and this reduces the interpenetration of the irregularities. However, at the same time, the number of irregularities is proportionately increased. As a result, the total frictional force is unchanged. Coefficients of static and kinetic friction between some surfaces are shown in Table 2.1. As is evident, the coefficient of static friction for two given surfaces is somewhat larger than the coefficient of kinetic friction. We have illustrated the concept of friction with surfaces sliding along each other, but frictional forces are encountered also in rolling (rolling friction) and in fluid flows (viscous friction). Rolling motion is not encountered in living systems, but viscous friction plays an important role in the flow of blood and other biological fluids. Whereas sliding friction is independent of velocity, fluid friction has a strong velocity dependence. We will discuss this in Chapter 3. Friction is everywhere around us. It is both a nuisance and an indispensable factor in the ability of animals to move. Without friction an object that is pushed into motion would continue to move forever (Newton’s first law, Appendix A). The slightest force would send us into eternal motion. It is the frictional force
TABLE 2.1 Coefficients of Friction, Static (μs) and Kinetic (μk) Surfaces
μs
Leather on oak
0.6
0.5
Rubber on dry concrete
0.9
0.7
Steel on ice
0.02
0.01
Dry bone on bone Bone on joint, lubricated
μk
0.3 0.01
0.003
Friction Chapter
2
23
that dissipates kinetic energy into heat and eventually stops the object (see Exercise 2-1). Without friction we could not walk; nor could we balance on an inclined plane (see Exercise 2-2). In both cases, friction provides the necessary reaction force. Friction also produces undesirable wear and tear and destructive heating of contact surfaces. Both nature and engineers attempt to maximize friction where it is necessary and minimize it where it is destructive. Friction is greatly reduced by introducing a fluid such as oil at the interface of two surfaces. The fluid fills the irregularities and therefore smooths out the surfaces. A natural example of such lubrication occurs in the joints of animals, which are lubricated by a fluid called the synovial fluid. This lubricant reduces the coefficient of friction by about a factor of 100. As is evident from Table 2.1, nature provides very efficient joint lubrication. The coefficient of friction here is significantly lower than for steel on ice. We will illustrate the effects of friction with a few examples.
2.1 STANDING AT AN INCLINE Referring to Fig. 2.2, let us calculate the angle of incline θ of an oak board on which a person of weight W can stand without sliding down. Assume that she is wearing leather-soled shoes and that she is standing in a vertical position as shown in the figure. The force Fn normal to the inclined surface is Fn ¼ Wcos θ
(2.2)
Ff ¼ μFn ¼ μs Wcos θ ¼ 0:6Wcos θ
(2.3)
The static frictional force Ff is
The force parallel to the surface Fp , which tends to cause the sliding, is Fp ¼ Wsin θ
Ff
FIGURE 2.2 Standing on an incline.
Fp
(2.4)
24 Physics in Biology and Medicine
The person will slide when the force Fp is greater than the frictional force Ff ; that is, Fp > F f
(2.5)
At the onset of sliding, these two forces are just equal; therefore, Ff ¼ Fp 0:6Wcos θ ¼ Wsin θ
(2.6)
or sin θ ¼ tan θ ¼ 0:6 cos θ Therefore θ ¼ 31°.
2.2 FRICTION AT THE HIP JOINT We have shown in Chapter 1 that the forces acting on the joints are very large. When the joints are in motion, these large forces produce frictional wear, which could be damaging unless the joints are well lubricated. Frictional wear at the joints is greatly reduced by a smooth cartilage coating at the contact ends of the bone and by synovial fluid which lubricates the contact areas. We will now examine the effect of lubrication on the hip joint in a person. When a person walks, the full weight of the body rests on one leg through most of each step. Because the center of gravity is not directly above the joint, the force on the joint is greater than the weight. Depending on the speed of walking, this force is about 2.4 times the weight (see Chapter 1). In each step, the joint rotates through about 60°. Since the radius of the joint is about 3 cm, the joint slides about 3 cm inside the socket during each step. The frictional force on the joint is Ff ¼ 2:4Wμ
(2.7)
The work expended in sliding the joint against this friction is the product of the frictional force and the distance over which the force acts (see Appendix A). Thus, the work expended during each step is Work ¼ Ff distance ¼ 2:4Wμð3cmÞ ¼ 7:2μW erg
(2.8)
If the joint were not lubricated, the coefficient of friction ðμÞ would be about 0.3. Under these conditions, the work expended would be Work ¼ 2:16 W erg
(2.9)
This is a large amount of work to expend on each step. It is equivalent to lifting the full weight of the person 2.16 cm. Furthermore, this work would be dissipated into heat energy, which would destroy the joint. As it is, the joint is well lubricated, and the coefficient of friction is only 0.003. Therefore, the work expended in counteracting friction and the resultant heating of the joint are negligible. However, as we age, the joint cartilage begins
Friction Chapter
2
25
to wear, efficiency of lubrication decreases, and the joints may become seriously damaged. Studies indicate that by the age of 70 about two-thirds of people have knee joint problems and about one-third have hip problems.
2.3 SPINE FIN OF A CATFISH Although in most cases good lubrication of bone-contact surfaces is essential, there are a few cases in nature where bone contacts are purposely unlubricated to increase friction. The catfish has such a joint connecting its dorsal spine fin to the rest of its skeleton (Fig. 2.3). Normally the fin is folded flat against the body, but when the fish is attacked, the appropriate muscles pull the bone of the fin into a space provided in the underlying skeleton. Since the coefficient of friction between the fin bone and the skeleton is high, the frictional force tends to lock the fin in the up position. In order to remove the fin, a force must be applied in a predominantly vertical direction with respect to the underlying skeleton. The erect sharp fin discourages predators from eating the catfish. Figure 2.3b is a simplified representation of the spine and the protruding fin. The shaded block represents the movable fin bone, and the horizontal block is the spine holding the fin. Assume that a force F at an angle θ is applied at point A to dislodge the bone. The force is shown to act at point A, 2.5 cm above point B. Dorsal spine
(A) A θ
2.5 cm
Fin bone
1/2 cm
Spine B
C
(B)
1 cm
FIGURE 2.3 (A) Catfish. (B) Simplified representation of the spine in the catfish.
26 Physics in Biology and Medicine
The dimensions shown in the figure are to be used in the calculations required for Exercise 2-3. The applied force tips the bone, and as a result reaction forces are set up at points B and C. The components of these forces normal to the fin-bone surface produce frictional forces that resist removal of the bone. Calculation of some of the properties of the locking mechanism is left as an exercise.
2.4 BIOTRIBOLOGY Tribology is a field of engineering and physics that studies friction. Traditionally, most of the studies in this field focused on reducing friction in industrial equipment such as electric motors, generators, gears, and internal combustion engines. More recently, during the past 20 years or so, the field has expanded to study friction in as it pertains to biology and medicine. This new subarea of tribology has been named “biotribology.” We have already touched on this subject in the preceding two sections where we described the effect of friction at the hip joint and the role of friction in the defensive positioning of the spine in the catfish. Here we examine briefly some of the other areas of this field. Experiments in biotribology present problems of reproducibility and control principally, because the properties of a given biological material, such as skin or mucus for example, change as a function of many variables such as the prevailing temperature, humidity, and time of day. The relevant materials also show wide variability from person to person. The properties of human skin that covers 1.5 to 2 m2 of the body are significantly different at the various regions on the body and depend significantly on the age of the individual. For example, depending on the location, the roughness of human skin (the distance between the lowest and highest point at a given location) varies from 10 to 200 μm. In spite of these challenges, relevant issues in biotribology have been identified and progress has been made in this important field. We will briefly discuss three active areas of biotribology.
2.4.1 Oral Biotribology The principal components of the oral cavity (mouth) are teeth, tongue, and saliva. The composition of saliva and its role in the chemistry and tribology of the mouth are now well understood. Most of the saliva is produced by three pairs of salivary glands. Two of the glands are located at either side of the mouth below the jaw bone. The third pair of glands is located between the ear and the jaw. In addition, several smaller glands, distributed throughout the mouth, contribute to the flow of saliva. Human saliva consists of about 99% water and a highly complex mixture of proteins and ions that give the saliva its remarkable properties necessary for the proper functioning of the oral system. Some of the proteins in saliva adhere strongly both to teeth and to soft tissue in the oral cavity. These adhered molecules form a substrate for the formation of a coating of saliva on oral surfaces that provides an excellent lubricant for these
Friction Chapter
2
27
surfaces. The coefficient of friction of such a coated surface is about 0.02, similar to that of synovial fluid. The coefficient of friction of the surface coated saliva is about two orders of magnitude lower than the uncoated surface or the surface coated with clear water. The low friction coating protects the teeth from excessive wear and also protects soft tissue from being bruised and damaged by hard foods. Another role of saliva is in the processing of food. In the process of chewing, the saliva is mixed with the food making the mixture more slippery promoting easy sliding down the esophagus into the stomach. A simple calculation shows that the thickness of the saliva layer on the oral surfaces is approximately 0.1 mm. (See Exercise 2-4.) In addition to its tribological properties, saliva is also a mild antiseptic containing a range of compounds that have antibacterial and antiviral properties. Some fraction of these molecules also promotes blood clotting. This protective and healing nature of saliva is probably why wounded animals, including humans, respond instinctively to an injury by licking the wound. These attributes of saliva are likely the reason for the observation that in most cases wounds in the mouth heal faster than wounds on other parts of the body. The process of licking of course also clears the wound of debris that is likely to retard healing. As is pointed out in the literature, licking of wounds is not universally recommended. Licking may introduce into the wound bacteria and viruses that are immune to the disinfectant properties of the saliva. Such complications, however, seem to be rare. Further saliva is somewhat basic and functions as a buffer that keeps the acidity of the mouth near the neutral point (pH 7). This is important because acid tends to leach out calcium and other minerals out of teeth making them susceptible to cavities and other structural damage. The normal wear of teeth is due to mastication (chewing). During normal wear, only about 40 μm of the tooth is worn off per year. A greater destructive effect on teeth is the increase in the consumption of soft drinks and sugar that have contributed to an increase in cavities and tooth decay worldwide. Soft drinks are mostly acidic and therefore have a direct deleterious effect on teeth. The effect of sugar is indirect. The oral cavity contains a variety of bacteria that feed on sugar. Some of the bacteria are helpful in maintaining oral health. They control the population of other bacteria that cause oral diseases such as oral candida, for example. However, some bacteria feed on sugar and produce acids as a byproducts that, as mentioned earlier, leach out the minerals that compose teeth. Here again saliva has a significant role in repairing the damage. The inorganic ions in the saliva can remineralize, at least partially, the eroded tooth material. However, saliva cannot fully compensate for the deleterious effects of a damaging diet.
2.4.2 Hair Biotribology Frictional forces act between hair fibers and between hair and objects in contact with hair such as a comb. In large measure, hair friction determines the esthetic
28 Physics in Biology and Medicine
properties of hair. Too much friction and the hair fibers stick together giving the hair a stringy appearance. Not enough friction makes styling difficult giving hair an unruly appearance. Millions of dollars annually are spent by the hairproducts industry to study frictional properties of hair, and how it is affected by products such as shampoo, hair conditioner, and hair spray. Measurement of hair friction coefficient is difficult but techniques have been developed to perform such measurements. The effect on hair friction of environmental conditions such as natural hair oil, sweat, dirt, hair dyes has been measured. These factors all tend to increase friction. Shampoos and hair conditioners are formulated to yield optimum hair properties as envisioned by the manufacturer. Shampoo is designed to clean the hair and is essentially a soap. (See also Chapter 7.) The main cleaning agents in shampoos are surfactants. These are molecules that have a hydrophilic (water-attracting) and a hydrophobic (water-repelling) components. The hydrophobic component attaches itself to hair oil, sweat, and other foreign components. The hydrophilic component attaches to the rinsing water and washes away the dirt. This is essentially the way all soaps work. Hair conditioners contain positive ion surfactants and large fatty alcohol molecules that replace the natural washed-away oils that make the hair soft and adequately lubricated. Both shampoos and conditioners contain a variety of inactive ingredients among them perfumes, foaming agents, preservatives, and coloring, designed to enhance the appeal of the products.
2.4.3 Biotribology of Textiles Friction is obviously present in areas of contact between skin and textiles. Under most conditions, such frictional contact does not cause problems. However, in some cases, repeated relative motion subject to friction can damage the skin. Most people have experienced an occasional blister, often on the heel or sole of the foot caused by motion between the skin and an ill-fitting shoe-sock combination. The coefficient of friction increases when the skin and textile are wet, making skin damage more likely. A simple blister is relatively easy to treat by improving the shoe-sock fit and cushioning the blister with padding. Bedsores (also called decubitus) are a much more serious condition found mostly in patients who require long periods of bed rest. They are caused by the pressure and friction at the areas of contact between the skin and the resting surface. Even though the patient appears to be at rest, everpresent tiny movements tend to frictionally abrade the skin. Pressure due to body weight reduces blood flow to the contact area, increasing the risk of serious ulceration and infection. Decubitus may also be a problem for people confined to wheel chairs who like wise remain in a fixed pressure bearing position for prolonged periods of time. Several research groups are working on the development of new textiles for bedsheets and other applications involving skin contact that would reduce the
Friction Chapter
2
29
friction on the skin of patients at risk of decubitus. Initially five qualities are sought. 1. The material should readily wick away moisture so that the area of contact be kept as dry as possible. 2. While covering the same overall area the material should present a smaller microscopic contact area. This can be achieved by increasing the free interfacial volume. 3. Reducing the penetration of the textile surface into the skin. 4. Making the fibers of the material more elastic resulting in reduced abrasiveness. 5. Reducing pressure on specific areas of the body. In trial tests, several new materials have yielded promising improvements.
EXERCISES 2-1. (a) Assume that a 50-kg skater, on level ice, has built up her speed to 30 km/h. How far will she coast before the sliding friction dissipates her energy? (Kinetic energy ¼ 12 mv2 ; see Appendix A.) (b) How does the distance of coasting depend on the mass of the skater? 2-2. Referring to Fig. 1.5, compute the coefficient of friction at which the tendency of the body to slide and the tendency to topple due to the applied force are equal. 2-3. (a) Referring to Fig. 2.3, assume that a dislodging force of 0.1 N is applied at θ ¼ 20° and the angle between the fin bone and the spine is 45°. Calculate the minimum value for the coefficient of friction between the bones to prevent dislodging of the bone. (b) Assuming that the coefficient of friction is 1.0, what is the value of the angle θ at which a force of 0.2 N will just dislodge the bone? What would this angle be if the bones were lubricated ðμ ¼ 0:01Þ? 2-4. Calculate the thickness of the saliva layer on the inside of the oral cavity and the tongue using the following measured values. (These are approximate values obtained by measuring the parameters for several people.): Volume of oral cavity 40 cm3, Volume of tongue 30 cm3. In your calculation, assume the shape of both the oral cavity and the tongue is spherical. Volume of residual saliva after swallowing all excess saliva 0.8 mL ¼ 0.8 cm3. Assume that this amount of saliva coats evenly the tongue and the inside of the oral cavity. Neglect the saliva coating the teeth.