“Transport phenomena” is the accepted name for the mathematical description of the fundamental phenomena of momentum, energy, and mass transport. This acceptance has developed over some 35 years and was initiated in 1960 by the classic book by Bird, Stewart, and Lightfoot, Transport Phenomena (Wiley). Concurrently, the digital Computer has evolved as an essential element in the analysis of chemical engineering Systems. Yet, rather surprisingly, these two fundamental developments have not come together in a book that presents the computer-based analysis of transport phenomena.

This book is intended to fill the need for an introductory presentation of computational transport phenomena. It is not intended as a replacement for any existing books in transport phenomena, rather, as a Supplement to these books. Thus each chapter has the following characteristics: (a) a detailed, worked example, including discussion of the problem System equations; (b) a brief introduction to the numerical methods used to analyze the problem System; (c) a Computer code for the solution of the problem System equations (focusing primarily on the routines specific to the problem, with some discussion of the library routines also required to make up a complete code); (d) discussion of the numerical solution, with emphasis on physical interpretation and the analysis of errors; and (e) when appropriate, a comparison of the numerical solution with an analytical solution, or a discussion of how the numerical solution goes beyond what can be done analytically, especially for nonlinear problems.

Each chapter was developed originally during our teaching of a graduate course in transport phenomena. Since each chapter is self-contained, the chapters can be selected in essentially any order and number; we have on occasion used only one chapter during courses in momentum, heat, and mass transfer, applied mathematics, and numerical analysis to illustrate the Utility and some of the basic features of the Computer analysis of transport problems. Chapter 5 gives the most complete, selfcontained discussion of the numerical Integration of partial differential equations applied to problems in transport phenomena; this chapter is therefore recommended to the reader who is interested in an introduction to the numerical solution of transport problems.

In the preceding chapter we saw that excretory organs have important roles in osmoregulation, that is, in the maintenance of the desired water and solute concentrations in the organism. This chapter will discuss how excretory organs work.

The functions of an excretory organ are all related to one basic principle: To maintain a constant internal environment, any material an organism takes in must be balanced by an equal amount removed. This, in tum, requires that the excretory functions must have a variable capacity that can be adjusted to remove judiciously controlled amounts of each of a tremendous variety of different substances.

The major functions of excretory systems are:

• 1. Maintenance of proper concentrations of solutes

• 2. Maintenance of proper body volume (water content)

• 3. Removal of metabolic end products

• 4. Removal of foreign substances or their metabolic products

The first two functions are necessary for osmotic regulation and were repeatedly brought up in Chapter 8. One major metabolic end product, carbon dioxide, is removed primarily by the respiratory organs; most other metabolic end products are removed by the excretory organs. Foreign substances may be removed either unchanged or after modifications that renders them harmless (detoxification) or more easily excreted.

There is a great variety of excretory organs. In spite of the morphological variety, the basic principles of the excretory processes can be reduced to two major functional domains, ultrafiltration and active transport.

ORGANS OF EXCRETION

Basic processes

There is a wide variety of excretory organs, but there are, in principle, only two basic processes responsible for the formation of the excreted fluid: ultrafiltration and active transport.

In ultrafiltration, pressure forces a fluid through a semipermeable membrane that withholds protein and similar large molecules but allows water and small molecular solutes, such as salts, sugars, and amino acids, to pass (see Appendix E).

Active transport is the movement of solute against its electrochemical gradient by processes requiring the expenditure of metabolic energy. If active transport is directed from the animal into the lumen of the excretory organ or organelle, we call it an active secretion. If the active transport is in the opposite direction, from the lumen back into the animal, we speak about an active reabsorption.

This book is about animals and how they function in their world. First of all it is about problems and their solutions. It is also about aspects of physiology that I myself happen to find particularly interesting. The book is aimed at students who want to know how things work, who want to know what animals do and how they do it.

The book deals with the familiar subjects of physiology: respiration, circulation, digestion, and so on. These subjects are arranged according to major environmental features: oxygen, food and energy, temperature, and water. This arrangement is important, for there is no way to be a good physiologist, or a good biologist for that matter, without understanding how living organisms function in their environment.

The book is elementary and the needed background is minimal. I have assumed that the student is familiar with a few simple concepts, no more than provided by a good high school text. I have, however, included in the text sufficient background information to make physiological principles understandable in terms of simple physics and chemistry.

The quantity and complexity of scientific information today are steadily increasing, and students are already overburdened with material to memorize. However, the mere recital of more facts does not signify understanding; we need a framework of principles on which to hang the facts. This book should help the student discover that many problems can be understood, once a few fundamental principles are familiar.

I also feel that clear concepts are more important than the learning of technical terms. However, because concepts cannot be conveyed without words, terminology is necessary. But terms are of no use unless they are clearly and accurately defined.

Much of this book explores how animals can live in environments that seem to place insurmountable obstacles in their way. The book discusses possible solutions. Animals with anatomical and physiological specializations often contribute much to our understanding of general principles. However, unless we look for these general principles, comparative physiology is apt to become a description of functions peculiar to uncommon animals - uncommon not because they are rare, but because they are outside our daily experience with other humans and with well known pets and laboratory animals such as dogs, cats, rats, and frogs. What we want is to place information into general concepts that help us understand how all animals function.

The preceding chapter dealt with food and feeding; this chapter will deal with the use of food to provide energy. Animals need chemical energy to carry out their various functions, and their overall use of chemical energy is often referred to as their energy metabolism.

Animals obtain energy mostly through the oxidation of foodstuffs. The amount of oxygen they consume can therefore be used as a measure of their energy metabolism. Much of this chapter will be concemed with the rate of oxygen consumption, which we often take to mean the rate of energy metabolism.

However, this is not always so. Some animals can live in the absence of free oxygen. They still utilize chemical energy for their energy needs, although the metabolic pathways are different. Such metabolic processes are known as anaerobic metabolism. This situation is normal for quite a few animals that live in oxygen-poor environments or tolerate prolonged or permanent lack of oxygen. They obtain energy through processes that do not utilize molecular oxygen.

The energy-requiring processes and reactions in the living organism use a common source of energy, adenosine triphosphate (ATP). This ubiquitous compound, through the hydrolysis of an “energy-rich” phosphate bond, is the immediate energy source for processes such as muscle contraction, ciliary movement, firefly luminescence, discharge of electric fish, cellular transport processes, all sorts of synthetic reactions, and so on.

ATP is formed at the various energyyielding steps in the oxidation of foodstuffs, and also in anaerobic energy-yielding processes. ATP is the universal intermediate in the flow of the food's chemical energy to energy-requiring processes in both aerobic and anaerobic organisms.

METABOLIC RATE

Metabolic rate refers to the energy metabolism per unit time. It can, in principle, be determined in three different ways.

The first is by calculating the difference between the energy value of all food taken in and the energy value of all excreta (primarily feces and urine). This method assumes that there is no change in the composition of the organism. It therefore cannot be used for growing organisms or in organisms that have an increase or a decrease in storage of fat or other material. The method is technically cumbersome and is accurate only if carried out over a sufficiently long period of observation to assure that the organism has not undergone significant changes in size and composition.

Water is the universal solvent for virtually all biological reactions and related phenomena. The following brief summary therefore is restricted to aqueous solutions. For a more extensive treatment, the reader is referred to an introductory chemistry or physical chemistry text.

SOLUTIONS AND CONCENTRATIONS

A 1 molar solution contains 1 mol of solute per liter of solution. Thus a 1 molar solution of sodium chloride contains 58.45 g NaCI per liter solution. In biological work it is common to refer to a one-thousandth of a 1 molar solution, a millimolar solution. This helps to eliminate small decimal fractions.

A 1 molal solution contains 1 mol of solute per kilogram water. For example, a solution of 58.45 g NaCI in 1 kg of water is a 1 molal solution. Because the volume of this solution is more than 1 liter, its concentration is less than 1.0 molar.

The molarity designation is often used in biological work and is convenient because it is easy to determine the volume of a given sample of a biological fluid, whereas it is cumbersome or impossible to determine its exact water content. For example, the volume of a blood sample is easily measured, and its content of sodium can readily be determined. Referring the sodium concentration to the amount of water in the sample is more difficult, for both plasma and red cells contain many other solutes, including substantial amounts of proteins. In physical chemistry, the molality concept is more useful; this includes the consideration of osmotic phenomena.

Concentrations are sometimes given as percent (%). Unfortunately, this expression is ambiguous and there is no accepted convention for how it should be used. This often leads to confusion. For example, does a 1% solution of sodium chloride contain 1 g NaCl and 99 g water? Or does it contain 1 g NaCI in 100 rnl solution? Or, as the term percent means per hundred, does it mean 1 g sodium chloride per 100 g water? Even more confusing is the expression milligram percent (mg %), which logically should mean “milligrams per 100 milligrams.” Usually it means the number of milligrams of a substance per 100 ml solution. Ambiguities can be avoided by using the appropriate units (e.g., 120 mg glucose per 100 ml blood) or often better, the molar concentration.

In the first parts of this book we discussed aspects of the environment that are important to animals: oxygen, food, temperature, water. We then discussed physiological processes and how they are controlled and integrated by nerves and hormones.

We shall now ask the question of how animals obtain information about their environment and how thIS information is used.

Virtually all animals depend on information about their surroundings. They need to find food and mates and escape from predators. They must find their way about and also assess important qualities of the environment - temperature, light, oxygen, and so on.

We shall first be concerned with the kind of information that is available to animals. Then we shall consider how such information is received, processed, and passed on to the central nervous system.

Most information about the environment is obtained through specialized sensory organs. Traditionally, sense organs are separated into exteroceptors that respond to stimuli coming from the outside, such as light and sound, and proprioceptors that refer to internal information, such as the position of the limbs. This separation does not have much inherent meaning and, at best, is a matter of convenience.

Another traditional classification of senses is based on the five most obvious senses of humans: vision, hearing, taste. smell, and touch. In reality our sensory equipment is not nearly so limited.

In this context the question of whether information can reach the central nervous system via other avenues, outside the sensory organs (extrasensory perception, or ESP), is irrelevant. In this chapter we are dealing with measurable physical quantities that can be recognized, described, and manipulated in controlled ways. Although some sensory mechanisms may still be unknown (this is true of some responses to magnetic fields), the word extrasensory by definition means that no sensory structure is involved.

SENSORY QUALITIES

A list of external stimuli to which at least some animals respond is quite extensive (Table 13.1). The listed categories are not discrete, and the separation is somewhat arbitrary. However, for convenience we shall follow this sequence in our discussion of the possibilities and limitations that apply to the use of the various kinds of available information. The information naturally falls into three major categories: electromagnetic and thermal energy, mechanical energy and mechanical force, and chemical agents.

We may think of movements primarily in connection with locomotion, i.e., an animal moving from place to place. However, even animals that remain attached and never move about (corals and sponges, for example), show a great variety of movements. Also consider how animals move water over their gills, or food through the intestinal tract, or blood through the vascular system.

The number of mechanisms used to achieve motion is limited, although their uses vary greatly. We shall discuss the three basic mechanisms, ameboid, ciliary, and muscular movements.

Ameboid movement derives its name from the motion of the ameba, the unicellular organism described in every biology textbook. Ameboid locomotion involves extensive changes in cell shape, flow of cytoplasm, and pseudopodal activity.

Ciliary locomotion is the characteristic way in which ciliated protozoans such as paramecium move. However, cilia are found in all animal phyla and serve a variety of functions. For example, cilia set up the currents that move water over the gills of bivalves or move fluid in the watervascular system of echinoderms. The respiratory passages of air-breathing vertebrates are lined with ciliated cells that slowly remove foreign particles that lodge on their surfaces. The sperm of most animals move with the aid of a tail, which in principle acts like a cilium.

Muscular movement is the fundamental mechanism used in an overwhelming majority of different movements. It depends on the use of muscle, which throughout the animal kingdom has one universal characteristic - the ability to exert a force by shortening.

In this chapter we shall be concerned mostly with muscle and its use in animal locomotion. One important aspect will be how animals can achieve the most economical use of muscle energy.

AMEBOID, CILIARY, AND FLAGELLAR LOCOMOTION

Ameboid movement

What we designate as ameboid movement is characteristic of some protozoans, slime molds, and vertebrate white blood cells. The movement of these cells is connected with cytoplasmic streaming, change in cell shape, and extension of pseudopodia. These changes are easily observed in a microscope, but the mechanisms involved in achieving the movement are not well understood and the mechanism underlying ameboid motility remains controversial (Harris 1994).

The temperature of most animals follows passively that of the surroundings. It would seem advantageous if they could free themselves from the vagaries of this environmental variable, and in this chapter we shall deal with animals that keep their body temperature more or less independent of the environmental temperature.

Birds and mammals live through most of their lives with body temperatures that fluctuate no more than a few degrees. We shall consider these animals first, and then discuss what other animals have achieved in keeping their temperature independent of the environment.

First, we should clarify what we mean by body temperature, by no means a simple concept. Second, to maintain a constant temperature, the heat gained and the heat lost from the organism must be equal. To understand these two processes, we must be familiar with the simple physics of heat transfer.

In a cold environment a high temperature can be maintained by reducing the heat loss and/or increasing the heat gain (heat production). Most birds and mammals do this very well. However, some mammals and a few birds seem to give up the fight against cold and permit their temperature to drop precipitously; they go into torpor or hibernation. Nevertheless, hibernating animals have not abandoned temperature regulation; on the contrary, hibernation is a well-regulated physiological state.

In a hot environment the problems of maintaining the body temperature are reversed: The animal must keep the body temperature from rising and is often compelled to cool itself by evaporation of water.

Not only birds and mammals, but certain other animals are amazingly adept at keeping their temperature above that of the environment. This applies, for example, to lizards that bask in the sun, to many insects, and amazingly, even to some fish that maintain parts of their body at temperatures approaching those of ·warmblooded” animals.

BODY TEMPERATURE OF BIRDS AND MAMMALS

What is body temperature?

The heat produced by an animal must be transported to the surface before it can be transferred to the environment. Therefore, the surface of the organism must be at a lower temperature than the inner parts, for if the temperature were the same throughout, no heat could be transferred. The conclusion is that the temperature of an organism of necessity cannot be uniform throughout.

In a very crude way, the living organism can be described as an aqueous solution contained within a membrane, the body surface. Both the volume of the organism and the concentration of solutes should be maintained within rather narrow limits. The reason is that optimal function of an animal requires a well-defined, relatively constant composition of its body fluids, and substantial deviations are usually incompatible with life.

The problem is that the proper concentrations of animal body fluids invariably differ from those of the environment. Animals must maintain appropriate concentrations, but the concentration differences tend to decline, upsetting the steady state of the intemal conditions. Animals can minimize the difficulties by decreasing (1) their permeabilities, and (2) the concentration gradients between the body fluids and the environment. Both strategies are used.

Even a greatly reduced permeability doesn't solve all problems. for there will always be some diffusive leak. Steady-state internal conditions can then be maintained only if the organism generates a counterflow that exactly equals the diffusive leak. Such a counterflow requires input of energy.

The problems of keeping water and solute concentrations constant vary with the environment and are entirely different in sea water, in fresh water, and on land. It is therefore helpful to treat these environments separately. We shall analyze the main physiological problems in each and see how different animals have solved their problems. We shall first deal with aquatic animals and then move on to terrestrial animals.

THE AQUATIC ENVIRONMENT

Before we discuss the physiological problems peculiar to an environment, it is helpful to be familiar with its most important physical and chemical characteristics.

More than two-thirds (71%) of the earth's surface is covered with water. Most of this is ocean; the total fresh water in lakes and rivers makes up less than 1% of the area and 0.01% of the volume of sea water (Sverdrup et al. 1942; Hutchinson 1967). On land, life exists in a thin film on, just below, and just above the surface; in water, organisms not only live along the solid bottom but extend throughout the water masses to the greatest depths of the oceans, in excess of 10 000 m.

Animals need food (1) to provide the energy needed to keep alive and to maintain body processes, for muscle contraction, and for many other processes, (2) as raw materials for building and maintaining cellular and metabolic machinery, and (3) for growth and reproduction.

Plants use the energy from sunlight and carbon dioxide from the atmosphere to synthesize sugars and, indirectly, all the complicated compounds that constitute a plant.

All animals use chemical compounds to supply energy and building materials. They must obtain these either directly by eating plants or by eating other organic material. Therefore, the organic compounds animals need are ultimately derived from plants and thus indirectly from sunlight.

There are exceptions to this universal dependence on sunlight. In a few locations in the deep ocean where no light penetrates, there are rich animal communities that utilize the peculiar chemical characteristics of geothermally heated water.

The subject of food has three major aspects, feeding, digestion, and nutrition.

We shall first deal with feeding, which refers to the acquisition and ingestion of food. Virtually all food, whether of plant or animal origin, consists of highly complex compounds that cannot be used without first being broken down to simpler compounds. We refer to these processes as digestion.

A variety of organic compounds can provide energy, but in addition, animals have specific needs for compounds they cannot synthesize, such as amino acids and vitamins. Both the need for food to provide energy and the need for specific food components belong to the subject of nutrition.

We shall first discuss food and food intake, proceed to the processes of digestion that make the food compounds available to the organism, and then briefly mention some specific nutritional requirements. Finally, we shall discuss how organisms may defend themselves by producing toxic substances that make them inedible to many animals.

FEEDING

Food is obtained by a diversity of mechanical means, and these determine the nature of the food a given animal can obtain and utilize. Major feeding mechanisms and examples of animals that use the different means to obtain food are listed in Table 4.1.

Physiology is about the functions of living organisms - how they eat, breathe, and move about, and what they do just to keep alive. To use more technical words, physiology is about food and feeding, digestion, respi­ ration, transport of gases in the blood, circulation and function of the heart, excretion and kidney function, muscle and movements, and so on. The dead animal has the structures that carry out these functions; in the living animal the structures work.

Physiology is also about how the living organism adjusts to the adversities of the environment - obtains enough water to live or avoids too much water, escapes freezing to death or dying from excessive heat, moves about to find suitable surroundings, food, and mates - and how it obtains information about the environment through its senses. Finally, physiology is about the regu­ lation of all these functions - how they are correlated and integrated into a smooth-functioning organism.

Physiology is not only a description of function; it also asks why and how. To understand how an animal functions, it is necessary to be familiar both with its structure and with some elementary physics and chem­ istry. For example, we cannot understand respiration unless we know about oxygen. Since ancient times breathing movements have been known as a sign of life or death, but the true meaning of respiration could not be understood until chemists had discovered oxygen .

The understanding of how living organisms function is helped enormously by using a comparative approach. By comparing different animals and examining how each has solved its problem of living within the constraints of the available environment, we gain insight into general principles that otherwise might remain obscure. No animal exists, or can exist, inde­ pendently of an environment, and the animal that utilizes the resources of the environment must also be able to cope with the difficulties it presents. Thus, a comparative and environmental approach provides deeper insight into physiology.

Examining how an animal copes with its environ­ ment often tends to show what is good for the animal. This may bring us uncomfortably close to explanations that suggest evidence of purpose, or teleology, and many biologists consider this scientifically improper. However, we all do tend to ask, Why?

LOGARITHMIC EQUATIONS

Logarithmic equations are of the general form:

The logarithmic form of this equation is:

log y = log a + b log x (2)

Equation (2) shows that log y is a linear function of log X; that is, by plotting log y against log x we obtain a straight line with the slope b.

Example: Rate of oxygen consumption plotted against body mass (Mb) (Figure 5.12, page 197).

The independent variable, body mass (Mb), is customarily plotted on the abscissa. The rate of oxygen consumption per unit mass is obtained by dividing both sides of equation (3) by Mb:

Example: Figure 5.10, page 194.

EXPONENTIAL EQUATIONS

Exponential equations are of the general form:

The logarithmic form of this equation is:

Equation (6) shows that log y is a linear function of x, and plotting log y against x gives a straight line. Use of semilog graph paper (linear abscissa and logarithmic ordinate) for plotting y against x gives the same result.

Example: Rate of oxygen consumption plotted against temperature (Figure 6.4, page 221).

Why is oxygen important? It is because most animals satisfy their energy requirement by oxidation of food materials, in the process forming carbon dioxide and water.

The process of oxygen uptake and release of carbon dioxide is called respiration. Aquatic animals take up oxygen from the small amount of this gas dissolved in the water, terrestrial animals from the abundant oxygen in the air.

Many small animals can take up sufficient oxygen through the general body surface, but most animals need special respiratory organs for oxygen uptake. Carbon dioxide follows the opposite path, being released from the general body surface or from the respiratory organs. The water formed in the oxidation processes merely enters the general pool of water in the body and presents no special problems.

The most important, and sometimes the only physical process in the movement of oxygen from the external medium to the cells is diffusion, a process in which a substance moves from a higher to a lower concentration. The movement of carbon dioxide in the opposite direction also follows the concentration gradients.

Diffusion may be aided by bulk movement, such as the movement of air in and out of the lungs, but concentration gradients remain as the fundamental driving force for moving the respiratory gases. To understand respiration it is therefore necessary to know about the respiratory gases, their solubility, and the physics of diffusion processes.

Life presumably originated in the sea, and most animals (except insects) are marine. Large-scale evolutionary adaptation to air breathing has occurred only among arthropods and vertebrates. Some snails are well adapted to terrestrial life, and a small number of other invertebrates live in various terrestrial micro-habitats.

Easy access to oxygen in the atmosphere permits a high rate of metabolism and a high degree of organizational development. The greatest drawback to breathing in air is the evaporation of water.

THE ATMOSPHERE

Composition of dry atmospheric air

The physiologically most important gases are oxygen, carbon dioxide, and nitrogen. They are present in atmospheric air in the proportions shown in Table 1.1. In addition, the atmosphere contains water vapor in highly variable amounts.