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Fluids (2012)

Page history last edited by Joe Redish 8 years, 4 months ago

Working content >MacroModels


Most fluids we know such as water and air are materials that change shape easily in response to forces.  On the other hand, for most solids such as steel beams, it is very hard to change their shape. But"easy" and "hard" are not a very precise definition.  By this definition a sponge may be considered fluid and honey could be mistaken for a solid! So, as we often do, lets first define fluids and solids more precisely.


In a fluid, the force determines how fast the shape of the fluid deforms, i.e. the force is determining a rate of deformation.  In a solid, the force determines the total amount of shape deformation.   So the deformation of a steel beam depends on the force with which you push on the end of the beam.  More significantly, when you stop pushing on the beam, the beam returns to its original shape.  In a fluid on the other hand, an applied force leads to a flow.  When you stop pushing on the fluid, the flow stops but the fluid will not return to its original shape.  


You probably know  simple definitions of solids, liquids, and gases from elementary school and may have seen them in every science course you have ever taken. Often they are defined sharply: "solids have a fixed volume and shape, liquids have a fixed volume and can change shape, gases have neither and expand to fill any container." we have stricken these out to help you to see these as precise definitions but as statements of approximate convenience.


While fluids are key to all biological systems, many parts of biological systems are complex mixtures of different kinds of substances, parts of which look like solids, parts like liquids, and parts like gases -- but they may be organized into a coherent object like a bone, a cell, or a vacuole. Other parts of biological systems look like solids in one direction and liquids in others!    Worse, whether a material feels like a fluid or a solid can depend on how fast you push on it.  Outside living systems,  silly putty is a nice example of such a material that is both solid and fluid like depending on time scale.  



The take-home message is that there are many states of matter, not just solids, liquids, and gases. For the simplest forms of uniform matter, the separation into solid, liquid, and gas can be made precisely and there are discontinuities in their properties when they change into one another. It is very important to know about this (think about the transitions from ice to water to steam). But this behavior is not true for all types of complex matter. 


Gases are fluids that are at a low enough density or whose molecules have high enough speeds that the interatomic attractive forces are not sufficient to hold the atoms or molecules together in a coherent whole. As a result, they will move to fill any container. They can consist of a single substance or a mixture. The most common gas biological systems interact with is air, since it is the primary source of oxygen for most organisms, and oxygen is a primary agent in the extraction of energy from chemical compounds.


Liquids are fluids in which interatomic forces are strong enough to hold the molecules of the substance together against external forces that are not too strong. Since the forces are not strong enough to lock the molecules into a fixed structure (solid), but they are strong enough to hold the substance together, liquids maintain an approximately constant volume (in contrast to gases) and can change their shape.


Liquids can be made of a single compound in which case they are either made of atoms or molecules.  (Only a few elements are liquid at or near room temperature -- mercury, bromine, and gallium -- so most commonly we are considering molecules when we talk about liquids.)  Liquids can also be mixtures of different compounds.  Although liquids can take on the shape of whatever container holds them, they still have inherent properties.  Just like solids, liquids have density and resist compression (have a bulk modulus).  The molecules of a liquid tend to stick together, or have some internal cohesion.  This gives them interesting properties like surface tension (surface cohesion), adhesion (sticking of the liquid to a solid surface), and viscosity (internal resistance to flow).  They also will move or flow, and their behavior when they flow plays an important role in many biological processes.


Because of their high density (liquids are often as dense or denser then solids), we don't have a simple model of their behavior as we did for the low density (ideal) gas.   However, it is still possible to start at the molecular level and work your way up from the motion of individual molecules to the properties of the "bulk" i.e. large quantities of fluid.  Molecular dynamics" simulations allow us to simulate the behavior of millions of water molecules and (just like we did for an ideal gas) determine pressure from the force of collisions of molecules, or temperature from the velocity squared of molecules.    This is for example yielding new insights into how water pushes against the fluctuating deformable wall of a cell. 


In addition, in the case of liquids, we can make a lot of headway simply using Newton's laws at the macroscopic level: We will parcel our fluid into sub-regions, and consider each sub-region as an "object" that could move if it was subjected to a net force.  Doing free-body diagrams and other macroscopic and Newtonian analysis generates some powerful results that tell us a lot about the properties of liquids.. Some of these properties are discussed on the follow-on pages.





Mark W. Denny, Air and Water (Princeton U. Press, 1995) chapters 4 and 5.

Steven Vogel, Comparative Biomechanics: Life's Physical World (Princeton U. Press, 2003) chapters 5 and 6.  


Karen Carleton and Joe Redish 10/23/11

Revision Joe Redish 10/27/12

Wolfgang Losert 10/27/2012

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