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Modeling Fluids at the Macro-, Micro-, and Mesoscales

Page history last edited by Mark Eichenlaub 2 years, 9 months ago

To help you prepare for Lab 3, in which we characterize random motion and examine the parameters that affect the diffusion constant, it will help you to consider some fluid models.


Modeling fluids at the macroscale - directed motion in response to a force: 

It is quite amazing how well we understand the fluid flows we encounter in everyday life.  The flow of water in a pipe and the flow of water in rivers can be modeled with high accuracy.  The Mississippi floods for example can be predicted with high degree of accuracy, with expected water levels predicted within a few inches, even though all these predictions are based on water that has to flow through complex channels.  The same laws can also be applied very successfully to blood flow, even though arteries and veins are orders of magnitude smaller.


One aspect of these macroscale fluid flow models is that, for a fluid sitting in a tank, the fluid moves only when it is pushed by external forces--when there is no force, there is no motion.   In our laboratories, one example of this macroscale fluid response to applied force is when we measure the motion of a bead dropped into a viscous fluid in a graduated cylinder in Lab 2.  The bead pushes the fluid out of the way when it is dropped, but we do not see the fluid spontaneously flow throughout the graduated cylinder.  When we observe the experiment, the fluid only seems to move when it is forced out of the way by the dropping bead, but not before or after the bead drops.  But does the fluid really only move when it is pushed by a force?  One way to test this hypothesis--that the fluid only moves when forced--is to directly apply a force in one direction, and then turn around and push in the opposite direction to try to get the fluid back to its original position.  We can directly label a small (say mm sized) region of fluid with dye and see how it moves when pushed.  The following video demonstrates what happens when we push a fluid, with a small region of dye embedded in it, in one direction and then push the fluid back into the opposite direction:  This video is based on a University of Maryland Lecture Demonstration.


Modeling fluids at the molecular scale (microscale) - undirected motion due to "temperature":

When we zoom in very closely though, we may notice that the macroscale model that corresponds so well to everyday life experience seems insufficient.  While the fluid only moves when it is forced on the macroscale (by macroscale we mean here the cm sized beads dropped into fluid and mm sized dye regions), we know from chemistry that the water molecules move due to their "thermal energy."  From "kinetic theory" we learn that having a temperature implies that the molecule has energy, in this case also kinetic energy.  In other words, at the microscale we expect the water molecules to move around--in fact we expect the water molecules to move around randomly.  This motion of water molecules in random directions could be called "thermal fluctuations."  If we were able to manufacture 0.2nm sized beads (and make them bright enough to see under the microscope) and embedded them in water, we would expect to see the bead being pushed around by the thermal forces--the pushing of the thermal water molecules.  In fact we can "see" thermal fluctuations with advanced instruments, but individual water molecules or ions move so fast and change direction so often, it is impossible to keep track of them.  


Seeing temperature at the cellular scale (mesoscale):      

Anyone who has observed a living cell under a microscope (we hope you have had that opportunity!) has seen motion inside the cell.  All the organelles seem to wiggle, and in fact in some cases the whole cell moves.  So does this motion indicate that the cell is "alive" or could the observed motion be the result of thermal fluctuations?  As discussed above, thermal forces lead to a constant wiggling of DNA, macromoelcular complexes, or proteins.  But for the much larger organelles, would the randomly moving water molecules, ions, and proteins that push against the organelles be enough to cause them to wiggle visibly, or would the pushing from the many surrounding objects cancel out? 


We can investigate this by using beads instead of organelles (the beads are clearly not alive!) of the typical size of mitochondria and other organelles inside a cell (1000nm = 1 micron).  In fact when we look at beads that are even bigger under a microscope (these are 2 micron beads) we see them moving--it turns out they are being pushed around by thermal forces.   Of course we cannot go to arbitrarily larger objects--cars and houses do not fluctuate noticeably when immersed in a fluid.  In fact, the larger the object, the less it will fluctuate and the slower it will fluctuate.  [One way we can think about this is as follows: The larger the object, the less likely the thermal forces will be unbalanced, and the less the more massive object will react to this imbalance when one is present.]  Here is a video of both 1 micron and 5 micron beads taken with a microscope--compare the motion exhibited by the smaller and larger beads.


So we can indeed see temperature at the cellular scale:  it manifests itself as a random motion of even micron scale objects.   Therefore, just because something is wiggling visibly under the microscope does not mean it is alive.  BUT, just because two things are wiggling does not mean they must wiggle for the same reason!   Are the wiggling of a bead and the wiggling of an organelle really similar or is the motion you see in a cell different from the motion of a bead in fluid?  To answer this question about "life and death" we have to learn how to describe and measure these types of random motion.  This is one of the goals of Lab 3, which you are about to begin.  We will also have to distinguish between random and directed motion, which you will learn to do in Lab 4.  All this hard work will pay off in Lab 5 (that is where the video on "motion inside the cell" came from):  We will analyze the wiggling of organelles in a living cell and from this analysis gain insights into cytoskeletal structure and rates of ATP hydrolysis. 



Kim Moore and Wolfgang Losert



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