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Summer Research Opportunities in Jerry Gollub's Research Group, Summer 2009

We expect to hire two undergraduates for research this summer.  Our work is concerned generally with "Particle Dynamics in Complex Fluid Flows." We use small-scale, well-controlled laboratory experiments to obtain a deeper understanding of this topic.

 

1.  Reversibility of Fluid Flows Containing Particles

At low Reynolds number, the Navier-Stokes equations that govern Newtonian fluid flow are invariant under time reversal. When the fluid contains a suspension of small particles, however, this symmetry can be broken spontaneously by irreversible particle interactions. Several years ago, in collaboration with David Pine at New York University, we studied the breakdown of time reversibility in a suspension of non-Brownian spherical particles that was subjected to slow oscillatory shear in a Couette geometry. Surprisingly, a sharp threshold was found in the applied strain for the breakdown of time reversal symmetry. In subsequent work, this collaboration discovered that the transition displays all the characteristics of a phase transition. Remarkably, below the critical strain amplitude the particles in the suspension are found to self-organize (over a characteristic time scale) into a configuration that can show reversibility, while above the threshold no such reversible configuration exists.

 

We are currently extending these studies of irreversibility and self-organization to suspensions subjected to oscillatory flow in microchannels. Unlike the Couette flow case, which has a uniform shear rate across the gap between two cylinders, the shear rate in a channel flow changes with distance away from the wall. It is well known that suspended particles tend to move from high shear to low shear, an effect termed shear-induced particle migration [106]. In a steady channel flow, therefore, particles tend to accumulate in the center of the flow away from the walls. Extrapolating from our previous findings, this non-uniform shear rate and the accompanying non-uniform particle concentration means that the critical strain amplitude for persistent irreversibility will vary across the channel width. Oscillatory flow of a suspension in a channel has been studied previously, though rarely from the perspective of reversibility and self-organization.

 

Using our robust particle-tracking techniques, we will study the self-organization of an oscillating suspension quantitatively. An apparatus has been constructed, and experiments are under way.  Simultaneously, numerical simulations of the experiments are being conducted for comparison.

 

The fundamental question to be investigated is how the microstructure evolves as a function of time and strain rate in a situation where the strain rate is spatially non-uniform. Will there still be a well defined phase transition? Will the active parts of the flow (where particle interactions remain chaotic) infect the quiescent regions?  

 

2.  Oscillatory Rheology

Rheology is the study of the relationship between stress (internal force per unit area) and strain rate (velocity gradients) for a fluid.  This relationship is an important part of determining the internal structure and flow properties of fluid systems.  For simple fluids, the relationship is linear, but for complex fluids, which are often of interest in a biological context, the relationship can be nonlinear.

 

While rheometers designed for rheological measurements are in wide use, there is considerable potential to implement them using microfluidic methods, and hence to determine the strain-rate dependent rheology for very small quantities of complex fluids.  In fact, we have developed such a device, starting with the work of former student Ben Polak, and continuing with collaborators at Penn, including Kerstin Nordstrom (a Bryn Mawr graduate, now a Ph.D. student), Assistant Professor Paulo Arratia, and Professor Douglas Durian.  We have successfully used the microfluidic device to study the rheological properties (nonlinear viscosity) of a complex fluid consisting of a suspension of soft particles of variable size, and to study this fluid at densities approaching the “jamming transition”, a topic of great current interest in soft matter physics.  We expect to submit a paper for publication during the next few months. 

 

Our next goal is to build an “AC rheometer” using microfluidic methods, in collaboration with Professor Arratia at Penn.   This device would work by means of oscillatory flows, which would allow both elastic and viscous forces to be measured.  (Only the viscous forces are available in the “DC” device already developed.)   This instrument would allow us to study the elastic forces that are prevalent in many complex fluids, especially polymer solutions.  When the fluid is driven into an oscillatory flow in a microchannel (about 50 microns wide), the component of the force that is out of phase with the driving provides additional information about the elastic properties of the fluid. 

 

Examples of fluids of interest include polymer solutions and also dense colloidal suspensions, where the viscoelastic effects may be responsible for particle migration.  DNA solutions and vesicle suspensions are also possible candidates for study.

 

This project is ideal for an undergraduate student with little experience because: 

              --It is an extension of an existing instrument with which we have experience.

              --The student would gain technical experience in microfluidics, particle tracking, and fluids.

              --The student would benefit from collaborating with scientists at Penn in addition to Haverford.

 

This work would lead naturally to a senior thesis and publication.

 

3.  Do Small Particles Follow the Flow in which they are Immersed?   

Over the past several years, we have been studying the motion of small particles in flows, to understand how their behavior changes as their inertia increases.  Peter O’Malley 2008 and former postdoc Nick Ouellette published a paper in Physical Review Letters showing that there are significant deviations between the fluid and the particles as the particle size becomes significant.  This work was extended to rod-shaped particles by Monica Kishore 2009, with results presented at the 2009 March APS meeting. 

 

This summer, we plan to extend the work to denser collections of particles, in order to examine the effects of interactions between the particles.   This is an area in which little work has been done in the past. 

 

4.  Flows Produced by Swimming Micro-organisms

During a sabbatic leave, Jerry Gollub has been studying the fluid flows produced by a collection of swimming algae cells.  These cells are driven by twin flagella, whose beating produces both oscillatory flows, and a net motion of the cell.  We are interested in the mixing produced by these cells, and in the possibility that this mixing could affect their growth or interaction.  This work, if continued at Haverford, would probably be done in collaboration with Prof. Karl Johnson, who is an expert on these amazing organisms.

 

 

Other student projects are also possible.

 

Please visit the lab, talk with Postdoc Jeff Guasto, and then write to Jerry Gollub to arrange a phone discussion.  We will only offer summer opportunities to students with whom we have spoken.