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The viscosity of xanthan was measured over seven decades of shear rate and three decades in polymer concentration (10-6000 ppm) in both salt free and 50 mM NaCl solution.  For the salt free solution, the scaling of the zero shear rate viscosity with polymer concentration agrees very well with a simple scaling model for concentrations above c*.  In the presence of salt, the scaling for both the zero shear rate viscosity and the relaxation time differ significantly from the salt free case.  The observed scaling of the zero shear rate viscosity with polymer concentration in 50 mM NaCl is well described by theory for neutral polymers in a Θ solvent. In salt free solution, four concentration regimes are identified with three associated critical concentrations (c* ≈ 70 ppm, c_e ≈ 400 ppm, and c_D ≈ 2000 ppm).  In salt solution, only three concentration regimes and two critical concentrations were observed (c* ≈ 200 ppm and c_e ≈ 800 ppm).  The smaller viscosities at the same polymer concentration and larger critical concentrations (c* and c_e) confirm a collapse in the polymer chains in the presence of salt.

Several findings for the xanthan gum system are not treated by theory and to our knowledge have not been observed in other polyelectrolytes.  First, in salt free solution near c*, a five fold increase in the zero shear rate viscosity was observed over a concentration range of ~15 ppm.  To our knowledge, the dramatic increase in η₀ near c* has not previously been reported and warrants further experimental and theoretical study. Next, in the salt free dilute regime, similar dependence was observed for both the zero shear rate viscosity (η₀ ~ c^1.6) and the relaxation time (τ ~ c^1.5) suggesting that all rheological properties in the dilute limit may exhibit a similar, non-trivial dependence on concentration.  Relaxation time scaling in the salt free dilute regime follows the expected concentration scaling for neutral polymers in the entangled regime.  Thirdly, the semidilute unentangled regime is rather narrow, spanning less than one decade in concentration, which disagrees with predictions that the semidilute unentangled regime spans three to four decades in concentration.  Finally, in the entangled concentration regime (above c_D in salt free and above c_e in 50 mM NaCl), the scaling of the zero shear rate viscosity shows a greater dependence on concentration in the presence of salt (η₀ ~ c^15/4 in salt free versus η₀ ~ c^14/3 in 50 mM NaCl).  This work shows that polyelectrolyte scaling theory may apply to rigid polyelectrolytes as well as flexible ones.  Although comprehensive study of chain stiffness and viscosity scaling of polyelectrolytes has not been completed, polyelectrolyte concentration relative to the critical entanglement concentrations appears to be a more important parameter than chain flexibility or rigidity.  Additional studies are needed to improve the understanding of viscosity scaling in entangled polyelectrolyte solutions for both flexible and rigid polyelectrolytes.

Laboratory scale drag reduction experiments are also being completed. An undergraduate student is performing heterogeneous and homogeneous drag reduction experiments with xanthan gum.  In order to achieve a baseline for the friction factors the friction data for water without any polymer additive was recorded in a spreadsheet and several graphs were made to show the relationships between differential pressure, flow rate, friction factor, and Reynold's number. 

The first set of experiments quantified drag reductions under various conditions.  Firs, homogeneous mixtures of the xanthan gum were studied and the friction factors did not decrease until the concentration reached 40 ppm by weight.  In addition, no noticeable break down of the polymer (or drag reduction) occurred for two hours in both the ½” and 1” pipe.  Next, homogeneous and heterogeneous mixtures of the xanthan were studied.  The more concentrated the stock solution was, the better the friction reduction.  The drag reduction increased from ~4% in the homogeneous case at 60 ppm to as high as 15% using 10,000 ppm stock solution of xanthan mixed to the same 60 ppm in the pipe flow.  This change in the friction reduction is due to the webs or “jelly fish” that are made when the xanthan gum tangles with itself.

Additional work on the effect of salt on xanthan viscosity and drag reduction are underway for year two of the project.  The first set of results have been submitted for publication.  The work finds that under entangled concentrations, the viscosity of polyelectrolyte solutions increase with the addition of salt (counter to the standard convention).  Details of this work will be reported in the next annual report.