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The Solution to a Nonlinear Lamm Equation in the Faxén Approximation.

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|December 12, 2019
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This study presents an exact solution for the Lamm equation with concentration-dependent sedimentation coefficients. The findings reveal how this concentration dependence influences sedimentation behavior and boundary sharpening.

Keywords:
Lamm equationSedimentationconcentration dependencenonlinear

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Area of Science:

  • Biophysics
  • Physical Chemistry
  • Mathematical Biology

Background:

  • The Lamm equation describes particle sedimentation in a centrifugal field.
  • Understanding concentration-dependent sedimentation is crucial for accurate modeling.
  • Previous solutions often simplify sedimentation coefficients, limiting applicability.

Purpose of the Study:

  • To derive an exact solution for the Lamm equation with a linear concentration-dependent sedimentation coefficient (s = s_0(1-kc)).
  • To analyze the impact of this concentration dependence on sedimentation profiles.
  • To elucidate the boundary sharpening phenomenon in this context.

Main Methods:

  • Utilized the Faxén approximation for sedimentation.
  • Developed an analytical solution for the Lamm equation under specific concentration dependency.
  • Transformed the solution to relate it to the linear case (k=0).

Main Results:

  • An exact solution was obtained for the Lamm equation with s = s_0(1-kc).
  • The solution can be expressed using a modified argument of the linear case solution.
  • The boundary sharpening phenomenon is clearly demonstrated in the derived solution.

Conclusions:

  • The derived solution provides a more accurate representation of sedimentation for certain concentration ranges.
  • The study highlights the significant effect of concentration-dependent sedimentation on boundary dynamics.
  • This work offers a valuable tool for analyzing sedimentation data in biophysical and chemical systems.