The Solution to a Nonlinear Lamm Equation in the Faxén Approximation
Irwin H Billick1, George H Weiss1
1National Cancer Institute, National Institutes of Health, Bethesda, Md.
Summary
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.
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.
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