where c is the solute concentration, t and r are the time and radius, and the parameters D, s, and ω represent the solute diffusion constant, sedimentation coefficient and the rotor angular velocity, respectively. The first and second terms on the right-hand side of the Lamm equation are proportional to D and sω2, respectively, and describe the competing processes of diffusion and sedimentation. Whereas sedimentation seeks to concentrate the solute near the outer radius of the cell, diffusion seeks to equalize the solute concentration throughout the cell. The diffusion constant D can be estimated from the hydrodynamic radius and shape of the solute, whereas the buoyant mass mb can be determined from the ratio of s and D
at the inner and outer radii, ra and rb, respectively. By spinning samples at constant angular velocityω and observing the variation in the concentration c(r,t), one may estimate the parameters s and D and, thence, the (effective or equivalent) buoyant mass of the solute.
References and notes
↑ O Lamm: (1929) "Die Differentialgleichung der Ultrazentrifugierung" Arkiv för matematik, astronomi och fysik21B No. 2, 1–4
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In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century.
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HydroGeoSphere (HGS) is a 3D control-volume finite element groundwater model, and is based on a rigorous conceptualization of the hydrologic system consisting of surface and subsurface flow regimes. The model is designed to take into account all key components of the hydrologic cycle. For each time step, the model solves surface and subsurface flow, solute and energy transport equations simultaneously, and provides a complete water and solute balance.
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A two-dimensional elastic membrane under tension can support transverse vibrations. The properties of an idealized drumhead can be modeled by the vibrations of a circular membrane of uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental mode.
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