Convective Depletion During The Fast Propagation Of A Nanosphere Through A Polymer Solution

A theory of nonlinear convective depletion is set up as a nanosphere translates fast through a semidilute polymer solution. For nanospheres a self-consistent field theory in the Rouse approximation is often legitimate. A self-similar solution of the convective depletion equation is argued to be feasible at high velocities. The nature of the thin boundary layer in front of the propagating particle is analyzed. One example of convective depletion is when a charged protein moves through a semidilute polymer under the influence of a high electric field. The protein velocity is then proportional to the fifth power of the field. The theory could be useful in interpreting the separation of protein mixtures by microchip electrophoresis.Comment: 12 pages, 2 figure

DNA Confined in Nanochannels: Hairpin Tightening by Entropic Depletion

A theory is presented of DNA hairpins enclosed in a nanochannel. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The free energy of the hairpin computed in the classical limit is significantly larger than what one would expect. As a result, the distance between hairpins or the global persistence length is often tens of micrometers long and may even reach mm sizes for 10 nm thin channels. The hairpin shape and size, and the DNA elongation are computed for nanoslits, and circular and square nanoschannels. A comparison with experiment is given.Comment: 13 pages, 4 figure

A Tree Swaying in a Turbulent Wind: A Scaling Analysis

A tentative scaling theory is presented of a tree swaying in a turbulent wind. It is argued that the turbulence of the air within the crown is in the inertial regime. An eddy causes a dynamic bending response of the branches according to a time criterion. The resulting expression for the penetration depth of the wind yields an exponent which appears to be consistent with that pertaining to the morphology of the tree branches. An energy criterion shows that the dynamics of the branches is basically passive. The possibility of hydrodynamic screening by the leaves is discussed.Comment: 7 pages, no figures, some updates and references added changed "damaged spring" to "damped spring" added subscript to surface area in section

Optimized Baxter Model of Protein Solutions: Electrostatics versus Adhesion

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.Comment: 40 pages, 9 figure

Collective diffusion coefficient of proteins with hydrodynamic, electrostatic and adhesive interactions

A theory is presented for lambda_C, the coefficient of the first-order correction in the density of the collective diffusion coefficient, for protein spheres interacting by electrostatic and adhesive forces. An extensive numerical analysis of the Stokesian hydrodynamics of two moving spheres is given so as to gauge the precise impact of lubrication forces. An effective stickiness is introduced and a simple formula for lambda_C in terms of this variable is put forward. A precise though more elaborate approximation for lambda_C is also developed. These and numerically exact expressions for lambda_C are compared with experimental data on lysozyme at pH 4.5 and a range of ionic strengths between 0.05 M and 2 M.Comment: 8 pages, 3 figures, 1 tabl