The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Trends in lipoplex physical properties dependent on cationic lipid structure, vehicle and complexation procedure do not correlate with biological activity

Using a group of structurally related cytofectins, the effects of different vehicle constituents and mixing techniques on the physical properties and biological activity of lipoplexes were systematically examined. Physical properties were examined using a combination of dye accessibility assays, centrifugation, gel electrophoresis and dynamic light scattering. Biological activity was examined using in vitro transfection. Lipoplexes were formulated using two injection vehicles commonly used for in vivo delivery (PBS pH 7.2 and 0.9% saline), and a sodium phosphate vehicle previously shown to enhance the biological activity of naked pDNA and lipoplex formulations. Phosphate was found to be unique in its effect on lipoplexes. Specifically, the accessible pDNA in lipoplexes formulated with cytofectins containing a γ-amine substitution in the headgroup was dependent on alkyl side chain length and sodium phosphate concentration, but the same effects were not observed when using cytofectins containing a β-OH headgroup substitution. The physicochemical features of the phosphate anion, which give rise to this effect in γ-amine cytofectins, were deduced using a series of phosphate analogs. The effects of the formulation vehicle on transfection were found to be cell type-dependent; however, of the formulation variables examined, the liposome/pDNA mixing method had the greatest effect on transgene expression in vitro. Thus, though predictive physical structure relationships involving the vehicle and cytofectin components of the lipoplex were uncovered, they did not extrapolate to trends in biological activity.