Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Effect of acyl chain length on transfection efficiency and toxicity of polyethylenimine

Polyethylenimine (PEI) is an efficient nonviral gene delivery vector because of its high buffering capacity and DNA condensation ability. In our study, the amino groups on the polymeric backbone were acylated using acetic or propionic anhydride to alter the protonation behaviour and the hydrophilic/hydrophobic balance of the polymer. The concentration of acylated primary amines was determined using trinitrobenzene sulphonic acid assay. Results showed that our modified polymers had lower buffering capacities in solutions compared to PEI. The polymers were complexed with plasmid encoding enhanced green fluorescent protein at three different ratios (1:1, 1:2 and 1:10 w/w DNA to polymer) to form polyplexes and their toxicities and transfection efficiencies were evaluated in HEK 293 cells. Acylation reduced the number of primary amines on the polymer and the surface charge, improving haemocompatibility and reducing cytotoxicity. The reduction in the concentration of amino groups helped to optimise DNA compaction and facilitated polyplex dissociation in the cell, which increased transfection efficiency of the modified polymers compared to the parent polymer. Polymers with buffering capacities greater than 50% and less than 80% relative to PEI, showed higher transfection efficiencies than PEI. The propionic anhydride modified polymers had appropriate interactions with DNA which provided both DNA compaction and polyplex dissociation. These systems interacted better with the cell membrane because of their slightly higher lipophilicity and formed polyplexes which were less cytotoxic than polyplexes of acetic anhydride modified polymers. Among the vectors tested, 1:0.3 mol/mol PEI:propionic anhydride in a 1:2 w/w DNA:polymer composition provided the best transfection system with improved transfection efficiency and reduced cytotoxicity.