Evolution of concentration field in a membrane system

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential (Δψs) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations (Ci/Ce) at the membrane/concentration boundary layers. We present the calculation procedure (Ci/Ce) based on novel equations derived in the paper containing the transport parameters of the membrane (Lp, σ, and ω), solutions (ρ, ν), concentration boundary layer thicknesses (δl, δh), concentration Raileigh number (RC), concentration polarization factor (ζs), volume flux (Jv), mechanical pressure difference (ΔP), and ratio of known solution concentrations (Ch/Cl). From the resulting equation, Δψs was calculated for various combinations of the solution concentration ratio (Ch/Cl), the Rayleigh concentration number (RC), the concentration polarization coefficient (ζs), and the hydrostatic pressure difference (ΔP). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m⁻³ (Cl) was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m⁻³ (Ch). It is shown that (Δψs) depends on the value of one of the factors (i.e., ΔP, Ch/Cl, RC and ζs) at a fixed value of the other three.

Laser interferometric investigation of solute transport through membrane-concentration boundary layer system

We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζ_s) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζ_s of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.

Laser interferometry analysis of ciprofloxacin and ampicillin diffusion from liposomal solutions to water phase

The paper presents experimental investigations of diffusion of antibiotics (ciprofloxacin or ampicillin) into the water phase from mixtures of neutral or negatively charged liposomes, and antibiotic-liposome interactions. Using the laser interferometry technique, the amounts and fluxes of released antibiotics, concentration field evolution, and the velocity of the concentration boundary layer's "growth" were determined. To avoid the limitations of membranes, a measurement system without the artificial boundary of phases with a free water-solution interface has been proposed. It was found that the diffusion of anionic and neutral liposomes into the water phase was insignificant and mainly the diffusion of antibiotics was measured. Differences in the diffusion kinetics of ciprofloxacin and ampicillin from liposomal solutions to the water phase were observed. Ampicillin diffused more efficiently than ciprofloxacin regardless of the liposomal solution type. Moreover, the amount of ampicillin and ciprofloxacin released from the anionic liposomal phase was higher than that from the neutral one. Our results confirm that ciprofloxacin at neutral pH shows little tendency to bind neutral liposomes. Additionally, it was also observed that ciprofloxacin disrupts negatively charged liposomes as a final effect of antibiotic-lipid interactions.

Diffusion with memory in two cases of biological interest

The complexity of a biological structure, such as membrane where the transport process may carry solid particles which may obstruct some of the pores, diminishing their size and making the permeability dependent on the local structure of the medium, suggests the introduction of a space-dependent diffusion constant. In this note, the profile concentration of diffusing solutes inside a cell membrane has been calculated on the basis of the Fick diffusion equation modified by introducing a memory formalism (diffusion with memory). This approach has been employed to describe the concentration profile inside the membrane when a sudden change of the concentration in the medium bathing one of its face is applied for a limited interval of time. A further application of the method concerns the so-called concentration boundary layer that occurs at the membrane-aqueous medium interface, where the solute concentration depends, even at considerable depth, on the local structure of the interface. These profiles are compared to some recent experiments concerning the diffusion of ethanol in a layer close to a nephrophane membrane. This approach generalizes the diffusion models based on the Fick equation to more complex systems, where a space-independent diffusion coefficient could be inappropriate to take into account the large variety of diffusion processes in biological systems.

Relevance of diffusion through bacterial spore coats/membranes and the associated concentration boundary layers in the initial lag phase of inactivation: A case study for Bacillus subtilis with ozone and monochloramine

Disinfectants are generally used to inactivate microorganisms in solutions. The process of inactivation involves the disinfectant in the liquid diffusing towards the bacteria sites and thereafter reacting with bacteria at rates determined by the respective reaction rates. Such processes have demonstrated an initial lag phase followed by an active depletion phase of bacteria. This paper attempts to study the importance of the combined effects of diffusion of the disinfectant through the outer membrane of the bacteria and transport through the associated concentration boundary layers (CBLs) during the initial lag phase. Mathematical equations are developed correlating the initial concentration of the disinfectant with time required for reaching a critical concentration (C*) at the inner side of the membrane of the cell based on diffusion of disinfectant through the outer membranes of the bacteria and the formation of concentration boundary layers on both sides of the membranes. Experimental data of the lag phases of inactivation already available in the literature for inactivation of Bacillus subtilis spores with ozone and monochloramine are tested with the equations. The results seem to be in good agreement with the theoretical equations indicating the importance of diffusion process across the outer cell membranes and the resulting CBL's during the lag phase of disinfection.