Biomedical subjects

D Vollhardt

Publications and source records attributed to D Vollhardt.

At least 19 recordsLinked to original sources

PubMed2006

Progress in characterization of Langmuir monolayers by consideration of compressibility.

Over decades, information about the rheological properties of the condensed monolayer phases has been obtained by introduction of a two-dimensional compressibility which is defined on the basis of the surface pressure-molecular area (Pi-A) features of the monolayer. Since the last decade, fundamental progress was attained in the experimental determination of the main characteristics of Langmuir monolayers in microscopic and molecular scale. Already smallest changes in the molecular structure of the amphiphile can result in changes in the molecular arrangement in the monolayer and thus, in changes of the main characteristics of the monolayer such as, the surface pressure-area per molecule (Pi-A) isotherms, the shape and texture of the condensed phase domains and the two-dimensional lattice structure. As the classical equations of state allowed only characterisation of the fluid (gaseous, liquid-expanded) state, thermodynamically based equations of state, which consider also the aggregation of the monolayer material to the condensed phase, have been developed. The present review focuses particularly to amphiphilic monolayers, the Pi-A isotherms of which indicate the existence of two condensed phases. For this case, the experimental results of the differences in the structure features and phase properties are discussed. The generalisation of the equation of state for Langmuir monolayers developed for the case that one, two or more phase transitions in the monolayer take place, is in agreement with the experimental results that the two-dimensional compressibility of the condensed phases undergoes a jump at the phase transition, whereas the compressibility is proportional to the surface pressure within one of the condensed phases. An example is presented which explains the procedure of the theoretical analysis of Pi-A isotherms indicating the existence of two condensed phases. An element of the procedure is the application of the general principle that the behaviour of any thermodynamic system is determined by the stability condition. An interesting anisotropy of the compressibility is revealed by GIXD studies of the S-phase of octadecanol monolayers. However, similar studies performed close to the LS-S-phase transition would result in a thermodynamically impossible negative compressibility. Close to this phase transition, the compressibility cannot be determined from the positions of the maxima because the monolayer is in a disordered state attributed to elastic distortions by fluctuations with the structure of the new phase in the surrounding matrix without destroying the quasi-long-range positional order.

Mechanics↗

PubMed2006

Effect of the exchange of substituent position in an amide amphiphile on the monolayer characteristics.

The monolayer characteristics of two very similar amphiphiles, N-tridecyl-beta-hydroxypropionic acid amide (C13H27-NH-CO-C2H4OH; THPA) and N-(beta-hydroxyethyl)tridecanoic acid amide (C13H27-CO-NH-C2H4OH; HETA), the chemical structure of which is only changed by exchanging the position of the two substituents at the acid amide group, are compared. These small changes in the chemical structure give rise to large differences in the phase behavior of the HETA and THPA monolayers, as concluded from the differences in the surface pressure-area (pi-A) isotherms. Since both amphiphiles have the same alkyl chain length, the shift of the fluid/condensed phase transition pressure pi(c) to higher temperatures from THPA to HETA indicates a stronger polar character of the THPA headgroup. Considerable differences between the HETA and THPA monolayers also exist in the domain morphology, although, in both cases, six arms usually grow from a round center. The fractal-shaped HETA domains grow by tip splitting under the formation of numerous doubloons so that branching is considerably limited. This suggests a certain fluidity of the HETA condensed phase. The main differences of the domains result from the higher crystallinity. The starlike THPA domains have dendritic character and can form curved dendrites, which are partially two-dimensional twins due to the formation of dislocations in the two-dimensional lattice structure. In the case of HETA monolayers, the grazing incidence X-ray diffraction studies reveal a hexagonal packing of the alkyl chains oriented perpendicularly to the surface in an LS phase. In the case of THPA monolayers, an oblique lattice is formed. However, at low temperatures, a second phase transition between two condensed phases occurs that is demonstrated by an abrupt transition between two different oblique lattice structures at the surface pressure where a cusp in the pi-A isotherms occurs at T < 10 degrees C.

Journal Article↗

PubMed2006

Nucleation in monolayers.

Two-dimensional monolayer material of a large number of amphiphiles is transformed into overgrown three-dimensional structures in a state of metastability and supersaturation. This process is described by a theoretical concept and characterised by sensitive experimental techniques. Two theoretical models compatible with each other are based on nucleation and growth of the formed 3D nuclei: (i) the model for limiting cases of nucleation and overgrowth of 3D nuclei with assumed shapes, and (ii) the generalised model under formation of lenticular nuclei. The latter model allows determination of the nucleation rate constant which renders possible the determination of the critical nucleus size and the free energy for the formation of critical nucleus in dependence on the surface pressure. A theoretical model developed on the basis of the classical nucleation theory is applied for this. An effective double-surface pressure-step method is introduced to distinguish between the nucleation and growth processes. Consequently, a critical surface pressure, the limiting surface pressure for the formation of 3D nuclei, and an equilibrium surface pressure, at which the 3D nuclei cease to grow, can be defined and experimentally determined. Despite the different boundary conditions, the constant surface pressure relaxation data can be theoretically described by these two consistent nucleation-growth models. In the most cases, the limiting case of progressive nucleation occurs but also instantaneous nucleation is observed. Direct evidence has been provided by AFM studies that constant surface pressure relaxation of monolayers is caused by nucleation-growth of 3D nuclei from the monolayer material. The quantitative analysis of growth and distribution of the 3D micrograins by AFM supports the mechanism obtained by application of the nucleation-growth theories. New instrumental techniques such as, BAM, AFM, GIXD and X-ray reflectivity provide detailed information on the characteristics of the 3D structures overgrown on the monolayer during constant surface pressure relaxation on microscopic and molecular scales.

Journal Article↗

PubMed2006

Semiempirical quantum mechanical calculations of dipolar interaction between dipyridamole and dipalmitoyl phosphatidyl choline in Langmuir monolayers.

Recent studies have shown that dipalmitoyl phosphatidyl choline (DPPC) monolayers respond cooperatively to the presence of dipyridamole (DIP) guest molecules even at small concentrations, which is a signature of molecular recognition. Using semiempirical quantum mechanical calculations for the DIP-DPPC system, we show that the incorporation of DIP causes large changes in the vertical dipole moment of the DIP-DPPC system, which can explain why measurable changes in surface potential are observed experimentally even at very low DIP concentrations. The calculations are also consistent with the anomalous concentration dependence of the surface pressure and surface potential isotherms for DIP-DPPC monolayers. Rather than saturation or a continuous increase in the effects caused by the incorporation of increasing amounts of DIP, the experimentally observed inversion in the behavior of the surface potential as the DIP concentration reaches 0.5 mol % would be caused by a change in DIP conformation, from a vertical arrangement for the DIP rings to a horizontal or intermediate arrangement. The strong dipolar interactions indicated in the calculations may also be the origin of the drastic changes in monolayer morphology seen in fluorescence microscopy images, with triskellion-shaped domains being formed for condensed DIP-DPPC monolayers.

1,2-Dipalmitoylphosphatidylcholine↗

PubMed2006

Surface pressure isotherm for the fluid state of Langmuir monolayers.

The equation of state for the monolayer comprised of the molecules of different sizes (water and biopolymers) is modified to describe the fluid (liquid-expanded and gaseous) state of the insoluble molecules monolayer. In contrast to the equation of state derived previously in ref 1, this equation does not involve either the Gibbs' adsorption equation or the differential equation for the chemical potential of the insoluble component, but it is based only on the equations for the chemical potential of the solvent in the bulk and in the surface layer. The results calculated from the proposed equations are in perfect agreement with the experimental Pi-A isotherms of the liquid-expanded state obtained for Langmuir monolayers of various types of amphiphilic compounds. The values of molecular areas of amphiphilic molecules estimated from the fitting of experimental data to the proposed equation are found to be quite similar to those measured in independent grazing incidence X-ray diffraction (GIXD) experiments.

Surface Properties↗

PubMed2006

Surfactant transfer through a liquid membrane: origin of spontaneous oscillations at the membrane/acceptor phase interface.

Instability due to surfactant redistribution in a liquid membrane system consisting of two solutions, namely source and acceptor, separated by a layer of immiscible liquid is studied theoretically and experimentally. The transfer of a surfactant from a source phase to an acceptor phase is often accompanied by spontaneous nonlinear oscillations of electrical potential and/or interfacial tension. The oscillations can be generated at each of the membrane interfaces. Here a mechanism of oscillation, which develops at the membrane/acceptor phase interface, is proposed on the basis of direct numerical simulation of the system evolution. Performed experimental studies confirm the theoretical results.

Alcohols↗

PubMed2006

Marangoni instability and spontaneous non-linear oscillations produced at liquid interfaces by surfactant transfer.

The systems producing non-linear spontaneous oscillations of the interfacial tension and electric potential are considered and the available criteria for development of convective instability by the surfactant transfer through a liquid interface are discussed. The non-linear oscillations are observed by the surfactant transfer from a point-like source situated in the bulk of liquid, by the transfer of two ionic solutes through a liquid interface in two opposite directions, and by the transfer of ionic solutes through a liquid membrane. All these systems are governed by more complicated mechanisms than merely arising oscillatory convective instability. The main experimental results obtained for these three systems as well as theoretical models proposed for their explanation are discussed.

Chemistry, Physical↗

PubMed2006

Quantum chemical analysis of the thermodynamics of 2D cluster formation of n-carboxylic acids at the air/water interface.

Within the framework of PM3 molecular orbital approximation the thermodynamic function characteristics for the formation and geometrical structure of monomers, dimers, trimers, and tetramers of nondissociated n-carboxylic acids C(n)H(2n+1)COOH with n = 5-15 are calculated. It is shown that spontaneous aggregation of homologous fatty acids for the homologues with carbon atoms numbers n > or = 13 at the air/water interface can take place, leading to the formation of infinite plane rectangular clusters, whereas for the homologues with n < 11 spontaneous decomposition of large aggregates is energetically preferable. At the same time, the formation of trimers is more probable for the lower homologues (8 < n < 13). These results agree well both with the experimental data reported by various authors and with thermodynamic models developed earlier for soluble and insoluble monolayers. The slopes of the regressions calculated for the dependencies of the thermodynamic parameters on the alkyl chain length for all the clusters considered are all equal to each other. This fact indicates that the contributions of the CH2 groups to the thermodynamic characteristics of alcohols and acids are the same, and the differences in the formation of clusters by these substances should be attributed only to the differences in the structure and interactions of relevant functional groups. Therefore, it enables one to describe both acids and alcohols within the framework of the developed method, and it makes it possible to extend the proposed approach onto other classes of amphiphilic compounds.

Air↗

PubMed2006

Distributions of ionic concentrations and electric field around the three-phase contact at high rates of Langmuir-Blodgett deposition.

A mathematical problem is formulated and numerically solved for addressing the electric field and ionic concentration distributions developing around the three-phase contact line during the Langmuir-Blodgett deposition of charged monolayers. Compared to a previous paper dealing with the same effect (J. Phys. Chem. B 2004, 108, 13449), the present analysis is not restricted to the case of low deposition rates and small concentration changes. The obtained results show that, for sufficiently high deposition rates, the subphase composition substantially changes in the immediate vicinity of the three-phase contact line. It is shown that the predicted changes in the subphase composition can drastically affect the adhesion work and the dynamic contact angle. On this basis, the influence of the concentration polarization effect on meniscus behavior is discussed.

Computer Simulation↗

PubMed2005

Nonlinear spontaneous oscillations at the liquid/liquid interface produced by surfactant dissolution in the bulk phase.

The results of theoretical and experimental studies of spontaneous nonlinear oscillations produced at the liquid/liquid interface by surfactant transfer from a point source situated in one of the bulk phases are presented. The theoretical analysis is based on the direct numerical simulation of the system evolution. The experiments are performed for the heptane/water interface using middle-chain aliphatic alcohols as surfactants. The results for the oil/water interface are compared with the corresponding data obtained for the air/water interface. The presented results allow the conclusion that auto-oscillations at the air/liquid and liquid/liquid interfaces are governed by very similar mechanisms but their characteristics are strongly dependent on the properties of the two contacting media, in particular, on the surfactant partition coefficient.

Models, Chemical↗

PubMed2005

The role of nonsurface-active species at interfacial molecular recognition by melamine-type monolayers.

The main characteristics of Langmuir monolayers are radically changed by molecular recognition of hydrogen bond nonsurface-active species. The change in the thermodynamic, phase, and structural features by molecular recognition of dissolved uracil or barbituric acid by 2,4-di(n-undecylamino)-6-amino-1,3,5-triazine (2C11H23-melamine) monolayers is characterized by combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and Grazing incidence X-ray diffraction (GIXD) measurements. Phase behavior of the 2C11H23-melamine monolayer and morphology of the condensed phase domains are changed drastically, but in a specific way, by molecular recognition of uracil or barbituric acid. The main characteristics of the interfacial system can be essentially affected by the kinetics of the recognition process. Pure 2C11H23-melamine monolayers show only small compact, but nontextured domains. The monolayers of 2C11H23-melamine-uracil assemblies develop well-shaped circular condensed-phase domains having an inner texture with alkyl chains essentially oriented parallel to the periphery and having a striking tendency to two-dimensional (2D) Ostwald ripening. The 2C11H23-melamine-barbituric acid monolayers form large homogeneous areas of condensed phase that transfer at smaller areas per molecule to a homogeneous condensed monolayer. BAM imaging of corresponding assemblies with ((CH3(CH2)11O(CH2)3)2-melamine having modified alkyl chains demonstrates the specific effect of the monolayer component. GIXD results reveal that molecular recognition of pyrimidine derivatives gives rise only to quantitative changes in the two-dimensional lattice structure. The striking differences in the main characteristics between the supramolecular species are related to their different chemical structures. Quantum chemical calculations using the semiempirical PM3 method provide information about the different nature of the hydrogen-bonding-based supramolecular structures.

Journal Article↗

PubMed2005

Effect of interfacial molecular recognition of non-surface-active species on the main characteristics of monolayers.

Recent progress in studies of the main characteristics of supramolecular assemblies formed by interfacial molecular recognition between an amphiphilic monolayer and a non-surface-active species, which is dissolved in the aqueous subphase, by complementary hydrogen bonding and/or electrostatic interaction at the air-water interface is reviewed. Systems consisting of an amphiphilic melamine-type monolayer and an pyrimidine derivative dissolved in the aqueous subphase are representative model systems for molecular recognition on the basis of complementary hydrogen bonding. Most of the studies have been performed with 2,4-di(n-undecylamino)-6-amino-1,3,5-triazine (2C11H23-melamine) monolayers as host component and thymine, uracil or barbituric acid as dissolved non-surface-active pyrimidine derivatives. The combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and Grazing incidence X-ray diffraction (GIXD) measurements is optimal for the characterization of the change in structure and phase behavior at the interfacial recognition process. The molecular recognition of all pyrimidine derivatives dissolved in the aqueous subphase changes drastically and in a specific way the characteristic features (pi-A isotherms, morphology of the condensed phase domains) of the 2C11H23-melamine monolayer. The small condensed phase domains of the pure 2C11H23-melamine monolayer are compact without an inner texture. The monolayers of the supramolecular 2C11H23-melamine entities with thymine or uracil form specifically well-shaped condensed phase domains with an inner alkyl chain texture essentially oriented parallel to the periphery. The completely different morphology of the 2C11H23-melamine-barbituric acid monolayers is characterized by the formation of large homogeneous areas of condensed phase that transfer at smaller areas per molecule to a homogeneous condensed monolayer. The striking differences in the main characteristics between the supramolecular entities are related to their different chemical structures: complementary hydrogen bonding of two thymine or uracil molecules by one 2C11H23-melamine molecule and a linearly extended hydrogen bonding network between 2C11H23-melamine and barbituric acid. The high values of hydrogen bonding energy obtained by quantum chemical calculations on the basis of the semi-empirical PM3 method state the high stability of the supramolecular entities. The GIXD results reveal that the formation of hydrogen-bond based superstructures between the polar head groups of the amphiphilic 2C11H23-melamine monolayer and the non-surface-active pyrimidine derivatives gives rise only to quantitative changes in the two-dimensional lattice structure of the alkyl chains. The alternative possibility to construct interfacial molecular recognition systems on the basis of acid-base interaction is demonstrated by the experimental results obtained by molecular recognition of the heptadecyl-benzamidinium chloride monolayers with dissolved non-surface-active phenylacetate ions. The formation of supramolecular assemblies causes also drastical changes of the surface features in these systems. Here, the development of a substructure in the condensed phase domains consisting of long filigree strings and the favoured formation of bilayers overgrowing the strings indicates a linearly extended amidinium-carboxylate interfacial structure of the base and acid component in alternating sequence.

Hydrogen Bonding↗

PubMed2005

Effect of buoyancy on appearance and characteristics of surface tension repeated auto-oscillations.

The effect of buoyancy on spontaneous repeated nonlinear oscillations of surface tension, which appear at the free liquid interface by dissolution of a surfactant droplet under the interface, is considered on the basis of direct numerical simulation of the model system behavior. The oscillations are the result of periodically rising and fading Marangoni instability. The buoyancy force per se cannot lead to the oscillatory behavior in the considered system, but it influences strongly both the onset and decay of the instability and therefore, affects appearance and characteristics of the oscillations. If the surfactant solution density is smaller than the density of the pure liquid, then the buoyancy force leads to a considerable decrease of the induction period and the period of oscillations. The buoyancy force affects also the dependence of the oscillation characteristics on the system dimensions. The results of the simulations are compared with the available experimental data.

Chemical Phenomena↗

PubMed2005

Molecular recognition kinetics of nonsurface active pyrimidine derivatives dissolved in the aqueous subphase by an amphiphilic melamine type monolayer: A theoretical approach.

Experimental studies show a drastic change of the characteristic features (Pi-A isotherms, morphology of the condensed phase domains) of the 2C11H23-melamine monolayers by molecular recognition of the pyrimidine derivatives uracil and thymine, largely affected by the reaction kinetics of the recognition process. A new approximate additive theoretical model is introduced for describing the molecular recognition kinetics. The theoretical approach is based on two assumptions: (i) first-order reaction kinetics for the molecular recognition of the nonsurface active pyrimidine derivatives dissolved in the aqueous subphase by the melamine type monolayer and (ii) applicability of the Pi-A isotherm equations derived previously for the description of melamine type monolayers in the fluid (gaseous, LE) state and the phase transition region to the condensed state. The rate constants for the molecular recognition reaction between the melamine type monolayer and the dissolved thymine and uracil are estimated, which are roughly proportional to the bulk concentrations of the pyrimidine derivatives and depend only slightly on the temperature. The theoretical estimates agree satisfactorily with the experimental results obtained under various conditions (Pi = const and dA/dt = const). This fact supports the validity of the first model proposed for the interfacial molecular recognition kinetics with nonsurface active substrates dissolved in the aqueous subphase by complementary hydrogen bonding.

Kinetics↗

PubMed2005

Thermodynamic and structural characterization of amphiphilic melamine-type monolayers.

Monolayers of amphiphilic melamine derivatives are good candidates for the formation of supramolecular structures by hydrogen-bonding of nonsurface active species dissolved in the aqueous subphase by molecular recognition. In the present work, the thermodynamic and structural properties of the Langmuir monolayers of a homologous series of a selected amphiphilic melamine-type are characterized. Good candidates for such studies are the decyl, undecyl, and dodecyl homologues of the 2,4-di(n-alkylamino)-6-amino-1,3,5-triazine (2CnH(2n+1)-melamine) monolayers because of their two-phase coexistence region in the accessible temperature range. The characterization of the structural and phase behavior is performed by a combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and Grazing incidence X-ray diffraction (GIXD) measurements. A comprehensive thermodynamic analysis provides good agreement between the experimental surface pressure - area (Pi-A) isotherms and the theoretical curves that were calculated on the basis of equations of state for a large region of monolayer stages developed by us in J. Phys. Chem. 1999, 103, 145. Theoretical curves calculated by application of equations of state only for the fluid monolayer state proposed recently by Rusanov (J. Chem Phys. 2004, 120, 10736) are in good agreement with the experiments in a limited temperature range. A rigorous equation is derived and applied to the experimental results for the calculation of the enthalpy of two-dimensional phase transition. The combination of BAM and GIXD illustrates that the microscopic long range ordering of the condensed monolayer phases is related to the lattice structure of the condensed monolayer.

Thermodynamics↗

PubMed2005

Interfacial molecular recognition of dissolved thymine by medium chain dialkyl melamine-type monolayers.

Systems consisting of an amphiphilic melamine-type monolayer and a pyrimidine derivative dissolved in the aqueous subphase are good candidates for the formation of interfacial supramolecular assemblies by molecular recognition of hydrogen-bond nonsurface-active species. In the present work, the change in the thermodynamic, phase, and structural properties as a result of molecular recognition of dissolved thymine by 2,4-di(n-undecylamino)-6-amino-1,3,5-triazine (2 C11H23-melamine) monolayers is studied. The combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and grazing incidence X-ray diffraction (GIXD) measurements is optimal for the characterization of the change in structure and phase behavior at the interfacial recognition process. The molecular recognition of the nonsurface-active thymine dissolved in aqueous subphase changes drastically the characteristic features (surface pressure-area isotherms, morphology of the condensed phase domains) of the 2 C11H23-melamine monolayer. It is demonstrated that the kinetics of the recognition process affect largely the main characteristics (phase behavior, morphology of the condensed phase domains) of the interfacial system. The monolayers of 2 C11H23-melamine-thymine assemblies form dumbbell-shaped condensed phase domains not yet observed in other Langmuir monolayers so far. GIXD results show that the molecular recognition of thymine causes only quantitative changes in the two-dimensional lattice structure. Complementary hydrogen bonding of two thymine molecules by one 2 C11H23-melamine molecule is concluded from the chemical structure of both components. Additional information about the nature of the hydrogen bonding on the basis of supramolecular assemblies is obtained by using the quantum chemical PM3 approximation. Energy and lengths of the hydrogen bonds of the optimized thymine-2 C11H23-melamine-thymine structure are calculated.

Chemistry, Physical↗

PubMed2005

Role of electrostatic interactions for the domain shapes of Langmuir monolayers of monoglycerol amphiphiles.

The role of electrostatic interaction in the domain morphology of amide, ether, ester, and amine monoglycerol monolayers (abbreviated as ADD, ETD, ESD, and AMD, respectively) with systematic variation in the molecular structure of the headgroup region is investigated. Experimental studies using Brewster angle microscopy (BAM) and grazing incidence X-ray diffraction (GIXD) show that the characteristic features of the condensed monolayer phase, such as domain morphology, crystallinity, and lattice parameters, are very different for these monoglycerols. Therefore, the intermolecular interactions of the four amphiphilic monoglycerols are investigated in detail. First, the dipole moments of four monoglycerols of similar structure but with different functional groups are calculated by a semiempirical quantum mechanical technique. The dipole moments for monoglycerols follow the sequence AMD < ETD < ESD < ADD for the population of conformers of compounds investigated. The dipolar repulsion energies for the amphiphilic monoglycerols are also calculated for different possible mutual orientations between the dipoles. The calculated dipolar energies also follow the same trend for different possible headgroup orientations. These results can explain the domain shape of the monoglycerols observed experimentally. Second, ab initio calculations on the basis of the HF/6-31G** method are performed for representative monoglycerol headgroup segments. The results show that the intermolecular interaction energy related to dimer formation follows the order ETD < ESD < AMD < ADD segments, similar to that observed in experiment except in the case of the AMD segment. The relative importance of intra- and intermolecular hydrogen bonding in dimers is analyzed. The enhanced role of the intermolecular interaction relative to intramolecular interaction in the case of AMD contributes to the relatively high intermolecular interaction energy for the particular conformation of the dimer of AMD segment as observed from ab initio calculation. The present work shows that the variations in headgroup molecular structure alter drastically the domain shape, and the theoretical calculations conclusively reveal the important role of the electrostatic interactions for the mesoscopic domain architecture.

Journal Article↗

PubMed2005

Ion redistribution and meniscus stability at Langmuir monolayer deposition.

Considering the deposition of charged Langmuir monolayers, it is necessary to take into account electrostatic interactions between the monolayer and the substrate surface. These interactions depend on the nature of ionizable surface groups and on the ionic composition of the subphase (e.g. pH, multivalent counterions, indifferent electrolytes). The non-uniformity of electric, concentration and hydrodynamic velocity fields leads to the formation of ion concentration profiles near the three-phase contact line during the deposition. This effect is similar to the effect of concentration polarization in membranes and electrode systems. The ions redistribution results in change of the monolayer ionization, adhesion work, dynamic contact angle, and, therefore, in the change of morphology, composition and structure of the deposited monolayer. With increasing withdrawal velocity the meniscus can become unstable because of concentration polarization in the solution.

Biophysics↗