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One permanent characteristic of the thermodynamics of small systems is environment-dependence, also known as ensemble-dependence. Fluid molecules in soft (deformable) nano-confinement offer a special ensemble that acts as a bridge between classical isobaric (NPT) and isochoric (NVT) ensembles. Here, we discuss the gas–liquid transition taking place in a soft nano-confinement where the cell volume is not fixed but changes when the system pressure is changed. The free energy of the system is calculated as a function of the size of the liquid droplet that appears in the gas phase. We discuss how the phase behavior changes when the condition of the confinement changes from rigid confinement to very soft confinement. For the simple fluid model studied, the coexistence and critical phase behaviors are found to be uniquely determined by αK (αK is the dimensionless elasticity constant of the wall of confined space and is proportional to its ability to resist deformation), and the confinement with moderate softness exhibits richer phase behavior. We then study the fluctuations of pressure, volume, and droplet size for fluid in soft confined spaces, which is again closely related to the wall softness. Under moderate softness, large fluctuations in both fluid pressure and volume are seen in the transition region where fluid pressure increases with volume expansion, accompanied by the strengthened fluctuation of droplet size.

Superhydrophobic surfaces have received tremendous attention due to their extraordinary physical characteristics and potential applications in various fields. However, the design of robust superhydrophobic surfaces showing both low adhesion and high antiwetting remains a great challenge. Here, we first introduce some important parameters for the characterization of the adhesion property of superhydrophobic surfaces and its physical meaning, including the apparent contact angle, rolling angle, and hysteresis angle. Then, we summarize the antiwetting property of superhydrophobic surfaces through thermodynamic and dynamic methods, and we point out the contradiction between low adhesion and high antiwetting of superhydrophobic surfaces. To achieve a trade-off between low adhesion and high antiwetting in superhydrophobic materials, we also review the recent progress made in regard to the optimal design of superhydrophobic surfaces by using chemical modification and physical design of microstructures. Finally, we review the application of superhydrophobic surfaces for drag reduction, with a few discussions and outlook. This Research Update is expected to provide useful guidance to rationally design superhydrophobic materials with low adhesion and high antiwetting properties and, thus, speed up the development of superhydrophobic materials or anti-icing materials.

The contact line pinning and supersaturation theory for the nanobubble stability has attracted extensive concerns from experimental investigators, and some experimenters argue that the contact line pinning is unnecessary. To interpret the experimental observations, we have proposed previously through molecular dynamics simulations that the deformation of soft substrates caused by surface nanobubbles may play an important role in stabilizing surface nanobubbles, while yet no quantitative theory is available for explanation of this mechanism. Here, the detailed mechanism of self-pinning-induced stability of surface nanobubbles is investigated through theoretical analysis. By manipulating substrate softness, we find that the formation of surface nanobubbles may create a deformation ridge nearby their contact lines which leads to the self-pinning effect. Theoretical analysis shows that the formation of nanobubbles on sufficiently rigid substrates or on liquid–liquid interfaces corresponds to a local free energy maximum, while that on the substrates with intermediate softness corresponds to a local minimum. Thus, the substrate softness could regulate the surface nanobubble stability. The critical condition for the self-pinning effect is determined based on contact line depinning, and the effect of gas supersaturation is explored. Finally, the approximate stability range for the surface nanobubbles is also predicted.

Micro-nanobubbles (MNBs) technology has emerged as an effective means of sewage treatment, while the molecular mechanism for its pollutant degradation is still unknown. In this paper, the reactive molecular dynamics simulation technique is used to study the degradation mechanism of pollutants caused by shock-induced nanobubble collapse. We first demonstrate that the propagating shock wave can induce nanobubble collapse, and the collapsing nanobubble has the ability to focus mechanical energy via the converging motion of liquid in the interior of the bubble, leading to the formation of a high-speed jet with a much higher energy density. We also unveil the mechanical nature of long-chain pollutant degradation and the mechanism of free radical generation. Due to the impacting jet, the high-gradient flow has the ability to stretch the long-chain molecule and cause mechanical scission of the molecule in a homolytic manner. Finally, our simulation results reveal that adding ozone molecules to the collapsing bubble would introduce an additional dehydrogenation mechanism.

Ethanol has great effects on the adsorption of phthalate acid esters (PAEs) on activated carbon (AC), which are usually overlooked and hardly studied. This study investigated the overlooked effects of ethanol on the adsorption of PAEs in alcoholic solutions. The adsorption capacities of dibutyl phthalate (DBP) on AC in solutions with ethanol contents of 30, 50, 70, and 100 v% were only 59%, 43%, 19%, and 10% of that (16.39 mg/g) in water, respectively. The ethanol content increase from 50 v% to 100 v% worsened the adsorption performances significantly with the formation of water–ethanol–DBP clusters (decreasing from 13.99 mg/g to 2.34 mg/g). The molecular dynamics simulation showed that the DBP tended to be distributed farther away from the AC when the ethanol content increased from 0 v% to 100 v% (the average distribution distance increased from 5.25 Å to 15.3 Å). The PAEs with shorter chains were more affected by the presence of ethanol than those with longer chains. Taking DBP as an example, the adsorption capacity of AC in ethanol (0.41 mg/g) is only 2.2% of that in water (18.21 mg/g). The application results in actual Baijiu samples showed that the adsorption of PAEs on AC had important effects on the Baijiu flavors.

GPI-Anchored proteins (GPI-APs) can be exogenously transferred onto bilayer membranes both in vivo and in vitro, while the mechanism by which this transfer process occurs is unknown. In this work, we used atomistic molecular dynamics simulations and free energy calculations to characterize the essential influence of cholesterol on insertion of the GPI anchors into plasma membranes. We demonstrate, both dynamically and energetically, that in the presence of cholesterol, the tails of GPI anchors are able to penetrate inside the core of the lipid membrane spontaneously with a three-step mechanism, while in the absence of cholesterol no spontaneous insertion was observed. We ascribe the failure of insertion to the strong thermal fluctuation of lipid molecules in cholesterol-free bilayer, which generates a repulsive force in entropic origin. In the presence of cholesterol, however, the fluctuation of lipids is strongly reduced, thus decreasing the barrier for the anchor insertion. Based on this observation, we propose a hypothesis that addition of cholesterol creates vertical creases in membranes for the insertion of acyl chains. Moreover, we find that the GPI anchor could also spontaneously inserted into the boundary between cholesterol-rich and cholesterol-depleted domains. Our results shed light on the mechanism of cholesterol-mediated interaction between membrane proteins with acyl chain and plasma membranes in living cells.

Red blood cells (RBCs), also called erythrocytes, have been experimentally proposed in recent decades as the biological drug delivery systems through entrapping certain drugs by endocytosis. However, the internalization pathway of endocytosis seems to conflict with the robust mechanical properties of RBCs that is induced by the spectrin-actin network of erythrocyte membrane skeleton. In this work, we employed a minimum realistic model and the dissipative particle dynamics method to investigate the influence of the spectrin-actin membrane skeleton on the internalization of nanoparticles (NPs). Our simulations show that the existence of skeleton meshwork indeed induces an inhibiting effect that effectively prevents NPs from internalization. The inhibiting effect is found to depend on the membrane-NP attraction, skeleton tension and relative size of the NP to the membrane skeleton mesh. However, our simulations also demonstrate that there are two possibilities for successful internalization of NPs in the presence of the membrane skeleton. The first case is for NPs that has a much smaller size than the dimension of skeleton meshes, and the other is that the skeleton tension is rather weak so that the formed vesicle can still move inward for NP internalization.

Heterogeneous bubble nucleation is one of the most fundamental interfacial processes ranging from nature to technology. There is excellent evidence that surface topology is important in directing heterogeneous nucleation; however, deep understanding of the energetics by which nanoscale architectures promote nucleation is still challenging. Herein, we report a direct and quantitative measurement of single-bubble nucleation on a single silica nanoparticle within a microsized droplet using scanning electrochemical cell microscopy. Local gas concentration at nucleation is determined from finite element simulation at the corresponding faradaic current of the peak-featured voltammogram. It is demonstrated that the criteria gas concentration for nucleation first drops and then rises with increasing nanoparticle radius. An optimum nanoparticle radius around 10 nm prominently expedites the nucleation by facilitating the special topological nanoconfinements that consequently catalyze the nucleation. Moreover, the experimental result is corroborated by our theoretical calculations of free energy change based on the classic nucleation theory. This study offers insights into the impact of surface topology on heterogenous nucleation that have not been previously observed. [ABSTRACT FROM AUTHOR]

Despite catalyzed by fusion proteins of quite different molecular architectures, intracellular, viral, and cell-to-cell fusions are found to have the essential common features and the nearly same nature of transition states. The similarity inspires us to find a more general catalysis mechanism for membrane fusion that minimally depends on the specific structures of fusion proteins. In this work, we built a minimal model for membrane fusion, and by using dissipative particle dynamics simulations, we propose a mechanism that the pulling force generated by fusion proteins initiates the fusion process and the membrane tension regulates the subsequent fusion stages. The model shows different features compared to previous computer simulation studies: the pulling force catalyzes membrane fusion through lipid head overcrowding in the contacting region, leading to an increase in the head-head repulsion and/or the unfavorable head-tail contacts from opposing membranes, both of which destabilize the contacting leaflets and thus promote membrane fusion or vesicle rupture. Our simulations produce a variety of shapes and intermediates, closely resembling cases seen experimentally. Our work strongly supports the view that the tight pulling mechanism is a conserved feature of fusion protein-mediated fusion and that the membrane tension plays an essential role in fusion. [ABSTRACT FROM AUTHOR]

Here, we study how nanobubbles nucleate on rough hydrophobic surfaces, using long-time standard simulations to directly observe the kinetic pathways and using constrained simulations combined with the thermodynamic integration approach to quantitatively evaluate the corresponding free energy changes. Both methods demonstrate that a two-step nucleation route involving the formation of an intermediate state is thermodynamically favorable: at first, the system transforms from theWenzel state (liquid being in full contact with the solid surface) to the Cassie state (liquid being in contact with the peaks of the rough surface) after gas cavities occur in the grooves (i.e., theWenzel-to-Cassie transition); then, the gas cavities coalesce and form a stable surface nanobubble with pinned contact lines (i.e., the Cassie-to-nanobubble transition). Additionally, the free energy barriers for the two transitions show opposing dependencies on the degree of surface roughness, indicating that the surfaces with moderate roughness are favorable for forming stable surface nanobubbles. Moreover, the simulation results also reveal the coexistence and transition between the Wenzel, Cassie, and nanobubble states on rough surfaces. [ABSTRACT FROM AUTHOR]

In this work, we focus on investigating how nanobubbles mediate long-range interaction between neighboring solid substrates in the presence of the contact line pinning effect caused by surface heterogeneities. Using the constrained lattice density functional theory (LDFT), we prove that the nanobubbles, which take the form of vapor bridges here, are stabilized by the pinning effect if the separation between two substrates is less than a critical distance. The critical distance strongly depends on the chemical potential (i.e., the degree of saturation) and could become extremely long at a special chemical potential. Moreover, under the pinning effect, the substrate chemistry only determines the stability of the vapor bridges and the range of the capillary force, but has less influences on the magnitude of the capillary force, indicating that the substrate chemistry or the apparent contact angle for droplets or bubbles on the substrates is no longer a direct parameter to determine the magnitude of capillary force. A qualitative analysis for the two dimensional vapor bridges by considering the feedback mechanism can explain the results from the LDFT calculations. [ABSTRACT FROM AUTHOR]

The adsorption of hydrogen both on square-packed single-walled carbon nanotube (SWCNT) arrays and on isolated nantoubes was investigated by a combination of a classical potential and density functional theory (DFT) method. DFT calculations indicated that the excess gravimetric storage capacity of exohedral adsorption of hydrogen on SWCNT array is as muchas 30%of that of endohedral adsorption when the van der walls( VDW ) gap was fixed at 0.335 nm.

We numerically study different forms of nanoscale gaseous domains on a model for rough surfaces. Our calculations based on the constrained lattice density functional theory show that the interconnectivity of pores surrounded by neighboring nanoposts, which model the surface roughness, leads to the formation of stable microscopic Cassie states. We investigate the dependence of the stability of the micro-Cassie states on substrate roughness, fluid-solid interaction, and chemical potential and then address the differences between the origin of the micro-Cassie states and that of surface nanobubbles within similar models. Finally, we show that the micro-Cassie states share some features with experimentally observed micropancakes at solid-water interfaces. [ABSTRACT FROM AUTHOR]

In this paper, we apply the molecular dynamics simulation method to study the stability of surface nanobubbles in both pure fluids and gas-liquid mixtures. First, we demonstrate with molecular simulations, for the first time, that surface nanobubbles can be stabilized in superheated or gas supersaturated liquid by the contact line pinning caused by the surface heterogeneity. Then, a unified mechanism for nanobubble stability is put forward here that stabilizing nanobubbles require both the contact line pinning and supersaturation. In the mechanism, the supersaturation refers to superheating for pure fluids and gas supersaturation or superheating for the gas-liquid mixtures, both of which exert the same effect on nanobubble stability. As the level of supersaturation increases, we found a Wenzel or Cassie wetting state for undersaturated and saturated fluids, stable nanobubbles at moderate supersaturation with decreasing curvature radius and contact angle, and finally the liquid-to-vapor phase transition at high supersaturation. [ABSTRACT FROM AUTHOR]

We report a theoretical study of nanobubble stabilization on a substrate by contact line pinning. In particular, we predict the magnitude of the pinning force required to stabilize a nanobubble and the threshold values of the pinning force that the substrate can provide. We show that the substrate chemistry and the local structures of substrate heterogeneity together determine whether or not surface nanobubbles are stable. We find that for stable nanobubbles, the contact angles are independent of substrate chemistry as its effects are cancelled out by the pinning effect. This prediction is in agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Atomic force microscopy (AFM) can work in a variety of environment with different humidities. When the tip of AFM approaches a sample, the measured adhesion force would be significantly affected by the presence of nanometer-sized liquid bridge. The formation and rupture of liquid bridges can occur either through equilibrium or nonequilibrium process. In this work, the liquid bridges are assumed to be in thermodynamic equilibrium with the surrounding vapor medium. To study theoretically the stability of liquid bridge, a constraint is added into the lattice density functional theory to stabilize a series of bridges with different radii at a given tip-substrate distance. With the help of the constraint, we can identify not only stable and metastable states but also transition states for the formation and rupture of liquid bridges. Using this constrained method we calculate the energy barriers involved in the formation and rupture of the liquid bridges, respectively, and then discuss their stability as well as the origin of the hysteresis behavior observed with atomic force microscope measurements. On the whole, the calculated force-distance curves are found to be qualitatively in agreement with experimental observations. The energy barriers for the formation and rupture of liquid bridges are also analyzed as a function of tip-sample distance, humidity, and tip-fluid interaction. [ABSTRACT FROM AUTHOR]

In this work, lattice Monte Carlo was used to study the effects of crowding on the self-assembly of surfactants. Simulation results show that crowding strongly shifts the critical micelle concentration (CMC) of surfactants from the bulk value. Two effects originated from crowding are found to govern the CMC shift: one is the depletion effect by crowding agents and the other is the available volume for micelle formation. The depletion effects inevitably result in the enrichment of surfactants in crowding-free regions and cause the decrease in CMC. On the other hand, the appearance of crowding agents decreases the available volume for micelle formation, which reduces the conformational entropy and impedes the micelle formation. Three factors, including the radius of crowding agents, the arrangement of crowding agents, and the volume fraction of crowding agents, are considered in this work to study the crowding effects. The trends of CMC shifts are interpreted from the competition between the depletion effects and the available volume for micelle formation. [ABSTRACT FROM AUTHOR]

In this work, extensive lattice Monte Carlo simulations were performed to investigate the influence of confinement on critical micelle concentration (CMC). It is found that the CMC of surfactants in a confined space is shifted from its bulk value, and the shift is affected by the presence of the confining boundaries, which induces both the finite size effect and the wall-surfactant interaction. In general, for strongly confined system (the system with narrow pore size), the finite size effect dominates the CMC shift because the confined space cannot accommodate fully developed micelles, and the rapid increase of the entropic loss due to the decrease of the pore size results in the rapid increase of CMC. In contrast, for a weakly confined space, the CMC shift depends on the interaction between the walls and surfactants. For the systems with two weakly hydrophilic surfaces, the local density depletion of the surfactants near the walls results in lower CMCs than the bulk value, and the CMC shifts to a higher value as the pore size increases. For the systems with moderately hydrophilic surfaces, the shifts of CMCs show a similar behavior as those for weakly hydrophilic surfaces, but the CMCs are near their bulk values in the range of weak confinement. For the systems with strongly attractive wall-surfactant interactions, the strong adsorption also results in lower CMCs than their bulk value, but the CMCs decrease with the increase of pore size. [ABSTRACT FROM AUTHOR]

The dependence of the adsorption isotherm and phase behavior of Lennard-Jones (LJ) fluid in cylindrical pores on the fluid–wall interaction was investigated using a discrete attractive potential model and the density functional theory. The discrete attractive potential contains two parts, a deep well (dw) and a tail. The results show that the chemical potential corresponding to capillary condensation has a weak dependence on the deep well potential near the pore wall, but exhibits a strong dependence on the tail potential near the pore center. On the contrary, the chemical potential of the formation of the first monolayer is strongly dependent on the deep well potential but almost independent of the tail potential. The shape of the adsorption isotherm plotted as density versus chemical potential is determined by the shape of the fluid–wall interaction, namely [variant_greek_epsilon][sub tail]–[variant_greek_epsilon][sub dw], rather than either the deep well potential or the weak tail potential separately. The critical temperature exhibits similar behavior in its dependence on [variant_greek_epsilon][sub tail]–[variant_greek_epsilon][sub dw]. There exists a region where layer transition and capillary condensation intersect. Adsorption isotherms, coexistence curves, and critical temperatures in this region exhibit distinct phase behaviors from other regions. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In contrast to stability theories of nanobubbles, the molecular mechanism of how nanobubbles lose stability is far from being understood. In this work, we try to interpret recent experimental observations that the addition of surfactants destabilizes nanobubbles with an unclear mechanism. Using molecular dynamics simulations, we identify two surfactant-induced molecular mechanisms for nanobubbles losing stability, either through depinning of a contact line or reducing vapor-liquid surface tension. One corresponds to the case with significant adsorption of surfactants on the substrates, which causes depinning of the nanobubble contact line and thus leads to nanobubble instability. The other stresses surfactant adsorption on the vapor-liquid interface of nanobubbles, especially for insoluble surfactants, which reduces the surface tension of the interface and leads to an irreversible liquid-to-vapor phase transition. Our finding can help improve our understanding in nanobubble stability, and the insight presented here has implications for surface nanobubbles involving with other amphiphilic molecules, such as proteins and contaminations. [ABSTRACT FROM AUTHOR]

Recent experimental measurements have shown that there exists a population of nanobubbles with different curvature radii, whereas both computer simulations and theoretical analysis indicated that the curvature radii of different nanobubbles should be the same at a given supersaturation. To resolve such inconsistency, we perform molecular dynamics simulations on surface nanobubbles that are stabilized by heterogeneous substrates either in the geometrical heterogeneity model (GHM) or in the chemical heterogeneity model (CHM) and propose that the inconsistency could be ascribed to the substrate-induced nanobubble deformation. We find that, as expected from theory and computer simulation, for either the GHM or the CHM, there exists a universal upper limit of contact angle for the nanobubbles, which is determined by the degree of supersaturation alone. By analyzing the evolution of the shape of nanobubbles as a function of substrate hydrophobicity that is controlled here by the liquid-solid interaction, two different origins of nanobubble deformation are identified. For substrates in the GHM, where the contact line is pinned by surface roughness, variation in the liquid-solid interaction changes only the location of the contact line and the measured contact angle, without causing a change in the nanobubble curvature. For substrates in the CHM, however, the liquid-solid interaction exerted by the bottom substrate can deform the vapor-liquid interface, resulting in variations in both the curvature of the vapor-liquid interface and the contact angle. [ABSTRACT FROM AUTHOR]

Lipid-based dispersion of hydrophobic nanoparticles (NPs) not only gives fundamental insight into how nanomaterials distribute in live cells and organisms, but also provides a quite general route to designing nanocarrier agents in triggered drug delivery and medical imaging. It is not clearly understood how hydrophobic NPs arrange in the interior of a membrane. In this paper, with computer simulation techniques, we demonstrate that hydrophobic NPs having a diameter compared to the hydrophobic thickness of the membrane are capable of clustering in the hydrophobic interior of a cell membrane. Except from the isotropic aggregation, an unexpected linear arrangement of spherical NPs, which is still not found from experiments, is identified here. The free-energy costs associated with linear and isotropic aggregations are computed explicitly to interpret aggregation behavior and the obtained phase diagrams give us a comprehensive understanding of where linear aggregation is expected. In this work we also shows that NP size and membrane tension play key roles in determining the NP aggregate, while the effects of NP concentration and membrane curvature seem to be relatively weak. [ABSTRACT FROM AUTHOR]

We use a dissipative particle dynamic simulation to investigate the effects of shape complementarity on the protein-protein interactions. By monitoring different kinds of protein shape-complementarity modes, we gave a clear mechanism to reveal the role of the shape complementarity in the protein-protein interactions, i.e., when the two proteins with shape complementarity approach each other, the conformation of lipid chains between two proteins would be restricted significantly. The lipid molecules tend to leave the gap formed by two proteins to maximize the configuration entropy, and therefore yield an effective entropy-induced protein-protein attraction, which enhances the protein aggregation. In short, this work provides an insight into understanding the importance of the shape complementarity in the protein-protein interactions especially for protein aggregation and antibody-antigen complexes. Definitely, the shape complementarity is the third key factor affecting protein aggregation and complex, besides the electrostatic-complementarity and hydrophobic complementarity. [ABSTRACT FROM AUTHOR]

Nanodroplets sitting on substrates in an open system are usually assumed to be thermodynamically unstable, and will eventually either evaporate or grow. However, as a counterpart of nanodroplets, nanobubbles located at the solid-liquid interface were recently demonstrated by numerous experiments to be unexpectedly stable. The accumulated evidence for the existence of stable nanobubbles poses a question of whether nanodroplets are stable. In this work we revisit the stability of nanodroplets upon smooth and rough substrates, concentrating on their evaporation dynamics. On smooth substrates, the droplets evaporate generally in the constant contact angle (CCA) mode, with a contact angle nonmonotonously depending on the fluid-substrate interaction, while on rough substrates, the droplets evaporate in the constant contact line (CCL) mode or the CCL-CCA mixed mode. Our results indeed predict the existence of stable nanodroplets on rough substrates: In situations where the contact line is pinned and the vapor is supersaturated but at a low level of supersaturation, nanodroplets are found to be anomalously stable. The stability of nanodroplets can be interpreted within the framework of the classical nucleation theory. [ABSTRACT FROM AUTHOR]

In this work, we present a theoretical method to determine the line tension of nanodroplets on homogeneous substrates via decomposing the grand free energy into volume, interface and line contributions. With the obtained line tension, we check the viability of Young equation and find that the chemical potential dependence (or equivalently, droplet curvature dependence) of the interface tensions is crucial for the viability of modified Young equation at the nanometer scale. In particular, the linear relationship between the cosine of contact angle and the curvature of the contact line, which is often used to determine the line tension, is found to be incorrect at the nanometer scale. [ABSTRACT FROM AUTHOR]

One key question in signal transduction is how the signal is relayed from the outer leaflet of a cellular membrane to the inner leaflet. Using a simulation model, a mechanism for the mediation of signal transduction is proposed here in which the coupling between membrane proteins in different leaflets can be achieved by the clustering of anchored proteins, without recruiting transmembrane proteins. Depending on the hydrophobic length of the anchored proteins, three coupling patterns, including face-to-face clustering, interdigitated clustering, and weak-coupled clustering, are observed in this work. This observation provides a possible explanation of how a particular downstream signaling pathway is selected. [ABSTRACT FROM AUTHOR]

In this work, we used the lattice Boltzmann (LB) method to simulate the generation of concentration gradients in microfluidic networks. We first developed a model of microfluidic networks, in which the flow velocity of the laminar flow in the microchannel and the diffusion of solute molecules govern the solute gradients generated, and the obtained results are comparable with experimental data. Our simulation results indicated that the relative positions of the branching plates in different levels, at which a microchannel is split into several daughter microchannels, exert significant effects on the shape of concentration gradients. We also performed extensive simulations to study the dependence of the shape of the concentration gradient on the velocity of the flow u, diffusion coefficients of solutes D, and the length of the microchannel L. A dimensionless parameter, (L/u)/(H2/D), in which His the hydraulic diameter of the main microchannel, was proposed in this work. It is found that for geometrically similar microfluidic networks, the parameter alone determines the shape of the generated concentration gradient. Therefore, the proposed parameter allows one to perform experiments or simulations with reduced models in microchannels and correlate the data to the other flows or geometry sizes. [ABSTRACT FROM AUTHOR]