Chemical Concentration Gradients Research Articles

Transport by Oscillatory Flow in Soils with Rate‐Limited Mass Transfer: 1. Theory

Oscillatory flow of fluid in a porous medium can generate a one‐way transport of heat or chemicals if there is a gradient of temperature or chemical concentration and a rate‐limited heat or mass transfer between the moving fluid and an immobile phase. For chemical transport in soils, the immobile phase can occur in stagnant porosity, by sorption, or by dissolution of a vapor in the pore water. As a function of oscillation frequency, the transport rate has a broad peak near the value ωτc = 1, where ω is the angular frequency of oscillation and τc is the characteristic equilibration time of the mobile phase. The transport rate is proportional to the gradient and to the square of the amplitude of periodic fluid displacement. A unique diffusivity derived from the analysis enables prediction of the long‐term transport by a diffusion calculation without fluid flow, thereby providing a tool for estimating the removal of contaminant vapors by passive soil vapor extraction (PSVE). We compared predictions of the analytic theory with numerical simulations of PSVE. The mobile–immobile model is also applicable to transport in other cases of oscillatory flow in porous media, including cyclic motion of water or gas due to tidal aquifers or earth tides.

Femtosecond laser machined microfluidic devices for imaging of cells during chemotaxis.

Microfluidic devices designed for chemotaxis assays were fabricated on fused silica substrates using femtosecond laser micromachining. These devices have built-in chemical concentration gradient forming structures and are ideally suited for establishing passive diffusion gradients over extended periods of time. Multiple gradient forming structures, with identical or distinct gradient forming characteristics, can be integrated into a single device, and migrating cells can be directly observed using an inverted microscope. In this paper, the design, fabrication, and operation of these devices are discussed. Devices with minimal structure sizes ranging from 3 to 7 lm are presented. The use of these devices to investigate the migration of Dictyostelium discoideum cells toward the chemoattractant folic acid is presented as an example of the devices' utility.

The Soret effect and isotopic fractionation in high-temperature silicate melts

Diffusion in condensed phases is a ubiquitous but poorly understood phenomenon. For example, chemical diffusion, which is the transport of matter associated with chemical concentration gradients (Fick's law), is treated as a separate process from thermal transport (the Soret effect), which is mass transport induced by temperature gradients. In the past few years, large variations in the proportions of isotopes of Mg, Ca, Fe, Si and O found in silicate melts subject to thermal gradients have been found, but no physical mechanism has been proposed. Here we present a model of diffusion in natural condensed systems that explains both the chemical and isotopic fractionation of Mg, Ca and Fe in high-temperature geochemical melts. Despite the high temperatures associated with these melts (T>1,000 °C), we find that consideration of the quantum-mechanical zero-point energy of diffusing species is essential for understanding diffusion at the isotopic level. Our model explains thermal and chemical mass transport as manifestations of the same underlying diffusion mechanism. This work promises to provide insights into mass-transport phenomena (diffusion and evaporation) and associated isotopic fractionations in a wide range of natural condensed systems, including the atmospheric water cycle, geological and geochemical systems and the early Solar System. This work might also be relevant to studies of mass transport in biological and nanotechnological condensed systems.

Nanofibrous scaffold with incorporated protein gradient for directing neurite outgrowth.

Concentration gradient of diffusible bioactive chemicals assumes many important roles in regulating cellular behavior. Among the many factors influencing functional recovery after nerve injury, such as topographical and biochemical signals, concentration gradients of neurotrophic factors provide chemotactic cues for neurite outgrowth and targeted renervation. In this study, a concentration gradient of nerve growth factor (NGF, 0-250μg/ml) was incorporated throughout the thickness of poly(ε-caprolactone)-poly(ethylene glycol) coaxial electrospun nanofibrous scaffolds (∼700μm thick with ∼800nm average fiber diameter). The existence of the protein gradient upon protein release was demonstrated using a customized under-agarose-PC12 neurite outgrowth assay. When exposed to scaffolds endowed with NGF concentration gradient (NGF-CG), a significant difference in the percentage of cells bearing neurite outgrowth was observed (7.1 ± 1.9% vs. 0.8 ± 0.3% for cells exposed to high vs. low concentration surface, respectively; p < 0.05). In contrast, no significant difference was observed when cells were exposed to scaffolds that encapsulated a fixed concentration of NGF. Direct culture of PC12 cells on the substrates demonstrated the cytocompatibility and the effect of diffusible NGF gradient on neurite outgrowth. A significant difference in the percentage of cells with neurite extensions was observed when PC12 cells were seeded on NGF-CG scaffolds (21.2 ± 3.6% vs. 10.4 ± 1.3% on high vs. low concentration surface, respectively; p < 0.05). Furthermore, Z-stack confocal microscopy tracking of neurite extensions revealed the chemotatic guidance effect of NGF concentration gradient. Directed and enhanced neurite penetration into the scaffolds towards increasing NGF concentration was observed. In vitro release study indicated that the encapsulated NGF was released in a sustained manner for at least 30days (80.4 ± 3.6% released). Taken together, this study demonstrates the feasibility of incorporating concentration gradient of diffusible bioactive chemicals in nanofibrous scaffolds via the coaxial electrospinning technique.

Toward Gradient Formation in Microfluidic Devices by using Slanted Ridges

AbstractSome lab‐on‐a‐chip applications require to establish a controlled spatial concentration gradient of (chemical) species, for example for iso‐electrical focusing or to study chemotactic properties of cells. We show that covering a microchannel floor with special grooves or ridges, well‐controlled concentration gradients can be created, depending on the geometrical design of the grooves or ridges. In our case, the pattern consists of ridges that are slanted with respect to the main channel direction. Similar patterns have been applied in the past to achieve mixing by introducing chaotic advection. We present experimental and numerical results that prove the mixing effectiveness of the ridges. In addition, making use of the local mixing capabilities of the ridge patterns, we show, using numerical simulations, how to achieve a concentration gradient across a microfluidic channel. magnified image

Activated T lymphocytes migrate toward the cathode of DC electric fields in microfluidic devices

Immune cell migration is a fundamental process that enables immunosurveillance and immune responses. Understanding the mechanism of immune cell migration is not only of importance to the biology of cells, but also has high relevance to cell trafficking mediated physiological processes and diseases such as embryogenesis, wound healing, autoimmune diseases and cancers. In addition to the well-known chemical concentration gradient based guiding mechanism (i.e. chemotaxis), recent studies have shown that lymphocytes can respond to applied physiologically relevant direct current (DC) electric fields by migrating toward the cathode of the fields (i.e. electrotaxis) in both in vitro and in vivo settings. In the present study, we employed two microfluidic devices allowing controlled application of electric fields inside the microfluidic channel for quantitative studies of lymphocyte electrotaxis in vitro at the single cell level. The first device is fabricated by soft-lithography and the second device is made in glass with integrated on-chip electrodes. Using both devices, we for the first time showed that anti-CD3/CD28 antibodies activated human blood T cells migrate to the cathode of the applied DC electric field. This finding is consistent with previous electrotaxis studies on other lymphocyte subsets suggesting electrotaxis is a novel guiding mechanism for immune cell migration. Furthermore, the characteristics of electrotaxis and chemotaxis of activated T cells in PDMS microfluidic devices are compared.

Screening the Optical Properties of Ag−Au Alloy Gradients Formed by Bipolar Electrodeposition Using Surface Enhanced Raman Spectroscopy

We report the synthesis of Ag-Au alloy gradients on stainless steel substrates using bipolar electrodeposition (BP-ED), a technique based on the existence of a potential gradient at the interface of a bipolar electrode (BPE) and an electrolytic solution. The interfacial potential gradient causes the rates of electrodeposition of Ag and Au to vary along the length of the BPE, leading to the electrodeposition of a chemical concentration gradient. The surface morphology of the electrodeposits was characterized using scanning electron microscopy (SEM), and their chemical composition was determined using energy dispersive X-ray spectroscopy (EDX). Self-assembled monolayers of a Raman-active probe molecule (benzene thiol) were allowed to form on the surface of the alloy gradients, and confocal Raman microscopy was employed to determine the alloy composition that resulted in the maximum surface enhanced Raman scattering (SERS) intensity. An alloy composition of ca. 70% Ag/30% Au was found to be optimum for SERS excited using 514.5 nm radiation, and it is explained on the basis of composition-dependent changes in the local surface plasmon resonance (LSPR) of the electrodeposited Ag-Au alloy.

A Microfluidic Device to Establish Concentration Gradients Using Reagent Density Differences

Microfabrication has become widely utilized to generate controlled microenvironments that establish chemical concentration gradients for a variety of engineering and life science applications. To establish microfluidic flow, the majority of existing devices rely upon additional facilities, equipment, and excessive reagent supplies, which together limit device portability as well as constrain device usage to individuals trained in technological disciplines. The current work presents our laboratory-developed bridged μLane system, which is a stand-alone device that runs via conventional pipette loading and can operate for several days without need of external machinery or additional reagent volumes. The bridged μLane is a two-layer polydimethylsiloxane microfluidic device that is able to establish controlled chemical concentration gradients over time by relying solely upon differences in reagent densities. Fluorescently labeled Dextran was used to validate the design and operation of the bridged μLane by evaluating experimentally measured transport properties within the microsystem in conjunction with numerical simulations and established mathematical transport models. Results demonstrate how the bridged μLane system was used to generate spatial concentration gradients that resulted in an experimentally measured Dextran diffusivity of (0.82 ± 0.01) × 10(-6) cm(2)/s.

Diffusion-Based and Long-Range Concentration Gradients of Multiple Chemicals for Bacterial Chemotaxis Assays

We present a diffusion-driven and long-range concentration gradient generator that uses hydrogel as a porous membrane to prevent convection flows but allow the diffusion of cell signaling molecules for the study of bacterial chemotaxis in a microfluidic device. Using this device, we characterized the critical concentrations associated with the chemotactic responses of cells that initially created a population band and then migrated in bands in the presence of multiconcentration gradients. In addition, this device can be used to study the preferential chemotaxis of bacterial cells toward different carbon sources: glucose, galactose, and mannose were preferred over arabinose and xylose, in this order. This was possible since the device is able to simultaneously produce long-range concentration gradients of different chemicals as well. The method presented in this study is easy to perform and the device is cheap to fabricate, so that we believe that these characteristics not only make this device a very useful tool to study the chemotaxis of various, motile microorganisms but also permit parallel experimentation and reduce the time and effort needed in characterizing bacterial responses to various chemicals.

Influence of Osmotic Suction on the Soil-Water Characteristic Curves of Compacted Expansive Clay

Unsaturated clays are subject to osmotic suction gradients in geoenvironmental engineering applications and it therefore becomes important to understand the effect of these chemical concentration gradients on soil-water characteristic curves (SWCCs). This paper brings out the influence of induced osmotic suction gradient on the wetting SWCCs of compacted clay specimens inundated with sodium chloride solutions/distilled water at vertical stress of 6.25 kPa in oedometer cells. The experimental results illustrate that variations in initial osmotic suction difference induce different magnitudes of osmotic induced consolidation and osmotic consolidation strains thereby impacting the wetting SWCCs and equilibrium water contents of identically compacted clay specimens. Osmotic suction induced by chemical concentration gradients between reservoir salt solution and soil-water can be treated as an equivalent net stress component, ( pπ ) that decreases the swelling strains of unsaturated specimens from reduction in ...

A porous 3D cell culture micro device for cell migration study

Cell migration under chemoattractant is an important biological step in cancer metastasis that causes the spread of malignant tumor cells. Porous polymeric materials are widely used to mimic the extracellular matrix (ECM) environment for applications such as three dimensional (3D) cell culturing and tissue engineering. In this paper we report a novel 3D cell culture device based on porous polymeric material to study cancer migration. We fabricated a porous channel on a polymeric chip using a selective ultrasonic foaming method. We demonstrate that a chemical concentration gradient could be established through the porous channel due to the slow diffusion process. We show that significant cell migration could be observed through the porous channel within 1-2 weeks of cell culturing when metastatic M4A4-GFP breast cancer cells were induced by 20% fetal bovine serum (FBS).We also developed a mathematical model to evaluate the diffusivity and concentration gradient through the fabricated porous structure.

Determination of the transport properties of a blended concrete from its electrical properties measured during a migration test

The Nernst–Planck equation describes ionic movements in saturated porous materials subject to chemical concentration gradients in the pore fluid and applied electric fields. When applied to a macroscopic system the equation supposes that the flux of each ion is independent of every other one. However, owing to the ionic exchange among different or similar species, there are ionic potentials that affect the final flux. These will distort the applied electric field and thus keep the electroneutrality of the sum of all the ionic species involved. The applied potential will fall linearly across the sample but an additional ‘membrane' potential will change with position and time. This paper summarises a theoretical and experimental investigation into the application of the non-linear electric membrane potential to the simulation of the migration of chlorides in concrete. A new electrochemical test has been developed and carried out with different samples of concrete blended with pulverised fuel ash (PFA) and ground granulated blastfurnace slag (GGBS). During the tests the transient current and the electrical membrane potential were measured. A numerical model developed previously using the classical equations, but including changes in the concrete membrane potential, was optimised using an artificial neural network (ANN). Based on the experimental results and the simulations, the intrinsic diffusion coefficients of chloride, hydroxide, sodium and potassium were obtained. Also, the initial hydroxide composition of the pore solution, the porosity, and the chloride binding capacity were determined. The results showed good agreement with the theory and can help to explain the complex phenomena that occur during a concrete migration test.

Microfluidic device for the combinatorial application and maintenance of dynamically imposed diffusional gradients

This article reports a microfluidic device for the generation of stable, steady-state, user-defined concentration profiles for the long-term maintenance of stable diffusion gradients. The microinstrument allows both dynamic temporal and dynamic spatial control over user-defined concentrations and concentration gradients of multiple chemicals. With this device, one can create an in vitro environment capable of approximating the complex in vivo biological condition for cellular studies. In addition, the device has potential application in combinatory drug discovery, electrophoretic applications, ligand binding, etc. 3D computer simulations and analysis of arbitrary concentration profiles are presented along with experimental validation using multiple diffusing species.

Microdevice to capture colon crypts for in vitro studies

There is a need in biological research for tools designed to manipulate the environment surrounding microscopic regions of tissue. In the current work, a device for the oriented capture of an important and under-studied tissue, the colon crypt, has been designed and tested. The objective of this work is to create a BioMEMs device for biological assays of living colonic crypts. The end goal will be to subject the polarized tissue to user-controlled fluidic microenvironments in a manner that recapitulates the in vivo state. Crypt surrogates, polymeric structures of similar dimensions and shape to isolated colon crypts, were used in the initial design and testing of the device. Successful capture of crypt surrogates was accomplished on a simple device composed of an array of micron-scale capture sites that enabled individual structures to be captured with high efficiency (92+/-3%) in an ordered and properly oriented fashion. The device was then evaluated using colon crypts isolated from a murine animal model. The capture efficiency attained using the fixed biologic sample was 37+/-5% due to the increased variability of the colon crypts compared with the surrogate structures, yet 94+/-3% of the captured crypts were properly oriented. A simple approach to plug the remaining capture sites in the array was performed using inert glass beads. Blockage of unfilled capture sites is an important feature to establish a chemical gradient across the arrayed crypts. A chemical concentration gradient (Cluminal/Cbasal>10) was demonstrated across the arrayed crypts for over 8 h. Finally unfixed colon crypts were demonstrated to be effectively captured by the micromesh array and to remain viable on the capture sites at 5 h after mouse sacrifice. The present study demonstrates the feasibility and potential for rationally microengineered technologies to address the specific needs of the biologic researcher.

Correlations in concentrations, xylem and phloem flows, and partitioning of elements and ions in intact plants. A summary and statistical re-evaluation of modelling experiments in Ricinus communis

Within the last two decades, a series of papers have dealt with the effects of nutrition and nutrient deficiency, as well as salt stress, on the long-distance transport and partitioning of nutrients in castor bean. Flows in xylem and phloem were modelled according to an empirically-based modelling technique that permits additional quantification of the uptake and incorporation into plant organs. In the present paper these data were statistically re-evaluated, and new correlations are presented. Numerous relationships between different compartments and transport processes for single elements, but also between elements, were detected. These correlations revealed different selectivities for ions in bulk net transport. Generally, increasing chemical concentration gradients for mineral nutrients from the rhizosphere to the root and from the xylem to leaf tissue were observed, while such gradients decreased from root tissue to the xylem and from leaves to the phloem. These studies showed that, for the partitioning of nutrients within a plant, the correlated interactions of uptake, xylem and phloem flow, as well as loading and unloading of solutes from transport systems, are of central importance. For essential nutrients, tight correlations between uptake, xylem and phloem flow, and the resulting partitioning of elements, were observed, which allows the stating of general models. For non-essential ions like Na(+) or Cl(-), a statistically significant dependence of xylem transport on uptake was not detected. The central role of the phloem for adjusting, but also signalling, of nutrition status is discussed, since strong correlations between leaf nutrient concentrations and those in phloem saps were observed. In addition, negative correlations between phloem sap sugar concentration and net-photosynthesis, growth, and uptake of nutrients were demonstrated. The question remains whether this is only a consequence of an insufficient use of carbohydrates in plants or a ubiquitous signal for stress in plants. In general, high sugar concentrations in phloem saps indicate (nutritional) stress, and high nutrient concentrations in phloem saps indicate nutritional sufficiency of leaf tissues.

Accuracy of direct gradient sensing by cell-surface receptors

Chemotactic cells of eukaryotic organisms are able to accurately sense shallow chemical concentration gradients using cell-surface receptors. This sensing ability is remarkable as cells must be able to spatially resolve small fractional differences in the numbers of particles randomly arriving at cell-surface receptors by diffusion. An additional challenge and source of uncertainty is that particles, once bound and released, may rebind the same or a different receptor, which adds to noise without providing any new information about the environment. We recently derived the fundamental physical limits of gradient sensing using a simple spherical-cell model, but not including explicit particle-receptor kinetics. Here, we use a method based on the fluctuation-dissipation theorem (FDT) to calculate the accuracy of gradient sensing by realistic receptors. We derive analytical results for two receptors, as well as two coaxial rings of receptors, e.g. one at each cell pole. For realistic receptors, we find that particle rebinding lowers the accuracy of gradient sensing, in line with our previous results.

An agarose-based microfluidic platform with a gradient buffer for 3D chemotaxis studies

The current state-of-art in 3D microfluidic chemotaxis device (microFCD) is limited by the inherent coupling of the fluid flow and chemical concentration gradients. Here, we present an agarose-based 3D microFCD that decouples these two important parameters, in that the flow control channels are separated from the cell compartment by an agarose gel wall. This decoupling is enabled by the transport property of the agarose gel, which-in contrast to the conventional microfabrication material such as polydimethylsiloxane (PDMS)-provides an adequate physical barrier for convective fluid flow while at the same time readily allowing protein diffusion. We demonstrate that in this device, a gradient can be pre-established in an agarose layer above the cell compartment (a gradient buffer) before adding the 3D cell-containing matrix, and the dextran (10 kDa) concentration gradients can be re-established within 10 min across the cell-containing matrix and remain stable indefinitely. We successfully quantified the chemotactic response of murine dendritic cells to a gradient of CCL19, an 8.8 kDa lymphoid chemokine, within a type I collagen matrix. This model system is easy to set up, highly reproducible, and will benefit research on 3D chemoinvasion studies, for example with cancer cells or immune cells. Because of its gradient buffering capacity, it is particularly suitable for studying rapidly migrating cells like mature dendritic cells and neutrophils.

Eddy viscosity and turbulent Schmidt number by kink-type instabilities of toroidal magnetic fields

The potential of the nonaxisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory the neutral-stability maps for m=1 are computed. Rigid rotation must be subAlfvenic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvenic rotation exists. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm=1 and becomes much weaker for Pm unequal 1. The effective angular momentum transport by the instability is directed outwards(inwards) for subrotation(superrotation). The resulting magnetic-induced eddy viscosities exceed the microscopic values by factors of 10-100. This is only true for superAlfvenic flows; in the strong-field limit the values remain much smaller. The same instability also quenches concentration gradients of chemicals by its nonmagnetic fluctuations. The corresponding diffusion coefficient remains always smaller than the magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the ratio of the effective viscosity and the diffusion coefficient. The magnetic instability transports much more angular momentum than that it mixes chemicals.

Logarithmic Sensing in Escherichia coli Bacterial Chemotaxis

We studied the response of swimming Escherichia coli ( E. coli) bacteria in a comprehensive set of well-controlled chemical concentration gradients using a newly developed microfluidic device and cell tracking imaging technique. In parallel, we carried out a multi-scale theoretical modeling of bacterial chemotaxis taking into account the relevant internal signaling pathway dynamics, and predicted bacterial chemotactic responses at the cellular level. By measuring the E. coli cell density profiles across the microfluidic channel at various spatial gradients of ligand concentration grad[ L] and the average ligand concentration [ L ] ¯ near the peak chemotactic response region, we demonstrated unambiguously in both experiments and model simulation that the mean chemotactic drift velocity of E. coli cells increased monotonically with grad [ L]/ [ L ] ¯ or ∼ grad(log[ L])—that is E. coli cells sense the spatial gradient of the logarithmic ligand concentration. The exact range of the log-sensing regime was determined. The agreements between the experiments and the multi-scale model simulation verify the validity of the theoretical model, and revealed that the key microscopic mechanism for logarithmic sensing in bacterial chemotaxis is the adaptation kinetics, in contrast to explanations based directly on ligand occupancy.

Clay membrane testing using a flexible-wall cell under closed-system boundary conditions

Membrane behavior represents the ability of porous media to restrict the migration of solutes, leading to the existence of chemico-osmosis, or the flow of liquid in response to a chemical concentration gradient. Membrane behavior is an important consideration with respect to clay soils with small pores and interactive electric diffuse double layers associated with individual particles, such as bentonite. The results of recent studies indicate the existence of membrane behavior in bentonite-based hydraulic barriers used in waste containment applications. Thus, measurement of the existence and magnitude of membrane behavior in such clay soils is becoming increasingly important. In this regard, the development and evaluation of a flexible-wall cell used to measure the membrane behavior of clay soils under closed-system boundary conditions is described. The advantages of a flexible-wall cell include complete control over the state of stress existing within the test specimen and the ability to back-pressure saturate and consolidate the specimen prior to membrane testing. Use of the developed flexible-wall cell is illustrated via tests conducted to measure the membrane behavior of a geosynthetic clay liner (GCL), a manufactured hydraulic barrier containing sodium bentonite. The results indicate that the membrane efficiencies of duplicate specimens of the GCL measured using the flexible-wall cell are both reproducible and similar to, but somewhat lower than, those previously reported for the same GCL using a rigid-wall cell under the same closed-system boundary conditions.