Antonio Ramos

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• Professor
• Professor (Full) at University of Seville

Electrophoresis describes the motion of charged particles suspended in electrolytes when subjected to an external electric field. Previous experiments have shown that particles undergoing electrophoresis are repelled from nearby channel walls, contrary to the standard description of electrophoresis that predicts no hydrodynamic repulsion. Dielectro...

Electric fields are commonly used for manipulating particles and liquids in microfluidic systems. In this work, we report stationary electro-osmotic flow vortices around dielectric micropillars induced by ac electric fields in electrolytes. The flow characteristics are theoretically predicted based on the well-known phenomena of surface conductance...

We experimentally demonstrate quadrupolar electro-osmotic flows around charged dielectric microspheres immersed in an electrolyte when subjected to an alternating current electric field. We present an electrokinetic model that predicts the flow characteristics based on the phenomena of surface conductance and polarization of the electrolyte concent...

Trapping and separation of particles near microfluidic constrictions are efficiently achieved using electric fields. The phenomenon has been attributed to the dielectrophoretic (DEP) force arising from the nonhomogeneous electric field within the constrictions, which predicts particle trapping at or away from the constriction tip. In this work, we...

We analyze, both analytically and numerically, the electrokinetic behavior of highly charged dielectric microparticles suspended in aqueous electrolytes. Specifically, we consider small particles subjected to nonuniform AC electric fields and describe their motion as resulting from the interplay between electrical forces—dielectrophoresis (DEP)—and...

While previous studies indicated the mobility reversal of an electrically-powered metallo-dielectric Janus particle (JP) with increasing frequency, here we report an intriguing second mobility reversal observed in optoelectronically-driven JPs. In contrast to the commonly used setup with parallel ITO-coated glass substrates to induce a uniform elec...

The use of AC electricThe use of AC electric [...]

Continuous particle focusing by using microfluidics is an effective method for separating particles, cells, or droplets for analytical purposes. Previously, it was shown that an alternating current across rectangular microchannels with slightly deformed side walls results in vortex flow patterns caused by alternating current electroosmosis (AC-EOF)...

Concentration-Polarization Electroosmosis (CPEO) refers to steady-state electroosmotic flows around charged dielectric micro-particles induced by low-frequency AC electric fields. Recently, these flows were shown to cause repulsion of colloidal particles from...

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface prop...

The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these applications are characterized by a finite amount of liquid in an impermeable domain....

Traveling-wave electrophoresis (TWE) is a method for transporting charged colloidal particles used in many microfluidic techniques for particle manipulation and fractionation. This method exploits the traveling-wave components of the electric field generated by an array of electrodes subjected to ac voltages with a phase delay between neighboring e...

Deterministic Lateral Displacement (DLD) exploits periodic arrays of pillars inside microfluidic channels for high-precision sorting of micro- and nano-particles. Previously we demonstrated how DLD separation can be significantly improved by the addition of AC electrokinetic forces, increasing the tunability of the technique and expanding the range...

We describe a user-friendly, open source software for single-particle detection/counting in a continuous-flow. The tool automatically processes video images of particles, including pre-conditioning, followed by size-based discrimination for independent detection of fluorescent and non-fluorescent particles of different sizes. This is done by intera...

We experimentally study the repulsion of charged microscopic particles with the channel walls during electrophoresis in microfluidic devices. For low frequencies of the electric fields (< 10 kHz), this repulsion is mainly due to the hydrodynamic interaction caused by the flow vortices that arise from the slip velocity induced by the electric field...

We consider the scattering of metal colloids in aqueous solutions by an insulating circular post under the action of an AC electric field. We analyze the effects on the particle of several forces of electrical origin: the repulsion between the induced dipole of the particle and its image dipole in the post, the hydrodynamic interaction with the pos...

Existing solutions for film dynamics fail when considering the most standard and straightforward implementation, a pinned film in an impermeable domain, such as used in liquid actuators or adaptive optical elements. We present a solution methodology to the linearized non-self-adjoint system that arises from this problem and validate it experimental...

Hypothesis The interaction of active particles with walls can explain discrepancies between experiments and theory derived for particles in the bulk. For an electric field driven metallodielectric Janus particle (JP) adjacent to an electrode, interaction between the asymmetric particle and the partially screened electrode yields a net electrostatic...

We present a theoretical model and experimental demonstration of thin liquid film deformations due to a dielectric force distribution established by surface electrodes. We model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the liquid–air interface through Maxwell stresses. By coupling thi...

We describe an improved method for determining the electroosmotic mobility and zeta potential of surfaces based on a current‐monitoring method. This technique eliminates the requirement for measurements of channel dimensions and sample conductivities, leading to a simple high precision measurement. The zeta potential of PDMS is measured for native...

Electric fields are commonly used to trap and separate micro- and nanoparticles near channel constrictions in microfluidic devices. The trapping mechanism is attributed to the electrical forces arising from the nonhomogeneous electric field caused by the constrictions, and the phenomenon is known as insulator-based-dielectrophoresis (iDEP). In this...

We present a theoretical model and experimental demonstration for deformations of a thin liquid layer due to an electric field established by surface electrodes. We model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the interface through Maxwell stresses. By coupling this force with the Y...

Advances in the miniaturization of microelectromechanical systems (MEMS) [...]

In contrast to the commonly used spherical Janus particles, here we use engineered Janus particles that are fabricated by means of the photolithography technique for precise control over their geometry and coated regions. Specifically, we study a "lollipop"-shaped complex particle, the head of which is coated with gold while its tail is left bare....

In contrast to the commonly used spherical Janus particles, here we used engineered Janus particles that are fabricated using photolithography technique for precise control over their geometry and coated regions. Specifically, we studied a lollipop-shaped complex particle where its head is coated with gold while its tail is left bare. Due to their...

Deterministic Lateral Displacement (DLD) is a microfluidic technique where arrays of micropillars within a microchannel deflect particles leading to size-based segregation. We recently demonstrated that applying AC electric fields orthogonal to the fluid flow increases the separation capabilities of these devices with a deflection angle that depend...

We study theoretically and numerically the electrokinetic behavior of metal microparticles immersed in aqueous electrolytes. We consider small particles subjected to non-homogeneous ac electric fields and we describe their motion as arising from the combination of electrical forces (dielectrophoresis) and the electroosmotic flows on the particle su...

We study experimentally the electrorotation (ROT) of semiconducting microspheres. ZnO microspheres obtained by a hydrothermal synthesis method are dispersed in KCl aqueous solutions and subjected to rotating electric fields. Two ROT peaks are found in experiments: a counterfield peak and a cofield peak at somewhat higher frequencies. These observat...

This paper describes the behaviour of particles in a Deterministic Lateral Displacement (DLD) separation device with DC and AC electric fields applied orthogonal to the fluid flow. As a proof of principle, we demonstrate tunable micro- and nano- particle separation and fractionation depending on both particle size and zeta potential. DLD is a micro...

The use of AC electric fields for manipulating and/or characterizing liquids and small particles in suspension is well-known [...]

We describe a novel particle separation technique that combines deterministic lateral displacement (DLD) with orthogonal electrokinetic forces. DLD is a microfluidic technique for continuous flow particle separation based on size. We describe new tunable devices that use a combination of AC electric fields with DLD to separate particles below the c...

We study theoretically the rotation induced on an uncharged metal nanocylinder immersed in an electrolyte by AC electric fields. We consider the rotation of the cylinder when subjected to a rotating electric field (electrorotation) and the orientation of the cylinder in an AC field with constant direction (electro-orientation). The cylinder rotatio...

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combinat...

We report the production of bicomponent Janus filaments of miscible aqueous fluids in a microfluidic electro-flow-focusing device under the action of an AC electric field. The production of liquid filaments can lead to the generation of microfibers by adding a subsequent process of polymerization. Janus microfibers are of paramount importance in bi...

In this work we analyse the orientation of silver nanowires immersed in aqueous solutions, under the effect of alternating electric fields in a broad frequency range, covering from a few Hz to several MHz. The degree of orientation is experimentally determined by electro-optical techniques, which present the advantage of measuring multiple particle...

In this work, we review the physics of the liquid ejection by the application of electric fields, paying special attention to the steady cone-jet mode of electrospray. We aim to provide a comprehensive view on the role of electrohydrodynamics effects, and how the full electrokinetic equations can be reduced or simplified into the Taylor-Melcher lea...

Net fluid flow of soap films induced by (ac or dc) electric fields in asymmetric frames is presented. Previous experiments of controllable soap film flow required the simultaneous use of an electrical current passing through the film and an external electric field or the use of nonuniform ac electric fields. Here a single voltage difference generat...

We report the production of droplet groups with a controlled number of drops in a microfluidic electro-flow-focusing device under the action of an AC electric field. This regime appears for moderate voltages (500–700 V peak-to-peak) and signal frequencies between 25 and 100 Hz, much smaller than the droplet production rate (\({\sim }\,{500}\) Hz)....

A number of experimental works have shown electric-field manipulation of nanowires dispersed in liquids. We demonstrate from first principles that the electrical response of semiconductor nanowires in liquids must be described by considering, at least, two mechanisms for interfacial polarization: the classical Maxwell-Wagner interfacial polarizatio...

Fluid flow of suspended liquid films induced by non-uniform alternating electric fields has been reported. The electric fields were generated by two rod-like electrodes perpendicular to the fluid surface. The observed fluid flow was explained qualitatively by considering a charge induction mechanism, where the electric field actuates on the charge...

Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we cons...

This viewpoint relates to an article by A Castellanos et al (2003 J. Phys. D: Appl. Phys. 36, 2584) and was published as part of a series of viewpoints celebrating 50 of the most inflential papers published in the Journal of Physics series, which is celebrating its 50th anniversary.

This paper reviews both theory and experimental observation of the AC electrokinetic properties of conducting microparticles suspended in an aqueous electrolyte. Applied AC electric fields interact with the induced charge in the electrical double layer at the metal particle–electrolyte interface. In general, particle motion is governed by both the...

We use a microfluidic flow-focusing device with integrated electrodes for controlling the production of water-in-oil drops. In a previous work, we reported that very long jets can be formed upon application of AC fields. We now study in detail the appearance of the long jets as a function of the electrical parameters, i.e., water conductivity, sign...

We theoretically study the rotation induced on a metal sphere immersed in an electrolyte and subjected to a rotating electric field. The rotation arises from the interaction of the field with the electric charges induced at the metal-electrolyte interface, i.e., the induced electrical double layer (EDL). Particle rotation is due to the torque on th...

Electroactuation of liquid–liquid interfaces offers promising methods to actively modulate droplet formation in droplet-based microfluidic systems. Here, flow-focusing junctions are coupled to electrodes to control droplet production in the well-known jetting regime. In this regime, a convective instability develops leading to droplet formation at...

The rotation of suspended liquid films induced by electric fields has been reported. The liquid film rotates when there is an electric current passing through the suspended film and simultaneously there is an external electric field which is perpendicular to the electric current. In this study, we propose an explanation of the phenomenon based on t...

The rotation induced by AC electric fields on metal nanowires has been studied theoretically and experimentally. In the experiments, the nanowires rotate close to the bottom of the device. The present work studies the effects of the wall on the Electrorotation and Electro-orientation of a metal nanowire numerically. The induced electrical rotation...

We describe the reversible assembly of an aqueous suspension of metal nanowires into two different 2-dimensional stable configurations. The assembly is induced by an AC electric field of magnitude around 10 kV/m. It is known that single metal nanowires orientate parallel to the electric field for all values of applied frequency, according to two di...

Fluid flows generated on soap films by non-uniform alternating electric fields are studied. Two parallel metal rods subjected to an AC voltage are placed perpendicular to the soap film, which is anchored in a dielectric frame. The fluid flow is generated by electrohydrodynamic induction. At very low signal frequencies there is induced surface charg...

The rotational diffusion of electrically polarized metal nanowires suspended in an electrolyte is studied. The alignment of a Brownian nanowire in an ac field with a given direction is not complete due to thermal (fluctuating) torques. The orientation distribution allows us to examine the electrokinetic torques acting on the nanowire for smaller vo...

The physical mechanisms responsible for the electrical orientation and electrical rotation of metal nanowires suspended in an electrolyte as a function of frequency of the applied ac electric field are examined theoretically and experimentally. The alignment of a nanowire in an ac field with a fixed direction is called electro-orientation. The indu...

We describe the physical mechanism responsible for the rotation of Brownian metal nanowires suspended in an electrolyte exposed to a rotating electric field. The electric field interacts with the induced charge in the electrical double layer at the metal-electrolyte interface, causing rotation due to the torque on the induced dipole and to the indu...

Electrorotation (ROT) data for solid titanium micrometer-sized spheres in an electrolyte are presented for three different ionic conductivities, over the frequency range of 10 Hz to 100 kHz. The direction of rotation was found to be opposite to the direction of rotation of the electric field vector (counter-field electrorotation), with a single rot...

Electric fields induce forces at the interface between liquids with different electrical properties (conductivity and/or permittivity). We explore how to use these forces for the manipulation of two coflowing streams of electrolyte in a microchannel. A microelectrode array is fabricated at the bottom of the channel and one of the two liquids is lab...

We present dielectrophoresis (DEP) and electrorotation (ROT) measurements of gold-coated polystyrene microspheres as a function of frequency and for several electrolyte conductivities. Particle rotation was counterfield with a maximum rotation rate observed at a single characteristic frequency. Negative DEP was observed for frequencies lower than t...

This paper presents a numerical study of DC-biased AC-electrokinetic (DC-biased ACEK) flow over a pair of symmetrical electrodes. The flow mechanism is based on a transverse conductivity gradient created through incipient Faradaic reactions occurring at the electrodes when a DC-bias is applied. The DC biased AC electric field acting on this gradien...

In this paper configurable AC electroosmotic array devices are investigated for the purpose of combined pumping and mixing in microcapillaries. The method relies on grouping similar electrodes together in terms of applied voltage, in order to create configurable asymmetries in periodic electrode arrays. Novel designs and excitation patterns are exa...

This paper studies the principles of fluid flow manipulation based on DC-biased AC-electrokinetics. This method makes use of planar parallel electrodes in a microfluidic channel in contact with an electrolyte solution, with a DC biased AC electrical signal applied to the electrode pair. Due to the application of DC bias, incipient Faradaic electrol...

We present experimental and numerical investigations of water flow in a microsystem induced by microwave electric fields. Microwave dielectric heating induces gradients of temperature which produce spatial variations in mass density and dielectric permittivity that lead to buoyancy and dielectric forces in the liquid, respectively. The experimental...

The electrical manipulation of fluids in microsystems has many existing and potential applications. This chapter reviews five different ways of electrohydrodynamic actuation in microdevices. First, we describe the basic equations of Electrohydrodynamics in the microscale, providing some basic concepts of electrical conduction in liquids. We also de...

Conical points of a leaky dielectric drop surrounded by a dielectric gas in an external ac electric field are investigated. A novel class of steady conical tips depending on the permittivity ratio and applied signal frequency is presented. It is found that conical solutions with very small angles are possible (angles much smaller than the classical...

Electric fields induce forces at the interface between liquids with different electrical properties (conductivity and/or permittivity). We explore how to use these forces for manipulating two coflowing streams of liquids in a microchannel. A microelectrode array is fabricated at the bottom of the channel and one of the two liquids is labelled with...

The physical principles behind the electrohydrodynamic (EHD) actuation in microsystems is presented by reviewing five different EHD micropumps. These are classified into two groups: micropumps that exert electric forces in the liquid bulk and micropumps that exert forces in the diffuse double layer. This review of five EHD micropumps allows us to a...

In this paper the Dielectrophoretic trapping of nanoparticles in parallel electrode arrays is investigated. The numerical simulations presented take into account the steric effect of the particle collection yielding more realistic results than the non-steric model. Furthermore, the effect of the AC electroosmotic motion of the electrolyte is taken...

Microelectrodes subjected to AC potentials are usually employed to induce electrolyte flow, commonly known as AC electroosmotic (ACEO) flows. In this work, we apply novel theoretical results for analysing the influence of Faradaic reactions on these flows. Specifically, we choose to analyse the electrokinetic flow induced by a pair of coplanar symm...

To explore control method of multiphase fluid path, experiments of two-phase fluid path driving were carried out, during which when applying AC electric signal on the electrodes subjected on the microchannel, the fluid with higher conductivity would occupy the microchannel, and when the signals disappeared, the fluid path restored. A 2D analytical...

Electrorotation (ER) experiments of gold-coated micrometer-sized spheres suspended in an electrolyte are presented for three different ionic conductivities over the frequency range of 100 Hz to 40 MHz. The direction of rotation was observed to be counter-field (opposite to the rotating field vector) with a single rotation peak. The maximum in rotat...

Among the most promising techniques to handle small objects at the micrometer scale are those that employ electrical forces, which have the advantages of voltage-based control and dominance over other forces. The book provides a state-of-the-art knowledge on both theoretical and applied aspects of the electrical manipulation of colloidal particles...

In this paper the effect of initial particle concentration on the dielectrophoretic trapping of particles is investigated. The numerical simulations incorporate the effects of the suspension motion due to the presence of the electric field and the steric particle effect. It is found that the initial concentration has a significant impact on both th...

In this paper the Dielectrophoretic trapping of micro-and nano-particles using a parallel co-planar electrode array is examined. More specifically, the effect of the sharpness of the electrode edges and the existence of surface imperfections such as holes or scratches on the electrode surface is investigated. This is an important issue as it can pr...

In this work, we extend previous analyses of ac electro-osmosis to account for the combined action of two experimentally relevant effects: (i) Faradaic currents from electrochemical reactions at the electrodes and (ii) differences in ion mobilities of the electrolyte. In previous works, the ac electro-osmotic motion has been analyzed theoretically...

Mixing within sessile drops can be enhanced by generating internal flow patterns using ac electrowetting. While for low ac frequencies, the flow patterns have been attributed to oscillations of the drop surface, we provide here the driving mechanism of the hitherto unexplained high-frequency flows. We show that: (1) the electric field in the liquid...

AC electro-osmotic (ACEO) pumping is experimentally demonstrated on a symmetric gold electrode array. Using asymmetric connection of electrodes to the applied AC voltage, spatial asymmetry along the array is created, which produces unidirectional flow of electrolyte. An aqueous solution of 100μM KCl is selected as the pumping fluid. The liquid velo...

Dielectrophoresis (DEP) has a high potential in the manipulation of low concentration microparticles in microsystem, which is an urgent project. The complex DEP expression was induced based on the basic DEP theory. The main factor of the conventional DEP force and the traveling wave DEP force was analyzed and 2D analytical model with star electrode...

The control and handling of fluids is central to many applications of the lab-on-chip. This paper analyzes the basic theory of manipulating different electrolytes and finds the two-dimensional model. Coulomb force and dielectric force belonging to the body force of different electrolytes in the microchannel were analyzed. The force criterion at the...

Net flow of electrolyte induced by Pt microelectrodes subjected to traveling-wave potentials is studied experimentally. Three different concentrations of KCl in water are considered in order to determine the effect of the electrolyte conductivity on the induced velocity. This work intends to generate more experimental data that can be compared to t...

Fluid manipulation is of capital importance for the lab-on-a-chip (LOC) technology. We analyse numerically the electrical manipulation of an electrolyte with a steep gradient in saline concentration by a microelectrode array subjected to ac voltages. The results show that the fluid with higher conductivity tends to replace the liquid with lower con...

AC electric fields are of increasing importance for the generation of fluid flows in microsystems. We analyse numerically the use of AC electric fields at microwave frequencies for electro-thermal actuation of water in microdevices. Water is heated because of its significant dielectric loss at microwave frequencies. Buoyancy and dielectric forces a...

To explore Traveling Wave Electroosmotic (TWEO) pumping microflow, a TWEO pumping model is established in a closed microchannel, and simulation and experiments are presented. Based on the TWEO driving mechanism, the mathematic models of an electric field and a flow field in the closed microchannel are established respectively to solve the electric...

The low concentration of microparticles collected in micro-electromechanical systems (MEMS) was studied. It was found in experiments that when applying low voltages and low frequencies on symmetrical electrodes, microparticles could be collected in a fixed area. Based on AC electric field, the authors established a 2D model of the symmetrical elect...

Pumping of electrolytes using ac electric fields from arrays of microelectrodes is a subject of current research. The behavior of fluids at low signal amplitudes (<2-3 V(pp)) is in qualitative agreement with the prediction of the ac electroosmosis theory. At higher voltages, this theory cannot account for the experimental observations. In some case...

Alternating current electric fields are of increasing importance for the development of microfluidic pumps. We report how microwave fields can induce water flow in microsystems, irrespective of saline concentration. A drop of water is placed on two parallel coplanar microelectrodes that are energized by a microwave generator. Fluid flow is observed...

AC electric fields are of increasing importance for the generation of fluid flows in microsystems. We analyse numerically the use of AC electric fields at microwave frequencies for electro-thermal actuation of water in microdevices. Water is heated because of its significant dielectric loss at microwave frequencies. Buoyancy and dielectric forces a...

Fluid manipulation is very important in any lab-on-a-chip system. This paper analyses phenomena which use the alternating current (AC) electric field to deflect and manipulate coflowing streams of two different electrolytes (with conductivity gradient) within a microfluidic channel. The basic theory of the electrohydrodynamics and simulation of the...

In this paper the concept of trapping biological nanoparticles, by utilizing Dielectrophoresis (DEP), is investigated in a system of parallel electrode arrays. The method is analyzed using a Smoluchowski equation that describes the time evolution of the concentration of the particles. A modification is introduced in the Smoluchowski equation in ord...

Using geometry asymmetry, ac electroosmosis (AC EO) experiments are presented on a traveling wave electroosmosis (TW EO) device. To compare AC EO and TWEO, 1.5 mS/m KCl electrolysis is selected as pumping solution. AC EO and TW EO flow velocities versus horizontal height were measured, which showed that the flow was generated at the electrodes. The...

Net fluid flow of electrolytes driven on an array of microelectrodes subjected to a travelling-wave potential is presented. Two sizes of platinum microelectrodes have been studied. In both arrays, at low voltages the liquid flows according to the prediction given by ac electroosmotic theory. At voltages above a threshold the fluid flow is reversed....

The interaction between ac electric fields and the induced charge in the double layer formed on top of electrodes generates steady motion of aqueous solutions. This phenomenon is termed ac electro-osmosis. Unidirectional fluid motion is obtained when the electrolyte is placed on top of an array of microelectrodes subjected to a travelling-wave pote...

Dielectrophoresis (DEP) is introduced as a force for the manipulation of Trophoblast Stem cells (TSc). TSc constitute one of the three fundamental stem cell types derived from the pre-implantation mammalian embryo, and can differentiate into all trophoblast cell types of the placenta. Use of these cells in research is expected to significantly cont...

Arrays of microelectrodes for pumping electrolytes in microchannels are currently under research. In this letter we demonstrate theoretically an enhancement in the performance of arrays of microelectrodes subjected to travelling wave potentials. Net fluid velocity can increase up to 2.7 times when the electrodes are raised above the channel bottom,...

An array of microelectrodes covered in an electrolyte and energized by a traveling-wave potential produces net movement of the fluid. Arrays of platinum microelectrodes of two different characteristic sizes have been studied. For both sizes of arrays, at low voltages (<2 V pp) the electrolyte flow is in qualitative agreement with the linear theory...

Fluid flow generated by ac signals in a point-plane microsytem is studied. KCl aqueous solutions are used and fluid flow is observed for frequencies ranging from 100 Hz up to 1 MHz or 20 MHz depending on the electrolyte conductivity. Possible mechanisms for the explanation of the observed fluid flow are exposed.

We analyze the AC electro-osmotic motion of a 1:1 aqueous solution, taking into account the difference in mobilities and diffusion coefficients between positive and negative ions. This model serves to understand the behavior of common systems as a solution of NaCl in water. We pay special attention to two cases. First, the case of slightly differen...