Directional drying of a colloidal dispersion: quantitative description with water potential measurements using water clusters in a poly(dimethylsiloxane) microfluidic chip.

We have developed a poly(dimethylsiloxane) (PDMS) microfluidic chip to study the directional drying of a colloidal dispersion confined in a channel. Our measurements on a dispersion of silica nanoparticles once again revealed the phenomenology commonly observed for such systems: the formation of a porous solid with linear growth in the channel at short times, slowing down at longer times as the evaporation rate decreases. The growth of the solid is also accompanied by mechanical stresses that are released by the delamination of the solid from the channel walls and the formation of cracks. In addition to these observations, we report original measurements using hydrophilic filler in the PDMS formulation used (Sylgard-184). When the PDMS matrix is in contact with water, water molecules pool around these hydrophilic sites, resulting in the formation of microscopic water clusters whose size depends on the water potential ψ. In our work, we have used these water clusters to estimate the water potential profile in the channel as the porous solid grows. Using a transport model that also takes into account solid delamination in the channel, we then linked these water potential measurements to the hydraulic permeability of the porous solid. These measurements finally enabled us to show that the slowdown in the evaporation rate is due to the invasion of the porous solid by air/water nanomenisci at a critical capillary pressure ψcap.

Microfluidic Evaporation, Pervaporation, and Osmosis: From Passive Pumping to Solute Concentration.

Evaporation, pervaporation, and forward osmosis are processes leading to a mass transfer of solvent across an interface: gas/liquid for evaporation and solid/liquid (membrane) for pervaporation and osmosis. This Review provides comprehensive insight into the use of these processes at the microfluidic scales for applications ranging from passive pumping to the screening of phase diagrams and micromaterials engineering. Indeed, for a fixed interface relative to the microfluidic chip, these processes passively induce flows driven only by gradients of chemical potential. As a consequence, these passive-transport phenomena lead to an accumulation of solutes that cannot cross the interface and thus concentrate solutions in the microfluidic chip up to high concentration regimes, possibly up to solidification. The purpose of this Review is to provide a unified description of these processes and associated microfluidic applications to highlight the differences and similarities between these three passive-transport phenomena.

Confined directional drying of a colloidal dispersion: kinetic modeling.

We derive a model to describe the dynamics of confined directional drying of a colloidal dispersion. In such experiments, a dispersion of rigid colloids is confined in a capillary tube or a Hele-Shaw cell. Solvent evaporation from the open end accumulates the particles at the tip up to the formation of a porous packing that invades the cell at a rate . Our model based on a classical description of fluid mechanics and capillary phenomena, predicts different regimes for the growth of the consolidated packing, l versus t. At early times, the evaporation rate is constant and the growth is linear, l ∝ t. At longer times, the evaporation rate decreases and the consolidated packing grows as . This slowdown is either related to the recession of the drying interface within the packing thus adding a resistance to evaporation (capillary-limited regime), or to the Kelvin effect which decreases the partial pressure of water at the drying interface (flow-limited regime). We illustrate these results with numerical relations describing hard spheres, showing that these regimes are a priori experimentally observable. Beyond this description of the confined directional drying of colloidal dispersions, our results also highlight the importance of relative humidity control in such experiments.

Collective diffusion coefficient of a charged colloidal dispersion: interferometric measurements in a drying drop.

In the present work, we use Mach-Zehnder interferometry to thoroughly investigate the drying dynamics of a 2D confined drop of a charged colloidal dispersion. This technique makes it possible to measure the colloid concentration field during the drying of the drop at a high accuracy (about 0.5%) and with a high temporal and spatial resolution (about 1 frame per s and 5 µm per pixel). These features allow us to probe mass transport of the charged dispersion in this out-of-equilibrium situation. In particular, our experiments provide the evidence that mass transport within the drop can be described by a purely diffusive process for some range of parameters for which the buoyancy-driven convection is negligible. We are then able to extract from these experiments the collective diffusion coefficient of the dispersion D(φ) over a wide concentration range φ = 0.24-0.5, i.e. from the liquid dispersed state to the solid glass regime, with a high accuracy. The measured values of D(φ) ≃ 5-12D0 are significantly larger than the simple estimate D0 given by the Stokes-Einstein relation, thus highlighting the important role played by the colloidal interactions in such dispersions.

Drying-induced stresses before solidification in colloidal dispersions: in situ measurements.

We first report an original setup that enables continuous measurements of stresses induced by the drying of confined drops of complex fluids. This setup is mainly based on a precision scale working with an electromagnetic force compensation technique that provides accurate measurements of forces, while allowing simultaneously controlled evaporation rates, in situ microscopic observations, and thus quantitative estimates of normal stresses. We then performed an extensive study of the drying of a charged colloidal dispersion using this setup. Stress measurements clearly show the emergence of large tensile stresses during drying, well-before the solidification stage evidenced by the invasion of the porous colloidal material by air. Combined measurements of solid deformation and concentration profiles (particle tracking, Raman micro-spectroscopy) help us to demonstrate that these stresses are due to the formation of a solid at a low volume fraction, which further undergoes drying-induced shear deformations up to the colloid close-packing, as also supported by large deformation poroelastic modeling. Above all, our results highlight the importance of repulsive colloidal interactions in the build-up of mechanical stresses during drying.

Role of Vapor Mass Transfer in Flow Coating of Colloidal Dispersions in the Evaporative Regime.

In flow-coating processes at low substrate velocity, solvent evaporation occurs during the film withdrawal and the coating process directly yields a dry deposit. In this regime, often referred to as the evaporative regime, several works performed on blade-coating-like configurations have reported a deposit thickness hd proportional to the inverse of the substrate velocity V. Such a scaling can be easily derived from simple mass conservation laws, assuming that evaporation occurs on a constant distance, referred to as the evaporation length, noted Lev in the present paper and of the order of the meniscus size. However, the case of colloidal dispersions deserves further attention. Indeed, the coating flow leads to a wet film of densely packed colloids before the formation of the dry deposit. This specific feature is related to the porous nature of the dry deposit, which can thus remain wet when capillary forces are strong enough to prevent the receding of the solvent through the pores of the film (the so-called pore-emptying). The length of this wet film may possibly be much larger than the meniscus size, therefore modifying the solvent evaporation rate, as well as the scaling hd ∼ 1/V. This result was suggested recently by different groups using basic modeling and assuming for simplicity a uniform evaporation rate over the wet film. In this article, we go a step further and investigate the effect of multidimensional vapor mass transfer in the gas phase on Lev and hd in the specific case of colloidal dispersions. Using simplified models, we first provide analytical expressions in asymptotic cases corresponding to 1D or 2D diffusive vapor transport. These theoretical investigations then led us to show that Lev is independent of the evaporation rate amplitude, and roughly independent of its spatial distribution. Conversely, hd strongly depends on the characteristics of vapor mass transfer in the gas phase, and different scaling laws are obtained for the 1D or the 2D case. These theoretical findings are finally tested by comparison with experimental results supporting our theoretical simplified approach.

Modeling Flow Coating of Colloidal Dispersions in the Evaporative Regime: Prediction of Deposit Thickness.

We investigate flow coating processes, i.e., the formation of dry coatings starting from dilute complex fluids confined between a static blade and a moving substrate. In particular, we focus on the evaporative regime encountered at low substrate velocity, at which the coating flow is driven mainly by solvent evaporation in the liquid meniscus. In this regime, general arguments based on mass conservation show that the thickness of the dry film decreases as the substrate velocity increases, unlike the behavior in the well-known Landau-Levich regime. This work focuses on colloidal dispersions, which deserve special attention. Indeed, flow coating is expected to draw first a solvent-saturated film of densely packed colloids, which further dries fully when air invades the pores of the solid film. We first develop a model based on the transport equations for binary mixtures, which can describe this phenomenon continuously, using appropriate boundary conditions and a criterion to take into account pore-emptying in the colloidal film. Extensive numerical simulations of the model then demonstrate two regimes for the deposit thickness as a function of the process parameters (substrate velocity, evaporation rate, bulk concentration, and particle size). We finally derive an analytical model based on simplified transport equations that can reproduce the output of our numerical simulations very well. This model can predict analytically the two observed asymptotic regimes and therefore unifies the models recently reported in the literature.

Investigation of the dynamics of growth of polymer materials obtained by combined pervaporation and micro-moulding.

We report an extensive study of the concentration process of aqueous polymer solutions confined within microfluidic channels, owing to the pervaporation of water through the matrix of the chip. Concentration of polymer continuously increases up to the formation of a dense material which eventually invades the channel. This technology can be used to fabricate micro-composites of different shapes starting from dilute inks. We use both theory and screening experiments to show that the dynamics of growth can be predicted by simple conservation equations. More precisely, we establish a quantitative prediction of the growth dynamics taking into account deformations of the soft channels of the moulds, and the solvent chemical activity of the polymer solution. The present results based on general transport equations for binary mixtures provide direct guidance for the design of micro-fabricated materials considering their shape, dimensions, time scale of fabrication, and chemical composition. This quantitative framework is indeed essential to engineer integrated polymer-based micro-devices by using combined pervaporation and microfluidic moulding.

Solidification of a Charged Colloidal Dispersion Investigated Using Microfluidic Pervaporation.

We investigate the dynamics of solidification of a charged colloidal dispersion using an original microfluidic technique referred to as micropervaporation. This technique exploits pervaporation within a microfluidic channel to extract the solvent of a dilute colloidal dispersion. Pervaporation concentrates the colloids in a controlled way up to the tip of the channel until a wet solid made of closely packed colloids grows and invades the microfluidic channel. For the charged dispersion under study, we however evidence a liquid to solid transition (LST) preceding the formation of the solid, owing to the presence of long-range electrostatic interactions. This LST is associated with the nucleation and growth of domains confined in the channel. These domains are then compacted anisotropically up to forming a wet solid of closely packed colloids. This solid then invades the whole channel as in directional drying with a growth rate which depends on the microfluidic geometry. In the final steps of the solidification, we observed the occurrence of cracks and shear bands, the delamination of the wet solid from the channel walls, and its invasion by a receding air front. Interestingly, this air front follows specific patterns within the solid which reveal different microscopic colloidal organizations.

Drying with no concentration gradient in large microfluidic droplets.

In most situations, drying is accompanied by the development of strong concentration gradients. Here, we evidence theoretically and experimentally that there exist microfluidic geometries for which confined drying becomes homogeneous, i.e., with no concentration gradient regardless of the type of solute involved in the process; ions, molecules, and colloids do concentrate in the same way providing a limited set of assumptions concerning the microfluidic geometry. It thus makes possible the establishment of phase diagrams of multi-component mixtures at the nanoliter scale.

Dynamics of unidirectional drying of colloidal dispersions.

We investigate the dynamics of unidirectional drying of silica dispersions. For small colloids (radii a < 15 nm), the minute recession of the drying interface inside the growing solid leads to a slowing down of the evaporation rate, as recently proposed by Wallenstein and Russel [J. Phys.: Condens. Matter, 2011, 23, 194104]. We first propose that Kelvin's effect, i.e. the reduction of the partial pressure of water in the presence of highly curved nanomenisci at the drying air-dispersion interface, has to be taken into account, notably for such small colloids. Our model can fit qualitatively the literature measurements, but with a crossover between the linear regime and the slowing down regime that scales as a(2), as compared to the model of Wallenstein and Russel that predicts a linear scaling. We then also present careful measurements of the dynamics of solidification, which clearly demonstrate that both models (taking into account or not Kelvin's effect) do not fit correctly the slowing down. This is consistent with a brief review of similar recent measurements. Nevertheless, the dynamics can be correctly estimated with a significantly lower effective permeability of the solid region. We suggest that this result may come from the polydispersity of the suspensions, and from the inhomogeneity of the flow within the fracturated solid region, as illustrated by infiltration experiments of a coloured dye.

Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient.

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Crystallization of Proteins on Chip by Microdialysis for In Situ X-ray Diffraction Studies.

This protocol describes the manufacturing of reproducible and inexpensive microfluidic devices covering the whole pipeline for crystallizing proteins on-chip with the dialysis method and allowing in situ single-crystal or serial crystallography experiments at room temperature. The protocol details the fabrication process of the microchips, the manipulation of the on-chip crystallization experiments and the treatment of the in situ collected X-ray diffraction data for the structural elucidation of the protein sample. The main feature of this microfabrication procedure lies on the integration of a commercially available, semipermeable regenerated cellulose dialysis membrane in between two layers of the chip. The molecular weight cut-off of the embedded membrane varies depending on the molecular weight of the macromolecule and the precipitants. The device exploits the advantages of microfluidic technology, such as the use of minute volumes of samples (<1 µL) and fine tuning over transport phenomena. The chip coupled them with the dialysis method, providing precise and reversible control over the crystallization process and can be used for investigating phase diagrams of proteins at the microliter scale. The device is patterned using a photocurable thiolene-based resin with soft imprint lithography on an optically transparent polymeric substrate. Moreover, the background scattering of the materials composing the microchips and generating background noise was evaluated rendering the chip compatible for in situ X-ray diffraction experiments. Once protein crystals are grown on-chip up to an adequate size and population uniformity, the microchips can be directly mounted in front of the X-ray beam with the aid of a 3D printed holder. This approach addresses the challenges rising from the use of cryoprotectants and manual harvesting in conventional protein crystallography experiments through an easy and inexpensive manner. Complete X-ray diffraction data sets from multiple, isomorphous lysozyme crystals grown on-chip were collected at room temperature for structure determination.

Microfluidic dialysis using photo-patterned hydrogel membranes in PDMS chips.

We report the fabrication of permeable membranes for microfluidic dialysis applications in poly(dimethylsiloxane) (PDMS) channels. A maskless UV projection device was used to photo-pattern long hydrogel membranes (mm-cm) with a spatial resolution of a few microns in PDMS chips integrating also micro-valves. We show in particular that multi-layer soft lithography allows one to deplete oxygen from the PDMS walls using a nitrogen gas flow and therefore makes possible in situ UV-induced polymerization of hydrogels. We also report a simple surface modification of the PDMS channels leading to strongly anchored hydrogel membranes that can withstand trans-membrane pressure drops up to 1 bar without leakages. We then measured the Darcy permeability of these membranes and estimated their cut-off by measuring the kinetics of diffusion of macromolecules of different sizes through the membrane. Finally, we illustrate the opportunities offered by such microfluidic chips for dialysis applications by observing in real time the crystallization of a model protein in a chamber of a few nanoliters.

A microfluidic device for both on-chip dialysis protein crystallization and in situ X-ray diffraction.

This paper reports a versatile microfluidic chip developed for on-chip crystallization of proteins through the dialysis method and in situ X-ray diffraction experiments. A microfabrication process enabling the integration of regenerated cellulose dialysis membranes between two layers of the microchip is thoroughly described. We also describe a rational approach for optimizing on-chip protein crystallization via chemical composition and temperature control, allowing the crystal size, number and quality to be tailored. Combining optically transparent microfluidics and dialysis provides both precise control over the experiment and reversible exploration of the crystallization conditions. In addition, the materials composing the microfluidic chip were tested for their transparency to X-rays in order to assess their compatibility for in situ diffraction data collection. Background scattering was evaluated using a synchrotron X-ray source and the background noise generated by our microfluidic device was compared to that produced by commercial crystallization plates used for diffraction experiments at room temperature. Once crystals of 3 model proteins (lysozyme, IspE, and insulin) were grown on-chip, the microchip was mounted onto the beamline and partial diffraction data sets were collected in situ from several isomorphous crystals and were merged to a complete data set for structure determination. We therefore propose a robust and inexpensive way to fabricate microchips that cover the whole pipeline from crystal growth to the beam and does not require any handling of the protein crystals prior to the diffraction experiment, allowing the collection of crystallographic data at room temperature for solving the three-dimensional structure of the proteins under study. The results presented here allow serial crystallography experiments on synchrotrons and X-ray lasers under dynamically controllable sample conditions to be observed using the developed microchips.

Microfluidic crystallization.

Microfluidics offers a wide range of new tools that permit one to revisit the formation of crystals in solution and yield insights into crystallization processes. We review such recent microfluidic devices and particularly emphasize lab-on-chips dedicated to the high-throughput screening of crystallization conditions of proteins with nanolitre consumption. We also thoroughly discuss the possibilities offered by the microfluidic tools to acquire thermodynamic and kinetic data that may improve industrial processes and shed a new light on nucleation and growth mechanisms.

Microfluidics with on-line dynamic light scattering for size measurements.

We present a detailed investigation on the feasibility of on-line dynamic light scattering measurements of colloidal sizes in a pressure-driven microfluidic flow. We review some theoretical arguments showing that such experiments are difficult to perform due to the Poiseuille flow that induces interferences of different Doppler shifts. Such a theoretical approach is however very useful to figure out the range of parameters where on-line size measurements are possible. We then build a dynamic light scattering setup around a microfluidic chip that enables us to estimate the size of Brownian scatterers flowing in PDMS-based microchannels, thus validating experimentally the theoretical estimations. We finally present a microfluidic chip that can mix two reactants in approximately 200 ms, and allows size measurements using dynamic light scattering at about 300 ms after complete mixing. Two applications are presented: the continuous monitoring of the viscosity of a two-fluid mixture, and the electrostatic co-assembly of oppositely charged nanoparticles and block copolymers.

In situ photo-patterning of pressure-resistant hydrogel membranes with controlled permeabilities in PEGDA microfluidic channels.

We report the fabrication of highly permeable membranes in poly(ethylene glycol) diacrylate (PEGDA) channels, for investigating ultra- or micro-filtration, at the microfluidic scale. More precisely, we used a maskless UV projection setup to photo-pattern PEG-based hydrogel membranes on a large scale (mm-cm), and with a spatial resolution of a few microns. We show that these membranes can withstand trans-membrane pressure drops of up to 7 bar without any leakage, thanks to the strong anchoring of the hydrogel to the channel walls. We also report in situ measurements of the Darcy permeability of these membranes, as a function of the deposited energy during photo-polymerization, and their formulation composition. We show that the use of PEG chains as porogens, as proposed in [Lee et al., Biomacromolecules, 2010, 11, 3316], significantly increases the porosity of the hydrogels, up to Darcy permeabilities of about 1.5 × 10-16 m2, while maintaining the strong mechanical stability of the membranes. We finally illustrate the opportunities offered by this technique, by investigating frontal filtration of colloidal dispersions in a straight microfluidic channel.

Engineering polymer MEMS using combined microfluidic pervaporation and micro-molding.

In view of the extensive increase of flexible devices and wearable electronics, the development of polymer micro-electro-mechanical systems (MEMS) is becoming more and more important since their potential to meet the multiple needs for sensing applications in flexible electronics is now clearly established. Nevertheless, polymer micromachining for MEMS applications is not yet as mature as its silicon counterpart, and innovative microfabrication techniques are still expected. We show in the present work an emerging and versatile microfabrication method to produce arbitrary organic, spatially resolved multilayer micro-structures, starting from dilute inks, and with possibly a large choice of materials. This approach consists in extending classical microfluidic pervaporation combined with MIcro-Molding In Capillaries. To illustrate the potential of this technique, bilayer polymer double-clamped resonators with integrated piezoresistive readout have been fabricated, characterized, and applied to humidity sensing. The present work opens new opportunities for the conception and integration of polymers in MEMS.