Self-Generated Diffusioosmotic Flows from ... - ACS Publications

Oct 15, 2012 - Calcium carbonate particles, ubiquitous in nature and found extensively in geological formations, behave as micropumps in an unsaturate...
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Self-Generated Diffusioosmotic Flows from Calcium Carbonate Micropumps Joseph J. McDermott,† Abhishek Kar,† Majd Daher,† Steve Klara,† Gary Wang,† Ayusman Sen,‡ and Darrell Velegol*,† †

Department of Chemical Engineering and ‡Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: Calcium carbonate particles, ubiquitous in nature and found extensively in geological formations, behave as micropumps in an unsaturated aqueous solution. The mechanism causing this pumping is diffusioosmosis, which drives flows along charged surfaces. Our calcium carbonate microparticles, roughly ∼10 μm in size, self-generate ionic gradients as they dissolve in water to produce Ca2+, HCO3−, and OH− ions that migrate into the bulk. Because of the different diffusion coefficients of these ions, spontaneous electric fields of roughly 1−10 V/cm arise in order to maintain electroneutrality in the solution. This electric field drives the diffusiophoresis of charged tracers (both positive and negative) as well as diffusioosmotic flows along charged substrates. Here we show experimentally how the directionality and speed of the tracers can be engineered by manipulating the tracer zeta potential, the salt gradients, and the substrate zeta potential. Furthermore, because the salt gradients are self-generated, here by the dissolution of solid calcium carbonate microparticles another manipulated variable is the placement of these particles. Importantly, we find that the zeta potentials on surfaces vary with both time and location because of the adsorption or desorption of Ca2+ ions; this change affects the flows significantly.

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INTRODUCTION Increasing demand for the miniaturization of devices has led to a need for better control of pumping, mixing, and moving fluids to meet the desired needs.1 Because pressure-driven mechanisms work poorly in tight or dead-end spaces, the need for an alternative mechanism to drive such flows is required.2−5 The advent of colloidal motors6−10 and micropumps11−13 provides alternative ways of attaining flows in microchannels and nanochannels through chemistry-based mechanisms. In this article, we show that the simple dissolution of calcium carbonate microparticles, a material ubiquitous in natural geologic formations, can self-generate electric fields of roughly 1−10 V/cm that pump fluids and tracer particles over distances many times greater than the carbonate particle radius. We also find that even for simple model systems the interplay between the chemistry and fluid dynamics is complex, providing significant opportunities for designing flows and transport in regions that were previously inaccessible. Electroosmotic pumping for applications in narrow channels has been explored in the literature.14−17 However, there arises a significant limitation: electroosmotic pumps need an external power source that is not feasible in many difficult-to-reach spaces. For example, placing electrodes in tight geometries can be challenging. However, diffusiophoresis is a transport mechanism that operates on the basis of the existence of a gradient of ion concentration; no electrodes are needed. This © 2012 American Chemical Society

mechanism has seen relatively little technological application, although it has recently been used in connection with DNA translocation and entrapment18 and colloidal transport.19−21 Diffusiophoresis converts the free energy of dissolution, precipitation, or chemical reactions into a directed motion of fluid and tracers. The flow mechanism of diffusioosmosis has been studied using both modeling22−24 and experiments25−27 via imposed salt gradients in 1D systems at steady state. However, self-generated ionic gradients can be established when a solid dissolves into ions in an unsaturated solution. Such dissolution can occur when the thermodynamic equilibrium between the mineral and the surrounding water is disturbed, such as when new surfaces become exposed, allowing further dissolution of the minerals in surrounding aqueous regions. This physical phenomenon produces local ion gradients originating at the mineral surface. The gradients in turn drive microflows and particle movement along charged surfaces and pores by the mechanism of diffusiophoresis. In our systems, we observe mesoscale flows with speeds reaching as high as 40 μm/s. In short, the dissolution of the mineral particles provides a type of “localized battery”, and the charged surfaces provide the “pump”, even though surfaces act as a Received: August 23, 2012 Revised: October 13, 2012 Published: October 15, 2012 15491

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ZEN3690). To measuring the ζ potential of the glass substrate, we used a SurPASS device (Anton Paar, VA) for the streaming potential. The ζ potentials of particles were measured at 298 K using disposable cuvettes (DTS1061) at ionic strengths of 0.1−50 mM and a pH of 5.8. For ζ-potential measurements of particles in salt solutions, the latex particles were first soaked in a salt bath for 15 min before the measurements were made. The ζ potential of the walls was measured under various salt conditions and pH values to observe consistency. Analysis of Pumping Behavior. Particle velocimetry was used to generate the plots in Figures 4 and S1. Particle tracking of tracer particles was done by using ImageJ for a given number of video frames. To produce the velocity vector field plots in Figure 4a,b, an appropriate number of tracers (between 700 and 1500) were analyzed over the entire region, encompassing a total analyzed time of ∼30 s. Figure S1 was prepared by analyzing 10−20 tracers surrounding a single microsphere over the course of ∼10 s for each value of the interparticle distance. Average interparticle distances were calculated from the surface fraction of calcium carbonate microspheres. For each sample, the tracer velocity versus the radial distance was fitted to an exponential decay function, from which both the maximum tracer speed and decay lengths were taken. In no case did we apply pressure to our system to drive flow.

resistance to flow. Thus, we can use diffusioosmosis to drive flows in regions that pressure-driven flows cannot access.

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MATERIALS AND EXPERIMENTAL METHODS

Materials. We synthesized our own CaCO3 and BaCO3 microparticles for experimental purposes. For calcium and barium carbonate microparticle synthesis, sodium carbonate (Na2CO3), calcium chloride (CaCl2), and barium chloride (BaCl2) were obtained from SigmaAldrich. Two sizes of surfactant-free sulfate-functionalized polystyrene latex microspheres (d = 1.4 μm ± 2.1% and 3.0 μm ± 2.4%, both had w/v = 8.0%) and one batch of surfactant-free amidine-functionalized polystyrene latex microspheres (d = 3.5 μm ± 2.1%, w/v = 4%) were purchased from Interfacial Dynamics Corporation (Portland, OR). These microspheres were used as tracers in our experiments to study flow behavior. The latex particles are abbreviated as sPSL for sulfatefunctionalized polystyrene latex and as aPSL for amidine-functionalized polystyrene latex throughout the entire text. Calcite samples (∼1 mm2) were obtained from Petrobras (Rio de Janeiro, Brazil). Gypsum and barite rock samples (10 × 2 × 2 cm3, broken into 100 μm shards) were obtained through Amazon.com and are sold through MMP, LLC (Denver, CO). Deionized (DI) water used in all aqueous solutions came from our Millipore Corporation Milli-Q system, with a specific resistance greater than 1 MΩ·cm (due to equilibration with CO2 in air). Negatively charged square glass coverslips (22 × 22 mm2) and Petri dishes (10 × 1.5 cm2) were obtained from VWR International. Borosilicate glass capillaries of 0.9 mm i.d. (part no. 8290-050) were obtained from Vitrocom for some of the experiments with natural rock specimens. Calcium and Barium Carbonate Microparticle Synthesis. A simple precipitation synthesis was used to synthesize the calcium and barium carbonate microparticles. In both cases, 25 mL of a 0.33 M solution of CaCl2 or BaCl2 was stirred at high velocity on a magnetic stirrer. An additional 25 mL of 0.33 M Na2CO3 was then rapidly added to the solution, which turned milky white as the carbonate particles precipitated. The solution was stirred for an additional 1 to 2 min and then quenched with 50 mL of DI water. To remove the remaining Na+ and Cl− ions, the particle solutions were rinsed by repeated centrifugation and resuspension in DI water using a Sorvall Biofuge Primo centrifuge from Kendro Laboratory Products. The rinsing procedure was typically repeated two to four times, with additional rinsing steps significantly affecting the microparticle size through carbonate dissolution. Using optical microscopy, we found the CaCO3 particles to be roughly spherical, with a polydispersity of ∼50% and an average radius of 7−10 μm. They were found to be stable to aggregation for at least a day. The BaCO3 particles were found to be smaller (d ≈ 1.5 μm, polydispersity ≈ 50%) and more shardlike. Observation of Pumping Behavior of Carbonate Microparticles. To observe the pumping behavior, we imaged the carbonate microparticles and tracers using a Nikon Eclipse TE2000-U inverted optical microscope, typically at 10× and 20× magnification. First, the concentrated carbonate particle solution was diluted to the desired concentration using DI water and an ultrasonicator (model 550T) along with a mini vortex mixer (with speed control), both obtained from VWR International, and then the microparticles were resuspended in the solution. Five hundred microliters was quickly pipetted into a glass-bottomed Petri dish. An additional 500 μL of a 0.1% w/v solution of tracer sPSL and aPSL particles was then added to the dish, and the solutions were mixed and observed. Observation of Pumping Behavior of Natural Rock Samples. Similar to the procedure in the previous section, calcite (CaCO3), barite (BaSO4), and gypsum (CaSO4·2H2O) rock samples were placed in DI water in a glass-bottomed Petri dish. Then, 0.1 vol % tracer particle solutions were added, and the resulting movement was observed using optical microscopy. In certain cases, the experiments were performed in open capillaries that contained the tracer particle solution to simulate the effect of dissolution in a microchannel or pore. Zeta Potential Measurements of Latex Particles and Substrate. For zeta potential (ζ) measurements of sPSL and aPSL particles, we used a Zetasizer Nano ZS90 (Malvern, MA, model

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RESULTS In the case of a solitary calcium carbonate micropump, particles settled onto glass in DI water and were surrounded by sPSL tracer particles, and the particle flow field was readily observed (Figure 1a). For negatively charged tracers, the particles were

Figure 1. Microflows for a single CaCO3 particle micropump and two interacting micropumps. These systems contained only calcium carbonate pumps and 1.4 μm sPSL tracers in DI water. (a, b) Timelapse images. The videos (S1 and S5) were filmed on a bare glass substrate using an inverted microscope. Optical microscopy time-lapse images were taken at 40× magnification with overlays every 0.2 s. The scale bars in these images are 10 μm.

pulled in rapidly from above the plate to the micropump particle surface (Figure 2a). The tracers collected near (Figure 2b) and moved down the surface of the micropump, and upon reaching the substrate, they were rapidly ejected radially outward into the solution (Supporting Information, videos S1 and S2). The movement of sPSL tracers away from the calcium carbonate particles was fast near the micropump’s surface and decayed with distance until Brownian motion dominated the particle movement tens of micrometers away. We observed tracers that approached the pump at shallow angles being ejected without ever reaching the micropump surface. During the dissolution process, there is an exclusion region of tracers near the pump particle on the glass surface. Some negatively charged tracers adhered to the surface of the calcium carbonate microparticle (Figure 2b) and were ejected only after the complete dissolution of the pump (Figure 2c). These flow fields can be compared to those observed for catalytic micropumps28 where there is a recirculating flow pattern around the pump surface originating from similar mechanisms. 15492

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Figure 2. Schematic of microflows for a single CaCO3 particle micropump with sPSL tracers and two images of the same micropump. These systems contained only calcium carbonate pumps (7 μm radius) and 3 μm sPSL tracers in DI water. (Inset, a) Axes and 3D view of our experimental setup. Scale bars in these images are 10 μm. The videos (S1 and S2) were filmed on a bare glass substrate using an inverted microscope. (a) x−z plane. Tracers in the bulk are attracted to the pump, some adhere, and the rest get pumped out into the bulk radially. (b) x−y plane. The sPSL tracers adhere to the surface of the pump, but not permanently. (c) x−y plane. A clear exclusion region of tracers develops around the micropump on the glass surface. These tracers, after being ejected, exhibit mostly Brownian motion.

Figure 3. Flows near CaCO3 particle micropumps with aPSL tracers. (Inset, a) Axes and 3D view of our experimental setup. (a) x−z plane. Schematic of flows near a micropump. The chemistry is given, and the E field points outward. The aPSL particles are pushed away from the calcium carbonate micropump by diffusiophoresis, so the flow lines of these tracers do not approach the micropump, as in Figure 2a. (b) x−y plane. The aPSL tracer particles do not aggregate on the surface of the calcium carbonate micropump, as do the sPSL tracers (compare with Figure 2b). These systems contained only calcium carbonate pumps (7 μm) and 3.5 μm aPSL microspheres in DI water. Scale bars in these images are 10 μm. The videos (Supporting Information, Videos S3 and S4) were filmed on a bare glass substrate using an inverted microscope. (c) x−y plane. Two interacting micropumps with no stagnation region of flow.

The aPSL microparticles (3.5 μm diameter) were observed to have different flow paths, as seen in Figure 3. Instead of being attracted from the bulk toward the micropump, these tracers are pushed away from the calcium carbonate surface because they are positively charged, so they do not aggregate near the micropump (Figure 3b). However, aPSL particles settle vertically by gravity when they are a few micrometers away from the region defined by the calcium carbonate particle (Figure 3a). They settle until they are near the glass surface, where they then are swept outward by the diffusioosmotic flow caused by the glass. This is in addition to their own diffusiophoretic velocity, which also seeks to move them outward in the self-generated electric field. Very rarely do any of the aPSL tracers settle vertically onto the micropump (Supporting Information, Video S3). We used video microscopy to quantify the speeds and directions of the tracers. Figure 4c,d was generated from velocity plots generated for a single micropump (Figure 4a) and two interacting pumps (Figure 4b). sPSL tracer speeds were found to decay roughly exponentially to around 1 μm/s at a distance of roughly 100 μm away from a solitary pump. In the case when two pumps are near enough that their flow fields interact, a stagnation point arises at the midpoint between the pumps (Figure 1b; Supporting Information, Video S5) for sPSL tracers. The sPSL tracers ejected from one CaCO3 particle move toward the other, and then escape in a direction orthogonal to the line of centers between the CaCO3 particles. However, this is not the case with aPSL tracers (Figure 3c), where there is no stagnation region between the calcium carbonate micropumps (Supporting Information, Video S4). Because the electric field points away from pump’s surface, the

positively charged aPSL tracers are pushed away from the particle and so do not settle close to it. In our systems, the dissolving CaCO3 gives rise to an electric field and so acts as a type of localized battery. Because of the nature of electrokinetic flows, any charged surface becomes a type of pump. On the lower left of our CaCO3 micropump, there are two large tracer particles attached (Figure 1b), likely through van der Waals forces. These attached and charged particles generate additional local electroosmotic flows in the solution. That is, the surfaces act as additional pumps rather than hindering flows, and the tracers favor movement along these surfaces. Further experiments (Supporting Information, Video S6) confirm the nozzling phenomenon: by adding additional fixed charge surfaces, the flow of tracers can be focused or directed in the solution. This opens the possibility to designing complex flow patterns in dissolving mineral systems. The idea of surfaces as pumps can be used to direct flow for any desired application in spaces that are otherwise difficult to access.

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DISCUSSION In trying to identify the mechanism of flow, we have examined the following phenomena: (1) thermally driven density flow resulting from the heat of dissolution that is not homogeneous throughout the solution; (2) concentration-difference densitydriven flow,29 originating from difference in fluid densities due to the species produced upon dissolution of calcium carbonate in the solution; and (3) diffusiophoresis30 originating from 15493

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∇p = η∇2 u + f ∇u = 0

(1)

where u is the velocity of the fluid, p is the pressure, η is the viscosity of the solution, and f is any external body force acting in the system such as gravity (ρg). When we assume steady state and a low Reynolds number for the system, analysis reveals that density-driven flow (U) scales as

U≈

L2(ρs − ρw ) η

g

(2)

Our estimate shows that density-driven flows account for a maximum of 1 μm/s for micrometer-size particles dissolving in an infinite sink. An interesting consequence of this scaling behavior is the dependence of density-driven flows on the characteristic size of the particle. Because the speed scales as L2, where L is the characteristic dimension of the calcium carbonate microparticle, we expect that density-driven effects will become important as the particle size increases. We in fact see such density effects experimentally when we use mineral chunks (e.g., calcite, barite, gypsum) of roughly 1 mm in size, but not for micrometer-sized particles. Because the pumping speeds that we observe here are not consistent with thermal- or density-driven flow mechanisms and because there is a dependence of the tracer particle transport on the surface potentials in the system, we now turn to diffusiophoresis and diffusioosmosis to provide an explanation of the observed behavior. The trajectory of the tracer movement can be changed by changing the magnitude or sign of the particle surface potentials in the system (cf. Figures 2 and 3). This suggests that our microflows are electrokinetic, here diffusiophoretic, resulting from the dissolution of CaCO3. The flow field we see for our system is similar to that of a different problem from the literature: that of an electroosmotic flow field resulting from a lone sphere attached to a flat, charged plate with an applied normal electric field.32 The circulating hydrodynamic flow lines cause the tracer particles to be pulled in from the top of the solution and ejected radially outward along the bottom plate. This similarity in the flow field in part suggests the electrokinetic mechanism and the nature of our micropump CaCO3 particles. How are our diffusiophoretic flows generated? First, it is important to recognize that in the presence of a large number density of CaCO3 particles the solution becomes saturated with calcium carbonate, halting further dissolution and generating no flows. CaCO3 is sparingly soluble in deionized water, with a solubility product constant of 3.36 × 10−9 M2 at 20 °C.23 However, when a dilute sample of CaCO3 microparticles exists in DI water, dissolution occurs at the particle surface into the fluid. Although after about 20 min the particles disappear from the system, during the dissolution process there is a radial concentration gradient of ions surrounding them. The concentration profile for these ions can be found from Fick’s second law and can be expressed as (details in Supporting Information)

Figure 4. Microflows for a single CaCO3 particle micropump and two interacting micropumps. These systems contained only calcium carbonate pumps and 1.4 μm sPSL tracers in DI water. (a, b) Vector field for the time-lapse images shown in Figure 1 (also Supporting Information, Videos S1 and S5). In the vector field plots, axes are the distance in micrometers. The black circles represent the location of the micropumps, and the vector arrows represent the tracer particle direction and speed in μm/s at the substrate surface. The plots were generated by tracking the movement of 750−1000 particles over 0.3 s. (c, d) Radial speed plots. (c) The radial speeds of all sPSL tracers sampled in b are plotted against the distance of those tracers from the center of the lone calcium carbonate micropump. (d) The radial speed of tracer particles within 6 μm of the line between the two micropumps in b (boxed area shown) is plotted against the distance of those tracers from the midpoint between the two pumps. In both cases, curves have been fitted using the theoretical radial velocity decay as discussed in eq 3 in the text and in the Supporting Information, section SIV. (c) The red line and blue dotted lines are coinciding oneand three-parameter fits for the cases of 0 (eq SIV.3) and small bath concentrations of CaCO3 (eq SIV.2), respectively, with both curves showing a v ≈ a/r dependency. (d) A two-parameter superposition of two single particle fits, again with form v ≈ a/(r ± b), was used, assuming no bath concentration of CaCO3. We anticipate that better fits can be achieved by taking the radially varying zeta potentials into account, as shown in Table 1. In fact, the analysis of the discrepancy between the fitted function and the observed speeds should lead to a better understanding of the concentration dependence of these surface potentials. Fitting curve equations and further discussion can be found in the Supporting Information (eqs SIV.4 and SIV.5).

concentration gradients of ionic species produced on dissolution. We do not apply pressure to drive flow in any of our systems. For thermally driven density changes, we estimate that negligible flows might arise because the heat of dissolution of calcium carbonate in water is only 427 J/g.31 Over the time that dissolution occurs, the heat would conduct over more than 1 cm in water. However, a simple heat balance shows that even if this heat were dissipated over a region as small as 1 mm in 20 min the temperature increase would be less than 0.001 C. For density increases due to dissolved CaCO3, we use scaling estimates from the Stokes equations to evaluate the effect. The Stokes equations are

⎡r−a⎤ a C(r , t ) = (Cs − C b) erfc⎢ ⎥ + Cb ⎣ 4Dt ⎦ r

(3)

where the particle has a radius a and the distance from the center of the particle is r, with erfc[ ] representing the complementary error function. D is the overall diffusion 15494

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coefficient, with the bulk concentration being Cb and the surface concentration being Cs. The complementary error function approaches unity at long time intervals (giving rise to steady-state conditions) with the concentration varying as a function of 1/r. The primary ions resulting from this dissolution are Ca2+, HCO3−, and OH−. These ions contribute to the electric fields generated in the system as a result of the differential diffusion described in the next paragraph.33 For the time scales of our observation, the solution acts as a sink because it is unsaturated with the ions produced upon dissolution of CaCO3. In a control test, calcium carbonate micropumps were suspended in saturated 0.5 mM CaCO3 solution with sPSL tracers dispersed in it, and the whole sample was placed under a microscope for observation. By having a saturated solution of the constituent ions, no concentration gradient forms, and the microparticles did not exhibit any pumping behavior on the glass surface, as expected. The electric field driving the diffusioosmosis arises from differential diffusion in the usual way. The three ions resulting from each molecule of dissolved calcium carbonate have different diffusion coefficients:34 at 20 °C, DOH− = 5.27 × 10−9 m2/s, whereas DHCO3− = 1.19 × 10−9 m2/s and DCa2+ = 0.792 × 10−9 m2/s. The ions cannot diffuse freely, however. A spontaneous electric field arises in order to maintain electroneutrality in the system (Figures 2a and 3a). Because the hydroxyl ion diffuses 4 times faster than the bicarbonate ion, the electric fields are (along with the concentration gradient) oriented radially outward from the calcium carbonate microparticle surface. This electric field acts not only on the ions but also on any charged colloidal particles or surfaces in the region. This electric field, which in our system is between 1 and 10 V/ cm, causes the electroosmotic and electrophoretic transport of the specimen described earlier. This overall process of an ion gradient effecting an electric field that drives electrokinetic transport is called diffusiophoresis.17 There is a further complexity behind our flow patterns and velocities of tracers. This is due to the chemistry of the system and the changing particle zeta potentials depending on the local CaCO3 and other ion concentrations. Table 1 lists the zeta

tracer movement reversed as expected (Supporting Information, Video 7) because now the particle zeta potential had a greater magnitude than the substrate zeta potential (ζp − ζw > 0, Table 1 values). At higher KCl concentrations (>100 mM), the motion slowed significantly because of ionic screening, which causes the diffusioosmotic flow mechanisms to become small, at least on the time scales of our experiments. It should be noted here that because of the dynamic nature of calcium ion systems that adsorb on the surfaces of walls and particles, the zeta potentials could decrease further in magnitude for longer exposure times. Zeta potentials in simple, static systems are well-studied, but dynamic changes in zeta potentials in mixed systems of mineral particles, interacting by dissolution, reaction, and precipitation, are much less well understood. In our system, the ionic concentration surrounding the pump changes significantly with radial distance, causing a zeta potential that changes spatially and, because the particles are moving with time, therefore temporally.37 The effect of multivalent ions such as Ca2+ on the surface charge of colloidal particles is especially important, as seen in the presence of fully dissociated salts (such as CaCl2).38 CaCO 3 particles are not the only ones that drive diffusioosmotic flows. Barium carbonate microparticles (Figure 5) synthesized in a manner similar to that for CaCO3 particles

Table 1. Zeta Potential Values (mV) in Various Solutions solution 3.0 μm sPSL glass coverslip 3.5 μm aPSL

DI water

0.5 mM CaCO3

10 mM KCl

0.5 mM CaCO3 + 10 mM KCl

−55 −70

−30 −35

−101 −62

−91 −54

+45

+5

+35

+7

Figure 5. Barium carbonate microparticle pumping of 1.4 μm sPSL tracer particles outward. Overlays are 0.33 s apart, and the scale bar is 20 μm.

show nearly identical behavior. In fact, the pumping of the tracers is even faster for comparable particle surface fractions because of the greater disparity in ionic diffusion coefficients between Ba2+ and OH−.

potential measurements of the tracers and wall under various solution conditions determined through the Malvern instrument for particles and SurPASS (Anton Paar, VA) for glass coverslips. The diffusiophoretic speed of the tracers depends on ionic strength gradients in the usual way. In addition, the speed also depends upon the absolute local concentration due to the adsorption of Ca2+ and the resulting change in particle zeta potentials over short distances. For example, the sPSL zeta potential, which is normally very negative in DI water, is suppressed in the presence of CaCO3 solution35 likely because of interactions between the calcium ions and sulfate groups. We found that this change can be manipulated by the addition of KCl ions to the system.36 When the micropump experiments were repeated with a 10 mM KCl solution, the direction of the

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CONCLUSIONS We have shown that self-generated ion gradients resulting from mineral particle dissolution or precipitation can drive significant microscale flows and particle movement in mineral systems. Diffusioosmotic pumping is an effective flow mechanism in microchannels and nanochannels,28 often superior to pressuredriven flows (Supporting Information). Whereas in pressuredriven flow the wall acts as a resistance to flow, in electrokinetic flows a charged wall acts as the pump. Diffusiophoretic flows are in μm/s and are able to move fluid from very tight regions 15495

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(i.e., small pores, even 1 μm or less), perhaps even over small distances such as tributaries, into more porous regions that traditional pressure-driven flow can access. Diffusioosmotic flows avoid channeling, where fluid simply goes around lowporosity regions. One application where a better understanding of diffusiophoretic pumping could have an immediate impact is in the geosciences and in petroleum engineering. Water injection and rock fracturing are commonly practiced in oil wells39,40 and now in gas shales, and ion gradients will occur as a result. Whereas the overall fracking flows involve high pressures and millions of gallons of water, the mechanism for obtaining the desired petroleum or gas out of tight rock formations could depend significantly on mineral-driven microflows. Thus, diffusiophoretic pumping might contribute to the associated enhanced oil recovery, especially that due to flooding with fresh water.41 Furthermore, in geological events such as earthquakes, spontaneous microflows might actively bleed chemical species from microchannels or nanochannels in rock to larger-scale bulk flows. The directionality obtained from this self-generated flow mechanism opens a new possibility of not only removing material from pores but also inserting material into pores. These microflows must be considered further as an important area of microfluidics and nanogeoscience.

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ASSOCIATED CONTENT

* Supporting Information S

Calcium carbonate’s aqueous chemistry and concentration profile for a dissolving microparticle in an infinite bath. Graph of tracer speeds due to the variation in separation of interacting micropumps. Complete solution for the diffusiophoretic speeds of tracer particles. Competing effects of pressure and diffusioosmotic flows in microchannels to nanochannels. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (814) 865-8739. Fax: (814) 865-7846. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Science Foundation (CBET 1014673) and U.S. Air Force (SC090340) for funding this project. We also thank Michael Hickner at Penn State for his guidance in using his streaming potential device to obtain the zeta potentials of the glass wall.

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REFERENCES

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