We present a new method to study flow of liquids near solid surface: Total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS). Fluorescent tracers flowing with the liquid are excited by evanescent light, produced by epi-illumination through the periphery of a high numerical aperture oil-immersion objective. The time-resolved fluorescence intensity signals from two laterally shifted observation volumes, created by two confocal pinholes are independently measured. The cross-correlation of these signals provides information of the tracers’ velocities. By changing the evanescent wave penetration depth, flow profiling at distances less than 200 nm from the interface can be performed. Due to the high sensitivity of the method fluorescent species with different size, down to single dye molecules can be used as tracers. We applied this method to study the flow of aqueous electrolyte solutions near a smooth hydrophilic surface and explored the effect of several important parameters, e.g. tracer size, ionic strength, and distance between the observation volumes.
© 2009 OSA
Liquid flow in confined geometries can only be accurately described if the flow at the interface between the fluid and the solid is thoroughly understood [1–10]. Such understanding would not only provide a fundamental advance in the physics of flow in microfluidic and nanofluidic devices, but is also important for a number of industrial and technological processes, such as flow in porous media, electro-osmotic flow, particle aggregation or sedimentation, extrusion and lubrication. While for many years the so called no-slip boundary condition (velocity equal to zero on the channel’s walls) was applied to describe macroscopic flows, recently it has been recognized that this condition does not always apply when channels with micro- and nano-sizes are considered [4,5]. Liquid flowing through such channels may slip on the channel walls. The effect is typically described by a non-zero, “slip” velocity, vs, at the channel wall or by the so called slip length b defined by b = vs/(dv/dz), where dv/dz is the shear rate and z is the axis normal to the wall. The existence and extend of slip and its dependence on surface properties and the shear rate are highly debated and no consensus has been reached so far. To rationalize this controversy, new experimental techniques are required.
Direct experimental approaches to flow profiling in microchannels, are commonly based on various optical methods to monitor fluorescent tracers flowing with the liquid. These methods can be divided in two categories:
- a) Imaging based methods use high resolution optical microscopes and fast cameras to track the movement of individual tracer particles on a series of images [11–16]. While providing a direct “picture” of the flow, the imaging methods bear also some disadvantages: relatively big tracers are needed, the statistic is rather poor, high tracer velocities cannot be easily measured.
- b) Fluorescence Correlation Spectroscopy (FCS) based methods measure the fluctuations of the fluorescent light emitted by tracers passing through a very small observation volume of a confocal microscope . A proper analysis of these fluctuations allows evaluation of tracers’ diffusion coefficient and flow velocity [18–21]. In particular, the so called double-focus fluorescence cross-correlation spectroscopy (DF-FCS), which employs two observation volumes (laterally shifted in flow direction), has proved to be a powerful tool for flow profiling in microchannels [22–25]. The main advantage of the FCS based schemes is that even single molecules can be used as tracers, the evaluation of the velocity is based on large statistics, and high tracer velocities can be measured.
During the last decades the above described methods have been developed to a state that allows to measure flow velocity profiles in microchannels. The situation, however, is different when the issue of boundary slip is considered. When applied to flow profiling in the close proximity of an interface, both the imaging and the FCS methods in their classical implementation suffer from the limited resolution of optical microscopes. New high resolution techniques need to be developed for addressing the boundary slip phenomenon.
In the proximity of an interface the normal resolution can be significantly increased using Total Internal Reflection Microscopy (TIRM) . In TIRM the effect of total internal reflection on the interface between two media with different refractive indices is used to create an evanescent wave that extends (and therefore can excite fluorescence) only in a tunable region of less than ~200 nm from the interface. During the last few years TIRM imaging was successfully applied for improving the resolution of particle tracking close to solid interfaces [14,15]. With respect to FCS, however, to date, TIR illumination was applied to diffusion studies only [27,28]. To the best of our knowledge there are no reports on TIR-FCS based velocimetry.
In this paper we present a new TIR-FCS based method that combines the extreme sensitivity and good statistic of FCS with the high normal resolution of the TIR illumination to study velocity profiles in the range 0-200 nm from an interface. We applied this method to study the flow of aqueous solutions near a smooth hydrophilic surface and explored the influence of several important parameters, e.g. tracer size and ionic strength of the solution.
2. Experimental methods
2.1. Basic concept and experimental setup
The experimental setup (Fig. 1 ) is based on a commercial, confocal FCS device (Carl Zeiss, Jena, Germany). It consists of the module ConfoCor 2 and an inverted microscope model Axiovert 200. For the evanescent wave excitation we used the 488 nm line of an Argon laser (~6 mW), fiber coupled to the epi-fluorescent illumination beam path of the microscope through the so called TIRF-Slider. This device, which can be conveniently plugged into the compartment for aperture diaphragm slider of the Axiovert 200 microscope, comprises a collimator and a prism based reflecting element whose tilt is controlled by an adjustment screw. The collimated laser beam is focused by the microscope tube lens on the back focal plane (BFP) of a high numerical aperture (NA) microscope objective (α Plan-Apochromat 100 × /1.46 Oil, Zeiss). These arrangements produce a parallel laser beam emerging from the objective and entering the flow channel through its bottom wall (glass cover slip). In our experiments the beam diameter was in the order of 20-25µm (at e−2).
By changing the tilt of the TIRF-Slider reflecting element, the angle of incidence, α 1, at the glass channel wall/flowing liquid interface can be adjusted in the range from 0 to 73°. If this angle exceeds a critical value (61° for water) total internal reflection (TIR) occurs at the interface producing an evanescent wave. The intensity distribution of this wave in the xy plane (parallel to the interface) is Gaussian. In the z direction (along the optical axis) the intensity I decays exponentially I = I 0exp(-z/dp) with a characteristic penetration depth d p. By changing the angle of incidence the penetration depth can be changed according to:
Here λL is the laser wavelength and, n1 and n 2 are the refractive indices of the glass channel wall and water, respectively. For a given position of the TIRF-slider adjustment screw, the angle of incidence was measured independently by out-coupling the laser beam using a glass prism mounted on the top of the objective. Then Eq. (1) was applied to determine the evanescent field penetration depth d p. Under our experimental conditions of TIRF, Fig. 1, d p could be varied between 80 and 200 nm.
Fluorescent light is collected by the same objective. After passing through the dichroic mirror it is equally split to enter two independent detection channels using a neutral 50:50 beam splitter. In each channel the fluorescent light passes through an emission filter and a confocal pinhole to finally reach the detectors, two fiber coupled single photon avalanche photo diodes (APD1, APD2). Each of the confocal pinholes PH1 and PH2 defines its own observation volume, whose lateral extend and position are determined by the size and position of the respective pinhole. In our experiments pinhole sizes of 100 µm were used. By proper adjustment of the pinholes, the two observation volumes can be laterally shifted from each other by a distance Δs (Fig. 2 ). The confocal pinholes are mounted on high precision motorized translation stages. After an initial calibration of the separation distance by monitoring the reflection profile of a golden stripe with well defined width (2 mµ) deposited on glass substrate, the distance Δs can be easily and reliably adjusted. Our experimental setup allowed tuning of Δs in the range from 0 to 2.5µm.
As the tracer particles moving with the flow pass consecutively through the two observation volumes, they will produce two time-resolved fluorescence intensities I 1(t) and I 2(t) that are independently recorded (Fig. 2). The time cross-correlation function can be calculated as and typically exhibits a local maximum. The position of this maximum τM is characteristic for the averaged tracer velocity close to the interface; only the region that is illuminated by the evanescent light contributes. This velocity is v = Δs/τM. By tuning dp the flow velocity at different distances to the interface can be probed.
For each penetration depth a series of 5 measurements with total duration of 150 seconds was performed and the corresponding cross-correlation curves were evaluated. The tracers’ brightness was ~30 kHz per particle for the quantum dots and latex FluoSpheres, and ~3 kHz per molecule for the Alexa 514.
2.2. Microchannel fabrication
The microchannel was fabricated using a three-layer sandwich construction (Fig. 3 ) as in earlier work . The lowest layer was a microscope cover slide made of borosilicate glass with a thickness of 170 µm, cleaned with 2% aqueous solution of Hellmanex and Argon plasma. The root-mean-square roughness of the glass surface was in the range of 0.3 nm and the water advancing contact angle below 5°. The channel itself was created by cutting out a strip in an adhesive polymer film (Tessa, Germany) with a thickness of 100 µm. Finally the top layer was a microscope slide with a thickness of 1 mm. In this way a flow channel with dimensions 50 mm × 2 mm × 100 µm was formed. This channel was hold by a chamber made from an aluminum support and a polycarbonate block. A hydrostatic pressure gradient was created by two beakers of different heights (Fig. 1), which allowed us to vary a shear rate near the wall in the range 0 – 5000 s−1.
2.3. Fluorescent tracers
As fluorescent tracers we used single dye molecules (Alexa 514, Molecular Probes, Inc) with a hydrodynamic radius RH = 0.8 nm as measured by conventional FCS, carboxylate-modified quantum dots (Qdot585, Molecular Probes, Inc.) with RH = 10 nm, and carboxylate-modified latex FluoSpheres 505/515 (Molecular Probes, Inc) with hydrodynamic radius of 28 nm. In all cases the final fluorescent tracers’ concentration was around 20 nM. Experiments were carried out in water and potassium phosphate (K2HPO4) aqueous solutions (pH = 9.0) with concentrations up to 10−2 mol/L.
3. Results and discussion
Typical cross-correlation curves measured for a different penetration depths of the evanescent field and fixed distance between the two observation volumes (Δs = 1 µm) are shown in Fig. 4 . The measurements were carried out with a 0.1 mM aqueous solution of K2HPO4 and quantum dots Qdot585 with hydrodynamic radius of 10 nm were used as tracers. The cross-correlation curves in the presence of flow have a bell shape with clearly defined maximum. The maxima are shifted to longer correlation times and their heights increase with decreasing penetration depth. The cross correlation vanishes when the flow is switched off.
The most accurate way to extract the flow velocity profiles in the proximity of the wall from the experimentally measured cross-correlation curves is to derive a theoretical expression for G(τ) that can be used for fitting the experimentally obtained data. Such expression can be derived starting from [22–24]:
Here, different spatial coordinates , are used for the two observation volumes. is the concentration of fluorescent tracers that may depend on the distance to the interface. The space-dependent molecular detection efficiencies (MDE) and of the two volume elements are determined by several factors: (1) the excitation intensity profile, which in our case is an exponentially decaying evanescent wave; (2) the space-dependent collection efficiency of the optics and of the pinhole, which is commonly described with ellipsoidal Gaussian function; (3) the quantum efficiency of the detector and the fluorescent tracers. The dynamics of the system is determined by the concentration fluctuation function . If the tracers are subject only to free translational diffusion with diffusion coefficient D, superimposed with a constant uniform flow, the function is a solution of an advection-diffusion equation [22–24].
As shown by Brinkmeier for the case of focused laser beam illumination  (as opposed to the evanescent illumination in our case) Eq. (2) can be solved analytically assuming that the local flow velocity and tracers concentration do not depend on the normal coordinate z, i.e. an average velocity can be used for all tracers inside the observation volume. Such an assumption is reasonable only if the observation volumes (laser foci) are far away from the channel walls. In the proximity of the wall, however, the situation is different and a distribution of flow velocity inside the observation volume has to be considered. Furthermore, the concentration of tracers may also depend on z due to the electrostatic repulsion or hydrodynamic effects. In a recent work  this situation was explored (again for focused laser beam illumination) and it was shown that Eq. (2) can be solved numerically yielding reasonable agreement with experimental data.
A comprehensive model for the experimentally measured cross correlation curves should combine the formalism described above with that used to analyze TIR-FCS autocorrelation curves in the no flow case . The development of such a model is complex and will be addressed in a later publication. Here, we will focus on the development of the experimental technique for TIR-FCCS flow studies and will relate the measured cross-correlation curve to the flow profile near the interface in a non rigorous way.
First we consider the bell shape of the cross-correlation curves. The evanescent field is probing not a single velocity but a range of velocities starting from a minimum value at the interface (0 if there is no boundary slip) and increasing with increasing distance from the interface. Therefore, the cross-correlation curve reflects a range of “flying times” τ. Furthermore the value of G(τ) for a given τ depends on: (1) the relative number of tracers crossing Δs with „flying time“ τ as compared to the number of all tracers crossing Δs for a certain acquisition time and (2) the fluorescent intensity of these tracers. The fluorescent intensity is directly proportional to the intensity of the excitation evanescent field. The tracers that are very close to the interface and contribute to the long times tail of the cross-correlation curve are excited stronger, because the evanescent wave is stronger. On the other hand, their relative number is low due to the low velocity and eventually these results in an decrease of G(τ) at longer lag times. The tracers that are far from the interface are flowing faster, crossing more often both observation volumes and therefore contributing stronger to G(τ). In the same time, however, at longer distances from the interface the evanescent wave intensity decreases leading eventually to a decrease in G(τ) that is reflected in the short times tail of the cross-correlation curve. The experimentally measured cross-correlation curves correspond to a weighted averaging over all velocities in the range of the evanescent field. Other factors contributing to the shape and height of cross-correlation curves will be discussed below.
If we denote the position of the maximum of G(τ) with τ M an “average” flow velocity can be calculated as v(τ M) = Δs/τ M. To some extend v(τ M) can be regarded as the flow velocity at a certain optimal probing distance from the interface. As shown in Fig. 4 with decreasing the evanescent field penetration depth d p the maximum of the cross-correlation curves shifts to longer lag times that correspond to a lower velocity. This observation reflects the fact that an evanescent wave with a short penetration depth is probing the flow nearer to the interface. In order to illustrate this quantitatively we have plotted in the inset of Fig. 4 the dependence of v(τ M) on the penetration depth. v(τ M) decreases with decreasing d p but even at very short penetration depths the values of v(τ M) are still rather high. Among other reasons this effect may be related to a depletion of the tracers’ concentration in the vicinity of the interface that may decrease the relative contribution of these “slow” tracers to the cross-correlation curve. As the experiments were performed in aqueous solution, the possibility for electrostatic repulsion between tracer particles and the micro-channel walls should be considered . Such electrostatic repulsion can be screened using high ionic strength.
Therefore, we carried out experiments using aqueous solution of K2HPO4 with different concentrations. For a given penetration depth d p, the value of v(τ M) decreases with increasing ionic strength (Fig. 5 ). This is a consequence of the increased tracer concentration in the proximity of the wall. The Debye length λD, which characterizes the range of the electrostatic repulsion force at given salt concentration was evaluated . The values are shown in Fig. 5. At 1-10 mM the electrostatic repulsion is sufficiently screened and a further increase of the salt concentration does not change significantly the velocity profiles.
Another factor that may influence measured cross-correlation curves is tracers diffusion. If the flow time of a tracer between the two observation volumes is long, a tracer that has entered the first volume at a certain position may diffuse further away in both lateral and normal direction and “miss” the second observation volume. This effect will lead to a decrease of the amplitude of the cross correlation function for fastly diffusing tracers. In addition, tracers that are very close to the channel wall in the first observation volume can only diffuse away from the wall (in normal direction) and therefore will be carried downstream at a larger velocity by the ambient shear flow. This should lead to a higher velocity for the fast diffusing tracers.
In order to explore experimentally the effect of tracer diffusion we have compared three tracers with different sizes and therefore diffusion coefficients. Figure 6a shows the cross-correlation curves measured with dye molecules (Alexa 514, RH = 0.8 nm), quantum dots (Qdot585, RH = 10 nm) and fluorescently labeled PS nano-beads (FluoSpheres, RH = 28 nm). All experiments were done for the same flow shear rate (4500 s−1) and at high salt concentration in order to screen the electrostatic repulsion and insure a uniform tracer concentration in the proximity of the wall. The distance between the two observation volumes was Δs = 1 µm and the evanescent wave penetration depth was d p = 200 nm.
With decreasing tracers size, i.e. increasing their diffusion coefficient, the amplitude of the cross-correlation function decreases. In particular when single dye molecules were used as tracers, a weak maximum in the cross-correlation curve was obtained. Its τM can be determined only with a significant error. This maximum disappeared completely when the penetration depth was less than 200 nm.
The second effect discussed above, i.e. the apparently higher flow velocity evaluated when fast diffusing tracers are used, is also visible in Fig. 6a. The maxima of the cross-correlation curves shift to shorter times (higher velocities) when smaller tracers are used. This is further illustrated in Fig. 6b, where the flow velocities determined from the maximum of the cross-correlation curves are plotted vs. the penetration depth d p. While such type of plots cannot be considered as flow velocity profiles they still contain important information for the dependence of tracer velocity on the distance to the channel wall. In the same graph we plotted (solid line) the expected flow velocity profile for the case of no slip boundary conditions and a shear rate of 4500 s−1; as measured by single focus FCS  in the same microchannel. The flow velocities v(τ M) for a given penetration depth d p are systematically higher than the expected flow velocities (assuming no slip) at distance dp from the interface. Furthermore, extrapolation of the v(τ M) vs. d p plots to d p = 0 shows non-zero tracer velocity at the interface. Again, the diffusion has a major effect and the “wall” velocities are smaller for the slower diffusing tracers. Nevertheless, even in the case of the PS nano-beads a rather high “wall” velocity of around 0.5 mm/s can be extrapolated. Such finding implies either a real boundary slip, which will be highly unexpected for a flow of aqueous solution near hydrophilic surface, or an apparent slip caused by the enhanced migration of the tracers in the flow direction due to the combined effect of diffusion and shear [24,25]. Another way to explore the effect of tracer diffusion is to change the distance between the two observation volumes Δs. If this distance is very small the observation volumes start overlapping and a cross-talk will appear. This will contribute to the so called pseudo autocorrelation . The effect of the pseudo autocorrelation, though, can be easily excluded by subtracting the forward and backward cross-correlation curves  (Fig. 7a ).
Figure 7b compares corrected cross-correlation curves, measured at four different values of Δs = 0.28, 0.5, 1, and 2.4µm. With increasing Δs and therefore increasing flow time the effect of diffusion increases as manifested by the strong decrease in the amplitude of the cross-correlation function. Furthermore, the flow velocity evaluated from the maximum of G(τ) increases with the increase of Δs.
With total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS) information on the flow of a liquid in close proximity (<200 nm) of the interface can be obtained. By tuning the evanescent wave penetration depth, the velocity at different distances to the interface can be probed. In order to extract precise quantitative information for the flow velocity profile, the effect of tracer diffusion and their interaction with the solid surface has to be addressed theoretically or by simulations. The size of the tracer molecules has to be optimized to minimize diffusion and maximize spatial resolution. As an example, we have applied TIR-FCCS to study the flow of aqueous electrolyte solutions near a smooth hydrophilic surface and explored the influence of several important experimental parameters, e.g. tracer size, ionic strength of the solution, and distance between the observation volumes.
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