The Influence of Electrolyte Flow Hydrodynamics on the Performance of a Microfluidic Dye-Sensitized Solar Cell

Featured Application

A microfluidic solar cell with energy storage capability–the solar redox flow batteries (SRFB).

Abstract

The dye-sensitized solar cells microfluidically integrated with a redox flow battery (µDSSC-RFB) belong to a new emerging class of green energy sources with an inherent opportunity for energy storage. The successful engineering of microfluidically linked systems is, however, a challenging subject, as the hydrodynamics of electrolyte flow influences the electron and species transport in the system in several ways. In the article, we have analyzed the microflows hydrodynamics by means of the lattice-Boltzmann method, using the algebraic solution of the Navier-Stokes equation for a duct flow and experimentally by the micro particle image velocimetry method. Several prototypes of µDSSC were prepared and tested under different flow conditions. The efficiency of serpentine µDSSC raised from 2.8% for stationary conditions to 3.1% for electrolyte flow above 20 mL/h, while the fill factor increased about 13% and open-circuit voltage from an initial 0.715 V to 0.745 V. Although the hexagonal or circular configurations are the straightforward extensions of standard photo chambers of solar cells, those configurations are hydrodynamically less predictable and unfavorable due to large velocity gradients. The serpentine channel configuration with silver fingers would allow for the scaling of the µDSSC-RFB systems to the industrial scale without loss of performance. Furthermore, the deterioration of cell performance over time can be inhibited by the periodic sensitizer regeneration, which is the inherent advantage of µDSSC.

1. Introduction

The goals set by the European Commission in the recently launched Green Deal forces member states of the European Union to reduce their greenhouse gas emissions by at least 55% by the year 2030 [1]. Meeting this target will require increasing the binding renewable energy target in the EU’s energy mix to 40%. However, the efficient use of renewable energy resources, such as solar, wind, or tidal, requires mitigation or fulfilling the mismatch between its inherent intermittent energy production and the electricity demand. The current progress in photovoltaic technology (PV) has led solar energy to be foreseen as the foremost source of renewable energy. According to the NREL chart of the highest confirmed conversion efficiencies for research cells [2], their up-to-date values range from 25.5% for perovskite and 26.7% for crystalline SI cells through 29.5% for perovskite/Si tandem cells, 29.1% for GaAs single-junction, and 39.3% for multijunction cells, all measured under non concentrated sunlight conditions. Although there is still a lot of room to optimize the efficiency of solar cells, the main problem is their variable output, depending on the conditions of sunlight. They can produce excess energy at some times, and then none at others. Many kinds of energy storage systems have been employed to compensate for the load on the power grid. One of them is redox flow batteries (RFB) that have emerged as relevant candidates to address sustainable energy generation. RFBs have a reasonably good energy density, flexible modular design and operation, excellent scalability, moderate maintenance costs, and long-life cycling. Their most attractive characteristics are the decoupled nature of their volumetric power and energy densities and their low self-discharge rate, making them suitable for long-duration storage [3].

The emerging technology that combines PV and RFB in one system is the solar redox flow battery (SRFB) [4]. It is a promising energy generation and storage technique that is cost-effective and balanced, with the electricity demand way of energy production. The system has been engineered in two architectures [5], (1) where the photoelectrode is integrated directly with RFB and the redox couples of RFB are shared with the photovoltaic cell (PVC) [6,7,8] (Figure 1); and (2) where PVC with an electrochemical module of RFB are stacked together, but each operates autonomously [9,10,11] (Figure 2). Figure 1 and Figure 2 show schematically the structure of SFRBs with photoanodes built on the basis of an n-type semiconductor, which introduces electrons to the working electrode.

For semiconductor-liquid junction cells (Figure 1), energy-level matching between semiconductors and redox species is crucial, as it determines the photovoltage of such cells. On the other hand, the stacked system of PV and RFB cells is integrated by their internal electrical junction only, and the redox couple of PV is thus independent of the RFBs redox couples. This configuration is easiest to realize and optimize because the difficulties in the overall device design and voltage matching can be greatly reduced.

Recently, the all-vanadium redox flow batteries (VRFB) get the most scientific and industrial attention [12,13] and are considered a promising candidate for large-scale energy storage systems [14]. Thanks to the ability of vanadium to exist in solution in four different oxidation states, vanadium ions in sulfuric or hydrochloric acidic-water solution are used at both compartments, as catholyte VO₂⁺/VO²⁺ (O_I/R_I in Figure 1 and Figure 2) and V²⁺/V³⁺ (R_II/O_II in Figure 1 and Figure 2) as anolyte. In VRB, the H⁺ ion is exchanged (X⁺ in Figure 1 and Figure 2) through the ion exchange membrane. The membrane is usually made from Nafion polymer. The best current densities were noticed for Nafion N212 [15]. During the charge/discharge cycles in RBFs, catholyte and anyolite are pumped into the stack of electrochemical cells from reservoirs. At the cells, the electrochemical conversion takes place and then catholyte and anyolite are collected back in the tanks.

The current collectors are put together with electrodes, making flow-through or flow-by configurations of cells, while the flow-by configuration is considered to be the best option [14]. The flow-by electrode can be realized in different ways by an interdigitated pattern of channels prepared in a porous electrode material or in the current collector. M. Messaggi and coworkers [16] have analyzed the influence of electrolyte flow hydrodynamics on VRFB performance. The two patterns of channels (Figure 3) were prepared in a graphite current collector, and the VRFB’s performance was examined experimentally and also in CFD simulations. They developed a full 3D model in ANSYS Fluent using several custom user-defined functions (UDFs) for the implementation of the electrochemistry, along with the standard fluid dynamics module.

Earlier, several successful applications of the finite volume method in the VRFB performance simulations have been reported in the literature [17,18,19]. Recently, E. Prumbohm and coworkers [20,21] used STAR-CCM+, a finite volume method package, to investigate the influence of the different flow patterns of electrolytes on the industrial scale VRFB cell performance and the total costs of the device. All of the research results presented in the above-mentioned works lead to the conclusion that channels pattern and electrolyte flow hydrodynamics have a great influence on VRFB performance. As a final result of construction optimization, the total costs of device production were reduced by half while maintaining the assumed efficiency of the device [21].

Another configuration of RFB and fuel cells, which perform to an even larger degree, depends on electrolyte flow hydrodynamics are membrane-less cells, which were originally developed for microfluidic fuel cell systems. The working principles of membrane-less cell designs rely on (a) single or multiphase phase co-laminar flows (Figure 4a); (b) co-laminar flows of electrolytes separated by a flowing stream of a supporting electrolyte (FSE) (Figure 4b); (c) half-cell reaction involving the deposition of solid active species on an electrode surface; and (d) the application of ionically inert solid separators [22].

The (a) and (b) system configurations are highly dependent on microflows hydrodynamic and the correct selection of the hydrodynamic conditions and channel geometry, which allows for the limitation of the unfavorable phenomenon of electrolyte mixing. It is worth emphasizing here that the advances in the theory of the fluid flow and cell design of microfluidic fuel cells (MFC), rather than in electrolyte and electrode kinetics, have been responsible for the continuous performance improvement (from power densities of <1 to >700 mW/cm²) in the period of 2004–2016 [22]. Such impressive growth of MFC performance was possible to be achieved, among other means, through the use of numerical methods in the analysis of microflows and parameters influencing them [23].

The first integrated with the RFB type of PVC was dye-sensitized solar cell (DSSC) [24,25,26]. The construction and working principle of the static n-type dye-sensitized solar cells is presented in Figure 5. DSSCs belong to the group of thin-film solar cells. The working electrode, sensitizer (dye), redox-mediator (electrolyte), and the counter electrode are four key elements of a DSSC [27,28]. In DSSC, a photon is absorbed by a photosensitizer adsorbed on nano-TiO₂ (semiconductor), generating an exciton (excited electron-hole couple) that self-separates, and the electrons are injected into the conduction band of TiO₂. Then, the electrons are collected on a transparent conducting oxide layer (FTO/ITO). Through the external circuit, electrons reach the counter electrode, where they are conducted to the carbon/nano-Pt layer. The electrons at the surface of the counter electrode reduce $I_3^{-}$ to $I^{-}$. Ions $I^{-}$ are transported through the gap between electrodes in the liquid electrolyte. The regeneration of the ground state of the dye takes place due to the acceptance of electrons from $I^{-}$ ion, $I^{-}$ gets oxidized to $I_3^{-}$ state, and, again, $I_3^{-}$ is transported back through the electrolyte layer to the counter electrode surface. The generation of current in the DSSC is a multi-stage process whose efficiency depends on the series resistance of all of the stages of electric charge transfer. The highest resistance limits the performance of the whole process [29,30]. The sheet resistance of the FTO layer is between 7 and 15 Ω/sq. Thus, this makes the scaling of the device difficult and acts as a limiting factor for an active cell area >1 cm² [27]. To increase the efficiency of the cell, silver fingers can be used to collect the current, but this solution may reduce the stability of the cell. Additionally, the diffusive transport of ions in the electrolyte layer may be the bottleneck, especially when the electrode gap is >50 µm. In this case, the diffusive transport resistances prevail. On the other hand, reducing the electrode gap leads to unstable cell operation and problems with electrolyte leakage. One of the possible solutions is to force electrolyte flow in microchannels placed between electrodes to enhance ion transport by convection. This should allow the gap height between the electrodes to be increased without increasing the mass transport resistance in the electrolyte layer.

G. P. Rutkowski and B. A. Grimes [31] have analyzed the influence of electrolyte flow on the DSSC cell performance. While circulating the electrolyte, they observed the photocurrent improved by 38% and 13% compared to the stationary conditions, depending on the system configuration. In their experiments, the microchannel’s height does not exceed 100 µm, and the active surface area of prepared cells varied between 0.25–1.0 cm², depending on the experiments. The three configurations of microchannels have been tested for the effectiveness of the controlled delivery of the electrolyte: linear (square chamber), series (serpentine), and parallel, obtaining the highest current densities for parallel configuration. Employing microfluidics in degraded devices allowed for the total replacement of the degraded active layer with a fresh payload of dye, resulting in a greater than 100% photocurrent recovery [31].

H. Feng et al. [32,33,34] investigated a microfluidic all-vanadium photoelectrochemical cell for solar energy storage under various operating conditions. The cell consisted of a TiO₂ photoanode, two microchambers with a depth of 500 μm, a Nafion 115 membrane separating microchambers, and a Pt coated carbon paper (counter electrode). The active surface area of the cell was 1.0 cm². They obtained more than twice as high values of photocurrent per unit surface area than in standard H-type cell configurations.

The new class of photovoltaic cells with an inherent opportunity for energy storage is an attractive direction of the development of so-called green energy sources, which better balance the resources of the power grid. However, the further development of SRFB and, in particular, DSSC-RFB devices requires some problems to be solved in addition to those well-defined problems related to cell durability and efficiency. Firstly, the scalability of the PV module has to be improved. Most of the research presented in the literature is based on the results obtained for cells with an area of a fraction of a square centimeter, while the efficiency of the cell is known to decrease with increasing surface area. Secondly, the construction of cells must allow the passage of much larger currents without loss of efficiency. We expect that, as in the case of fuel cells, microfluidic DSSC-RFB devices can bring a significant improvement in the efficiency of large-scale cells if they are properly designed. CFD models are a proven utility tool that can facilitate this task.

In this paper, we intend to analyze the phenomena accompanying laminar flows in µDSSC channels using numerical and experimental methods. The research will focus on the issues related to the upscaling of the DSSC system. The microflows hydrodynamics will be investigated using the micro Particle Image Velocimetry (μPIV) method for several channels geometries and numerically by means of our open-source lattice-Boltzmann method (LBM) solver-Microflow 3D. Optimized photovoltaic cells with a large active surface and flow-by-channel microstructure will be prepared and the key parameters influencing its efficiency will be analyzed, with particular emphasis on the future integration with the RFB system.

2. Description of the LBM Model and Simulation Parameters

All numerical models of RFB systems available in the literature use solvers of the control volume method to solve boundary value problems. The boundary value problems are formulated as a system of partial differential equations (PDE) of the conservation of macroscopic properties (mass, momentum, and energy) complemented with the initial and boundary conditions. These models belong to the so-called category of macroscopic models of fluid. In our study, we will formulate the model of microflows in the framework of the lattice-Boltzmann method (LBM), which, instead of solving conservation equations of macroscopic properties, uses the Boltzmann Transport Equation (BTE) to describe the statistical behavior of a thermodynamic system in the nonequilibrium state.

The BTE equation arises from Boltzmann’s kinetic theory of gases, which belongs to the category of mesoscopic models of fluid systems. Contrary to molecular dynamics (microscopic fluid model), where molecular movement is governed by Newton’s dynamics, LBM does not track individual molecules. Rather, it tracks distributions or representative collections of molecules [35]. The LBM is not just another numeric algorithm of solving the PDE’s system but rather a new way of describing the physical state of matter and dynamic systems. Although LBM was devised with the specific intent of providing an alternative to the discretization of the NSE, with his strong physical background, it is now a full-featured method whose applicability goes beyond the macroscopic physics of fluids described by NSE [36,37].

For computational microfluidics, LBM presents several advantages that go directly out from its mesoscopic nature, including the physical representation of microscopic interactions and the easiness of dealing with complex boundaries. In addition, LBM-like algorithms have been developed to solve microfluidics-related processes and phenomena such as heat transfer, electric/magnetic field, and diffusion [38]. However, in most publications, the resolved microflow cases relate to simplified geometries selected for the code validation or algorithm performance analysis, with no practical reference to the real processes and devices. In the study, we exploit the LBM to perform an in-depth analysis of microflows in micro photovoltaic DSSC cells to explain the underlying phenomena and their influence on cell performance and scalability.

For a description of the fluid flow phenomena in microchannels, we use the discretized in momentum ${ℝ}^3$ space on the D₃Q₁₉ lattice form of BTE [39] with an external body force term. The collision operator was approximated with the most popular Bhatnagar-Gross-Krook model [40], while the external body force term was approximated with the He-Shan-Doolen scheme [41]. A detailed description of the model and an analysis of its accuracy, as well as the results of the validation of the algorithm, were discussed in detail in our previous publication [42]. We used our open-source Microflow 3D (MF3D) solver of the CFD/LBM method to solve boundary value problems [43]. The model solution was obtained for three full-3D periodic channel geometries; periodic segments of numerical grids are presented in Figure 6, Figure 7 and Figure 8. In Figure 6, the periodic segment of the serpentine channel is shown. In Figure 7, the hexagonal channel grid segment is presented, while in Figure 8, the circular channel grid segment is shown.

In Figure 6, Figure 7 and Figure 8b,c the details of the grid are shown in the close-up views that present the grid nodes distributions on the grid’s walls, edges, and corners. All the channels have a rectangular cross-section and dimensions similar to the experimentally investigated systems. We applied “periodic boundary” nodes (type 4) at the inlet and outlet from the geometries, which are located on the left/right sides of segments, and “velocity 0” (type 40–46) at the top and bottom surfaces and at the flat parts of curved and oblique boundaries (Figure 6c and Figure 8b). At edges and corners, the full-way bounce-back (type 61) nodes are applied (Figure 6b, Figure 7b,c and Figure 8b,c). A detailed description of the algorithms associated with the specific type of node can be found in the MF3D documentation [44].

A summary of the grid statistic, solution parameters, and performance data is collected in

Table 1. Grid statistics, solution parameters, and performance data.

Parameter/Grid	Serpentine	Hexagonal	Circular
Grid parameters
Total number of computational nodes	7,230,630	858,319	876,339
Number of fluid (type 1) nodes	5,866,128	690,651	705,879
Number of full-way bounce-back (type 61) nodes	32,082	11,094	9128
Number of “velocity 0” (type 40) nodes	1,326,894	153,478	158,318
Number of “periodic” (type 4) nodes	5526	3096	3014
The ratio of boundary nodes to the total number of computational nodes (%)	18.87	19.53	19.45
Solution parameters
The free solution parameter: relaxation time, τ	1.0	1.0	1.0
Convergence criteria: the mean scaled residue of the average velocity for subsequent iterations	1 × 10−8	1 × 10−8	1 × 10−8
Convergence criteria: the mass flow error for subsequent iterations, (%)	0.1	0.1	0.1
Performance data 1
Total number of iterations (time steps) needed to obtain converged solution	33,600	1500	1500
Computation time (s)	6778	33.3	33.6
MLUPS (Million Lattice Updates per Second)	39.5	39.5	39.7

¹ A personal computer equipped with Intel Core i9-9900K CPU 3.60 GHz × 8, 32 Gb of DDR4 3000 MT/s, working under the control of Linux Mint 19 Tara, was used for solving the model.

.

In MF3D, all of the solution parameters are collected in two text files: case_params.cfg and thread_params.cfg. The thread_params.cfg file links boundary surfaces and selected grid volumes (called threads) that are defined in separate text files with boundary or initial conditions. All of the configuration and geometry files necessary to run the simulations are available in the additional resources of the article (Supplementary Files: S1—the MF3D serpentine channel case, S2—the MF3D hexagonal channel case, and S3—the MF3D circular channel case). The detailed description of the MF3D case preparation protocol was provided in our previous article [42]. The flow simulations were performed for the force-induced fluid flow. The force density vector was set to 9810 (N/m³) along the x-axis direction, and its constant value was fixed for the whole fluid region of the hexagonal and circular grids, while in the serpentine grid the force was set only for the red-marked region in Figure 6a along the x-axis direction.

A quick glance at the performance data collected in Table 1 leads to the conclusion that a commonly used measure of code performance, MLUPS, says little about the real computation time of real-world steady-state solutions. The hexagonal and circular grids are nearly the same and give the same computation time. The serpentine grid is about 8.5 times larger than the other two. However, the computation time is 200 times longer (!) for the same solution parameters and convergence criteria as set for the hexagonal and circular grids, while the MLUPS is the same in all cases. This is because the shape of the channel is elongated, and 22.5 times more iterations are needed to propagate solution values along the grid. Long channels with low heights are standard elements of the construction of microfluidic devices. We can expect that a similar unfavorable phenomenon will accompany all of the calculations of microfluidic systems. The multigrid method or specially accelerated LBE algorithms, dedicated to steady-state solutions of flows, could solve the problem with the simulation performance drop [45].

3. Experimental Setup for Measurement of Microflows Hydrodynamics

To study the microflows hydrodynamics experimentally, we used the micro Particle Image Velocimetry (µPIV) technique. The µPIV method is a quantitative method that can be used to characterize the performance of microfluidic systems with spatial resolutions better than one micron [46]. We can distinguish between two types of µPIV systems: those capable of measuring two-dimensional, two-component velocity fields (2D2C) and more sophisticated systems that are able to measure volumetric three-component (3D3C) fields [47]. The planar 2D2C configuration consists of an inverted microscope, a single or double CCD/CMOS camera, and a pulsed laser or continuous LED light source [48]. It is also possible to use configurations with the stereoscopic microscope. In contrast with the standard PIV method, the light source illuminates the whole volume of fluid with suspended tracer fluorescent particles in it. The major difficulty arises from the fact that, in contrast with standard PIV, where the measurement plane is defined by a laser light sheet, the measurement plane in µPIV is determined by the depth of focus of the optical system. Further, the amount of light scattered by the particles reaching the camera sensor must be sufficient to register their displacements. At the same time, the use of high-speed cameras with short exposure times, tracer particles of a small diameter, and a large magnification of microscope lenses drastically reduce its amount. The main steps of the PIV measurement technique involve (1) twice imaging of flowing in a channel suspension of tracer particles, (2) the evaluation of the particle image displacement with digital image processing algorithms, and (3) the conversion of the particle image displacement into physical space by a proper calibration.

We have used in our investigations a slightly different configuration of the 2D2C measurement system. As the surface area of microfluidic DSSC is relatively large and the channels are wide, we cannot use the inverted microscope equipped with large magnification lenses. The schematic view of our μPIV system configuration is shown in Figure 9. Our system consisted of a standard stereoscopic microscope Motic K-400L (1) equipped with a Common Main Objective (CMO) (2) and Moticam 2300 CMOS camera (3). The specially designed microfluidic systems (4) with optically transparent top and bottom surfaces, made from poly(methyl methacrylate) (PMMA) with the same channel’s configuration as used in our DSSC chips were used in µPIV experiments. The microsystem placed on the transparent microscope stage (5) was illuminated from the bottom by the LED illuminator consisting of 60 diodes placed on the ring shape (6). This configuration formed dark-field-like lighting conditions with bright, well-lit tracer particles on the dark background. The depth of field of the lens covered the entire depth of the channel. To find the mean fluid velocity in the XY plane, neglecting the fluid velocity gradient along the Z-axis, we have used polyamide round particles with a large diameter of 50 µm PSP-50 (Dantec Dynamics, Denmark), which was about half of the microchannel height (120 µm). The microsystem was connected with a syringe pump (7) that delivers the suspension of tracer particles to the microsystem at a constant flow rate. The suspension flowing out of the microsystem was collected in the reservoir (8). During the experiments, we recorded short films that were captured and saved on the computer (9) as AVI files. The movies were split into frames, and the pairs of images were analyzed in the PIVlab software [49].

In Figure 10, the microsystems used in the study of flow are presented. The height of each microchannel was 0.12 mm and the straight-line length was 41 mm (distance between the liquid supply points).

The other dimensions of the channels were as follows: (a) the serpentine channel width was 4.3 mm, the total channel length was 110.8 mm, the height of segment was 15.3 mm, the width of the segment was 10.0 mm, the length of the straight section of the channel was 5.8 mm, the arc radiuses were 4.5/0.3 mm (outer/inner); (b) the hexagonal channel maximal width w_max = 4.5 mm, the minimal width w_min = 2.3 mm, the segment length was 4.0 mm; (c) the circular channel w_max = 4.2 mm, w_min = 1.7 mm, and the segment length was 4.0 mm.

4. Microfluidic Dye-Sensitized Solar Cells Fabrication and Tests Conditions

The PDMS-free prototypes of μDSSC were fabricated by a laser ablation technique using a commercially available system (Versa Laser VLS 2.30, Universal Laser System Inc., Scottsdale, AZ, USA) equipped with a 30 W CO₂ (wavelength 10.6 µm) pulsed laser source and a high-power density focusing optic (HPDFO). The system was used for cutting through, drilling, and engraving construction materials: glass substrates, adhesive film layers, and PMMA sheets. The schematic drawing of the cell assembly is shown in Figure 11b. The device consists of five layers: the photoanode with a fluorine-doped tin oxide (FTO) layer (4) and the silver highly conductive paths (5), the adhesive film layer (2) of 120 µm thickness (7955 MP, the acrylic adhesive 200 MP 3 M, St. Paul, MN, USA), the conductive (FTO) glass counter electrode (3) with the silver highly conductive paths (5), the adhesive film layer (2) of 120 µm thickness, and the PMMA made base (1) of 3 mm thickness. The polyethylene tubing 1.09/0.38 mm (OD/ID) was glued into holes after folding the layers.

The fabricated DSSCs were of n-type configuration, whose operation principles were presented in Figure 5. The conductive glass substrates TCO13–15 (15 Ω/sq) of 1.3 mm thickness, coated on one side with fluorine-doped tin oxide, were purchased from Solaronix (Switzerland). Before applying functional layers, the glass substrates were cleaned in deionized water in an ultrasonic bath and rinsed in isopropanol. The low electrically resistive silver paths were prepared on the FTO surfaces using a silver glass frit paste Elcosil SG/SP (Solaronix, Switzerland). The photoanode active layer of 1.5–2.0 µm thick was prepared onto the FTO glass substrate using nano-TiO₂ precursor Ti-Nanoxide T600/SC–the anatase particles of dia. 15–20 nm suspension (Solaronix, Switzerland) and stained for 72 h by soaking after firing in the anhydrous ethanol solution (0.5 mM) of Ruthenium-based and organic dyes mixture (1:1 mol): N719 (Ruthenizer 535-bisTBA, CAS: 207347-46-4), and SQ2 (5-carboxy-2-[[3-[(2,3-dihydro-1,1-dimethyl-3-ethyl-1H-benzo[e]indol-2-ylidene)methyl]-2-hydroxy-4-oxo-2-cyclobuten-1-ylidene]methyl]-3,3-dimethyl-1-octyl-3H-indolium) (Solaronix, Switzerland). Sensitized photoanode was washed in isopropanol and dried at room temperature. The counter electrode was prepared on the FTO glass substrates by the deposition of a thin layer of nano-Pt catalyst Platisol T (Solaronix, Switzerland). Each thin layer was deposited onto the substrate using a spin coater (Laurell Technologies, North Wales, PA, USA) according to the standard procedures recommended by the reagent supplier. The fabricated prototype of µDSSC with the serpentine microchannel is shown in Figure 11a.

The acetonitrile-based low viscosity electrolyte with redox couple iodide/tri-iodide (30 mM acetonitrile solution) with additives of ionic liquid, lithium salt, pyridine derivative, and thiocyanate: Iodolyte HI-30 (Solaronix, Switzerland) was used in the experiments. Ionic and electrical conductivity measurements were carried out at room temperature using Voltcraft multimeters (Conrad Electronic, Switzerland). DC Electrical Load Rigol DL3021 (China) was used to obtain the I-V curve. The microfluidic DSSC was examined at room temperature and lighting conditions of LED 100 mW/cm² with CRI > 95, using the led reflector WIFI 100B (Fomei, Czech Republic) as a light source.

5. Results and Discussion

5.1. Algebraic Solution of the Navier–Stokes Equation for a Duct Flow

In dealing with the liquid flows in minichannels and microchannels of the characteristic length-scale above 1 µm, in the absence of any wall surface effects such as the electrokinetic or electroosmotic forces, the flow is not expected to experience any fundamental changes from the continuum approximation employed in macrofluidic applications [50]. In this case, the fully developed flow hydrodynamics of a fluid can be described by the Navier-Stokes equation (NSE) or Boltzmann equation (BE) with the same relevance. However, we have to remember that the traditional NS model of fluid flows with no-slip boundary conditions works only for a certain range of the governing parameters. (1) The fluid is a continuum, which is satisfied when more than 1 million molecules are located in the smallest volume in which appreciable macroscopic changes take place. This is the molecular chaos restriction. (2) The flow is not too far from thermodynamic equilibrium, which is satisfied if there is a sufficient number of molecular encounters during a small time period, compared to the smallest time-scale for flow changes. During this time period, the average molecule would have moved a small distance compared to the smallest flow length scale [51]. In the free-molecule flow regime, or when the slip flow must be considered (Kn > 0.001), the alternative continuum equations (e.g., Burnett) are needed to close the NE, while the BE is still applicable.

Spiga and Morini (S&M) proposed an algebraic solution of the NSE for the fully developed laminar flow of Newtonian fluids in the rectangular duct, which was derived using the finite Fourier transform [52]:

$$\frac{u\left(x\text{'},y\text{'}\right)}{P}=v\left(x\text{'},y\text{'}\right)=\frac{16\beta { }^2}{{\pi }^4}{\displaystyle \sum }_{i\_odd}^{\infty }{\displaystyle \sum }_{j\_odd}^{\infty }\frac{sin\left(i\pi \frac{\xi }{a}\right)sin\left(j\pi \frac{\eta }{b}\right)}{ij\left(\beta { }^2{i}^2+j^2\right)}$$

(1)

where

$$P=\frac{a^2}{\mu }\left(\frac{-dp}{d\zeta }+\rho g\zeta \right)$$

(2)

and a and b are the total channel width and height, respectively, along the ξ and η axes, while pressure drop dp is along the ζ axis (Figure 12a). μ is the fluid dynamic viscosity. The dimensionless coordinates are x’ = ξ/a (0 ≤ x’ ≤ l) and y’ = η/a (0 ≤ y’ ≤ β, where β is the aspect ratio b/a). Hence, the average velocity u_m over the domain cross-section perpendicular to the direction of fluid flow ζ can be expressed as:

$$\frac{u_m}{P}=v_m=\frac{64}{{\pi }^6}{\displaystyle \sum }_{i\_odd}^{\infty }{\displaystyle \sum }_{j\_odd}^{\infty }\frac{1}{i^2{j}^2\left(i^2+\frac{j^2}{{\beta }^2}\right)}$$

(3)

The commonly used simplified Purday’s model (PM) [53]:

$$\frac{u\left(x,y\right)}{u_{max}}=\left[1-{\left(\frac{y}{b/2}\right)}^n\right]\left[1-{\left(\frac{x}{a/2}\right)}^m\right]$$

(4)

approximates the velocity profile of fluid flowing in the z-direction of the rectangular duct (Figure 12b), with the aspect ratio β ≤ 0.5, and where n = 2 and m takes on values from 2.37 for β = 0.5 to ∞ for β = 0. The integration of Equation (4) over the duct cross-section yields:

$$\frac{u\left(x,y\right)}{u_m}=\left(\frac{m+1}{m}\right)\left(\frac{n+1}{n}\right)\left[1-{\left(\frac{y}{b/2}\right)}^n\right]\left[1-{\left(\frac{x}{a/2}\right)}^m\right]$$

(5)

and

$$\frac{u_{max}}{u_m}=\left(\frac{m+1}{m}\right)\left(\frac{n+1}{n}\right)$$

(6)

where u_m is the average velocity in the channel and u_max is the maximal fluid velocity at the middle of the channel’s height. For β = 0, the u_max/u_m = 1.5, which is the well-known value for the laminar flow between two parallel plates [54].

Natarajan and Lakshmanan [55] proposed the empirical equation for m and n calculation:

$$m=1.7+0.5{\beta }^{-1.4}$$

(7)

and

$$n=\{\begin{array}{l}2 for \beta \le 1/3\\ 2+0.2\left(\beta -1/3\right) for \beta >1/3 \end{array}$$

(8)

In Figure 13a, calculated from Equations (1) and (3), the normalized velocity profile u(x,y)/u_m for the channel’s height of 0.12 mm and the width of 4.3 mm in the dimensionless coordinate system (Figure 12b, −0.5a < x < 0.5a and −0.5b < y < 0.5b) is compared with the profile calculated from Equation (5). The mean and median differences between the two models were, respectively, 0.01158% and 0.4746% (SD of divergence 1.8416%). The distribution of divergence between the velocity profiles calculated from the models is presented in Figure 13b. The biggest discrepancies are observed only close to short walls, around 15%. Both models predict u_max/u_m values in the middle of the channel’s height close to the 1.5 limit (1.5269 and 1.5192, respectively, for the S&M and PM models).

In Figure 14, the normalized velocity u/u_m profiles in the middle of the channel’s height and normalized y-mean velocity u_my/u_m profiles are compared for both models. For both profiles, the difference between the two models is really small (0.074% and 0.11%, respectively, for u/u_m and u_my/u_m) and noticed only close the side walls. For 94% of the channel width, the y-mean velocity is close to the channel’s mean velocity u_my/u_m ≈ 1.0, which results in the ratio u_max/u_my being equal to u_max/u_m. We have defined the y-mean velocity as the mean value for the entire height of the channel at the given point. The µPIV system we have used measures the u_my rather than the local velocity. In our further analysis, we will normalize the values of local velocity magnitude obtained from simulations and µPIV by the average velocity in a channel. The u_m was calculated for the numerical data as a surface integral of local velocity magnitudes divided by the surface area of the cross-section, while, for experimental data, as the arithmetic average of measured velocity magnitudes along the cross-section line. Those u_m values are convergent to the values of u_m calculated as the ratio of volumetric flow rate to the channel’s cross-section area at the limit of an infinite number of points.

It is interesting for the further system scale-up process analysis to distinguish how large the discrepancies from the fully developed velocity profile are observed in microchannels; therefore, the simulation and experimental results will be compared with the S&M model. All calculations were performed in Matlab. The calculation script is available in additional resources of the article (Supplementary File S4).

5.2. The Results of Microflows Hydrodynamics Simulations

In Figure 15, the normalized velocity distributions, velocity vectors, and velocity streamlines in the middle of the height of a channel for three channels’ configurations are shown.

For velocity normalization, we used the mean values of u_m calculated for the whole channel’s segment. As the channel’s cross-section area changes in hexagonal and circular geometries, we used averaged values of u_m for these configurations.

$$u_m=\frac{u_{m_{min}}+u_{m_{min}}\frac{w_{max}}{w_{min}}}{2}$$

(9)

where u_{m_min} is the mean velocity at the cross-section 3 (Figure 15) and w_min and w_max are the channel’s widths, respectively, at inlet and cross-section 3. The values of u_m [m/s] calculated from simulated data, used for normalization, were 1.664 × 10⁻³, 13.11 × 10⁻³, and 15.50 × 10⁻³, respectively, for serpentine, hexagonal, and circular channels.

In all of the channel configurations, the regions with high-velocity magnitudes exist red to yellow color marked in Figure 15, regardless of whether the contractions occur in the channel geometry, like in circular or hexagonal configurations, or not, like in the serpentine channel. It is quite surprising that, in the case of the serpentine channel, fluid velocities four times higher than the average value occur in the bend. Additionally, the stagnant region occurs in all of the channels (navy blue marked). The circular-shaped channel appears to be the worst configuration, with the greatest observed velocity gradients across the channel. In Figure 16, the velocity profiles across the channels are compared. The courses of the profile lines are shown in Figure 15.

For the hexagonal and circular channels (Figure 16b,c), we observe similar axisymmetric profile plots with inlet “buffalo horns-like” shapes caused by channel contractions. The velocity gradients are higher for circular configuration, while, for both cases, the maximal values of u/u_m are about two times higher than predicted by the S&M model for fully developed duct flow. For the serpentine duct (Figure 16a) the velocity distributions are much more uniform, and the velocities, excluding the small part of the bend, are close to those predicted by the S&M model values (profiles 3 and 4).

5.3. The Results of Analysis of Microflows by the µPIV Method

In Figure 17, Figure 18 and Figure 19, the velocity distributions in microchannels experimentally determined by the µPIV method are presented and compared with the results of the LBM simulations and with the S&M model. The normalization of µPIV velocity data follows the same procedure as described for simulation data, except that u_{m_min} was calculated as an average value of experimental data for profile 3 (Figure 15). The calculated values of u_m [m/s], used for normalization, were: 1.78 × 10⁻³, 2.28 × 10⁻⁴, and 1.57 × 10⁻⁴, respectively, for serpentine, hexagonal, and circular channels.

The consistency of the experimental results with the simulation results is satisfactory in all cases. For the serpentine channel, the velocities in the bend region (Figure 17c) seem not to be properly determined by our µPIV system configuration. This can be caused by the too low tracer particles concentration in flowing fluid in this region caused by the inertial particle separation phenomena or by the high curvature of the bend geometry, which, combined with high fluid velocities, prevented the proper recognition of tracer particles displacement. Except for this small discrepancy, our simple configuration of the µPIV measuring system properly predicted regions with high and low velocities (dead zones) and the shape of velocity profiles.

The higher fluctuations (noise) of experimental results presented in Figure 18 and Figure 19, compared to the results in Figure 17, come from the increased microscope magnification. The algorithm of the PIV method uses the interrogation regions in which the mean values of tracer particle velocity are determined. With the same size of interrogation regions and the same picture resolution used, the results presented in Figure 17 are more averaged by the PIV algorithm. We have found that the primary source of observed discrepancies between measured and modeled velocity profiles come from the PIV measurement noise and the fluctuations of concentration of tracer particles.

The S&M model is not applicable for the prediction of velocity distributions in the hexagonal and circular microchannels, where the contractions highly influence the velocity profiles, making them highly variable (Figure 18 and Figure 19). For the straight sections of the serpentine microchannel, the S&M model’s compliance with experimental and simulation data is satisfactory (Figure 17d), which allows for its use for the scale-up of the serpentine microchannels of flow-by industrial-scale DSSC-RFB system when the straight sections are much longer than the bend sections.

5.4. Influence of Electrolyte Flow Hydrodynamics on µDSSC Cell Performance

The equivalent circuit of DSSC can be represented as in Figure 20 [56]. In this equivalent circuit, a constant current source J_cell in which electrons are generated by dye molecules is in parallel with an impedance Z₁ associated with electron transfer at the TiO₂/dye/electrolyte interface [57]. The main source of power loss in DSSC is the series resistance, which is the sum of the resistances of photoanode R₁, electrolyte R₂, counter electrode R₃, and transparent conducting oxide (TCO) R_s. Resistance R₂ and capacitance C₂ are elements of Nernst diffusion impedance Z₂, relating to the carrier transport of ions within the electrolyte, while the resistance R₃ and capacitance C₃ are elements of impedance Z₃ due to redox reaction at the platinum counter electrode. The shunt resistance R_sh is responsible for back electron transfer across the Ti${\mathrm{O}}_2$/dye/electrolyte junctions, which is mainly caused by the leakage of current in the case of impurities or defects in the cell manufacturing process. In perfectly manufactured cells, this resistance is large compared to other resistances, which prevents current loss in DSSC.

Under short circuit conditions, the injected electrons flow through the TCO layer to the counter electrode via the external circuit. The resistance of TCO mainly contributes to the series resistance of a cell, so the R_s should be reduced in order to improve the efficiency of DSSC. Although R_s can be decreased with low sheet resistance of TCO, the transmittance of TCO will be reduced at the same time [57]. We have prepared several FTO glass electrodes to investigate the influence of R_s on the DSSC performance. In Figure 21, the experimental results of the surface distribution of resistances of FTO glass with or without silver path are compared.

Silver paths with a thickness of several micrometers reduce the electrical resistance of DSSC electrodes by almost four times and lead to an even distribution of current density on the surface (Figure 21a,c,e,g). Important for the scale-up process is that the resistance of the electrode with silver paths is not dependent on its size, as the silver paths resistance is below 0.1 Ω/cm² and the current is not limited by the resistance of the electrode.

Liu at al. [57] have found that, in a standard DSSC under short circuit conditions, electron transport was predominately affected by the series resistance Rs in TCO and R₃ at the electrolyte/Pt-TCO interface. They found that, compared with R_s and R₃, the diffusion resistance R₂ influences both the electron transfer and charge transport. R₂ not only limited the electron extraction from the TiO₂ layer to the external circuit under the short circuit conditions but also influenced the electron transfer from the TiO₂ film to tri-iodide in the electrolyte. The diffusion resistance of the electrolyte R₂ is relatively small and equals approximately 1.6–3.4 Ω when the thickness of the electrolyte layer is about 60 µm. At the same time, the resistances at the phase boundaries can reach up to 2.9–3.1 Ω and 5.8–21.4 Ω, respectively, for R₃ and R₁ [57]. These resistances are combined with R_s resistance and subsequently affect the deterioration of the efficiency of the cell.

The properly chosen hydrodynamic conditions in the electrolyte can reduce not only the diffusive resistance R₂ but also the interfacial resistances R₁ and R₃, reducing the interfacial electron transfer resistances contained in them. To investigate the effect of the electrolyte hydrodynamics on the microfluidic cell performance, we have analyzed the influence of electrolyte flow rate on the cell efficiency (Equation (10)), fill factor (Equation (11)), and the maximal power of the system (P_mp in Figure 22).

$${\eta }_{cell}=\frac{P}{P_{in}}·100\%=\frac{J_{sc}·V_{oc}·FF}{P_{in}}$$

(10)

where

$$FF=\frac{J_{mp}·V_{mp}}{J_{sc}·V_{oc}}·100\%$$

(11)

J_sc [mA/cm²] is the short-circuit current density, V_oc [V] is the open-circuit voltage, J_mp [mA/cm²] and V_mp [V] are current density and voltage at maximum power P_mp [mW/cm²], and FF [%] is the fill factor, which is the measure of the ideality of the solar cell. FF is the ratio of maximal power P_mp to the theoretical maximal power P_max that would be output at V_oc and J_sc (Figure 22).

The experimental investigations were performed for serpentine, hexagonal, and circular channels. The results of the experiments are shown in Figure 22 and Figure 23. The flow rate was adjusted in the range of 0–40 mL/h.

Each measurement was repeated several (a minimum of three) times. The mean standard deviation (SD) of measured power densities varied between 1–4%, depending on the flow conditions and channel configuration. For the serpentine channel and flow rates between 5 and 20 mL/h, the SD varied between 1–2%, while, for no-flow conditions and the flow rate of 40 mL/h, the SD varied between 3–4%. The highest flow rate was limited by the maximal possible pressure induced by the syringe pump. The value of the cell’s maximal power has changed little with the flow rate but was always noticed at a voltage of 0.4 V (Figure 22) that is mainly influenced by the properties of the dye used and the quality of the manufacture of each cell. We have not noticed the large influence of the channel’s configuration on the µDSSC maximal power density. Only for the hexagonal channel configuration was the measured power density a little bit lower compared to the other two configurations.

The electrolyte flow hydrodynamics have also little impact on the I-V curve shapes (Figure 23). The influence of the electrolyte flow rate on the short-circuit current density, fill factor, efficiency, and the open-circuit voltage is analyzed in Figure 24. For serpentine configuration (Figure 24b) the increase of V_OC from initial 0.715 V to 0.745 V is clearly noticed, while for circular and hexagonal channels (Figure 24a,c), the change of V_OC with the flow rate is not clear. The J_sc in all cases (Figure 24a–c), after reaching the maximal value at a flow rate of 1 mL/h, rapidly decreases to the nearly constant value.

The values of FF clearly rise with the increase of flow rate in the range of 0–10 mL/h for all configurations. For the serpentine and circular configurations, the FF increases about 13%, while, for the hexagonal configuration, as much as 24% (from 28 to 37). The value of FF is nearly constant above the electrolyte flow rate of 10 mL/h.

The primary parameter characterizing the cell is its efficiency. Here, again, the clear dependence of cell efficiency on electrolyte flow is observed only for the serpentine channel configuration (Figure 24b). It rises from 2.8% for no-flow conditions to 3.1% for electrolyte flow above 20 mL/h. For circular and hexagonal configurations, the efficiency of PVCs seems to be constant and not dependent on hydrodynamic parameters and equals about 3.0% and 2.8% for circular and hexagonal configurations, respectively.

6. Summary and Conclusions

The dye-sensitized solar cell integrated with a redox flow battery belongs to a new class of green energy sources with an inherent opportunity for energy storage. It has great potential to resolve the underlying problem of most renewable energy sources—variable, time-dependent energy production, unbalanced with the power grid demand. However, the development and scale-up to the industrial scale of such systems require solving a number of problems, including the development of systems allowing for the passage of much larger currents without a loss of efficiency. One of the possible ways to reach high power densities is microstructurization, which at the same time makes it possible to microfluidically link the photovoltaic and RFB cells. The successful engineering of microfluidically linked systems is, however, a challenging subject, as the hydrodynamics of fluids have a complicated physical background and influence the electron and species transport in the system in several ways, both in the bulk and at interfaces.

In the article, we have analyzed the fluid flow hydrodynamics in three microchannels of serpentine, hexagonal, and circular geometry in several ways: (1) by means of CFD/LBM simulations, (2) by the algebraic solution of the Navier-Stokes equation for duct flow, and (3) experimentally by the µPIV method. The Spiga and Morini algebraic model predicts the velocity profile in a microchannel with a sufficient accuracy only for straight segments of the serpentine microchannel, but, keeping in mind that large scale systems would have long segments of channels, it can be used for the successful scaling of the serpentine system. Although the serpentine channel has no contractions, like hexagonal or circular geometries, the regions with high-velocity magnitudes-about four times larger than average, exist close to the inner bend. Despite this, we can say that those small areas affect the whole channel flow hydrodynamics less than channel contractions in the other two cases, where the discrepancies from the plug-like-flow velocity profile occur in the whole flow domain. The experimentally determined velocity profiles in microchannels, obtained from our simple µPIV measurement system, confirmed our observations based on the results of the calculations. We expect that, in RFBs, the electrolyte flow hydrodynamics will influence the electron and species transport in anode/cathode and membrane interfaces in a similar way as in DSSCs.

The answer to the question of how the flow hydrodynamics influence the cells’ performance is not so simple. The target of flow hydrodynamics optimization in µDSSC is to achieve the evenest distribution of velocities in the channel with high fluid mixing that reduces diffusive resistances. However, such conditions are characteristic for turbulent flows that are hard to reach in the case of microflows. High electrolyte flow rates induce high-pressure drops and shear stress, which, despite the reduction of the mass transport resistances, led to the mechanical destruction of the active layers of electrodes manifested by breaks and can unfavorably lower shunt resistance. As a result, one can observe unstable or deteriorated cell operation or even its mechanical destruction after a short time of operation. The mild laminar flow electrolyte is therefore the preferable operation condition of µDSSCs and SRFBs. The hexagonal and circular configurations are kinds of straight channels with fluctuating width that hydrodynamics is mainly influenced by periodic channel’s cross-section changes. Such configurations may potentially benefit from the additional mixing of the fluid that is forced by the channel’s contractions. Unfortunately, our investigations do not confirm this assumption and lead to the final conclusion that the pug-flow-like velocity profile that is characteristic for microchannels of constant widths leads to stable, balanced, and predictable flow conditions that seem to be most beneficial for PVC. We have noticed that, in the case of hexagonal and circular channels geometry, where high unevenness of flow occurs, the dependence of the main cell parameters on the electrolyte flow rate was unclear, but the performance of the cell under dynamic flow conditions was always higher than in the stationary conditions. On the other hand, a clear increase in cell efficiency was observed with an increase in the flow rate in the range of 0–10 mL/h in the serpentine channel. Above the flows of 10 mL/h, stabilization of the main cell parameters was observed.

From the engineering point of view, the channels’ flow hydrodynamics should be easily predictable (described by the simple algebraic formula) and stable over time (steady-state). The channel configuration has to be also easily scalable without a loss of efficiency and has to be easily and cheaply accomplished. Therefore, several parameters have to be considered when choosing the optimal geometry of industrial scale µDSSC. One of the default configurations is a straight channel. Unfortunately, the straight channel configuration is not simply scalable, and the serpentine channel is in fact the meandering straight channel. The serpentine channel can be inscribed in any configuration of a repetitive segment of a commercial-scale PV module with a high surface utilization and allows for the incorporation of short silver paths that reduce the loss of the efficiency of large-scale PVCs.

In conclusion, although the hexagonal or circular configurations are the straightforward extensions of standard photo chambers of solar cells, those configurations are hydrodynamically less predictable and unfavorable due to large velocity gradients. The serpentine channel configuration with silver fingers would allow for the scaling of the DSSC-RFB integrated systems to the industrial scale without a loss of performance (efficiency and stability). Furthermore, the deterioration of the performance of µDSSC over time can be inhibited by the periodic sensitizer regeneration, which is the inherent advantage of microfluidic PV systems [31]. Our next investigations will follow this finding to construct a highly efficient microfluidic DSSC integrated with an all-vanadium RFB system.