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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The efficiency of three different biosensor flow cells is reported. All three flow cells featured a central channel that expands in the vicinity of the sensing element to provide the same diameter active region, but the rate of channel expansion and contraction varied between the designs. For each cell the rate at which the analyte concentration in the sensor chamber responds to a change in the influent analyte concentration was determined numerically using a finite element model and experimentally using a flow-fluorescence technique. Reduced flow cell efficiency with increasing flow rates was observed for all three designs and was related to the increased importance of diffusion relative to advection, with efficiency being limited by the development of regions of recirculating flow (eddies). However, the onset of eddy development occurred at higher flow rates for the design with the most gradual channel expansion, producing a considerably more efficient flow cell across the range of flow rates considered in this study. It is recommended that biosensor flow cells be designed to minimize the tendency towards, and be operated under conditions that prevent the development of flow recirculation.

Flow cells facilitate analyte delivery to biosensor surfaces for a range of applications such as detecting pathogenic bacteria [

There are a vast array of designs for flow cells, but the most common systems include an impinging jet of analyte delivered directly onto the sensor surface (

The flow within most flow cells will be laminar (as opposed to turbulent), that is, under a given flow rate the velocity at any given point will be constant. The Reynolds number,

There has been very little work published on the impact of the design and operation of flow cells on the accuracy of biosensor measurement. Rare exceptions are Cooper and Compton [

Techniques for analyzing such flow systems include both computational and laboratory based approaches. Computational Fluid Dynamics (CFD) simulations provide a numerical method for predicting the flow system response to specified flow conditions and flow system design [

This work presents, for the first time, a complete and holistic application of flow analysis techniques to a biosensor flow cell. It will illustrate the relevance of fundamental flow principles and flow cell design to biosensor operation. It also investigates flow cell response to variations in design and prevalent flow conditions. Finally it presents a framework for the design and use of flow cell systems to the sensor community. This has been achieved through a combination of experiments and validated CFD simulations.

This work determines (both experimentally and computationally) the efficiency of the flow cell in reaching the composition of the influent. Efficiency is assessed both in terms of the volume of influent and the time required for the process. For this study, a model flow cell has been designed to (ultimately) accommodate a biosensor constructed upon a screen printed electrode for which the working, reference and counter electrodes are contained within an 8 mm diameter circular region (e.g., the Dropsens C223AT electrode [

The entire flow chamber was 30 mm in length and consisted of small rectangular flow channels of 1 mm joining the inlet and outlet ports to a wider central region (_{1}^{3} + _{2}^{2} + _{3}_{1}^{3}), _{2}^{2}), and _{3} = 0, and subject to the size constraints given above, with

The experimental flow cell was manufactured from two transparent PMMA blocks of dimensions 60 × 30 × 10 mm with a 1.5 mm thick PTFE gasket placed between them (_{20}H_{10}Na_{2}O_{5}) was used as a model analyte, allowing quantification of the analyte concentration within the flow cell by measurement of fluorescence intensity. A mercury lamp (Dolan Jenner MHR 100, Boxborough, MA, USA) fitted with a fiber optic light guide was positioned to shine vertically upwards through the flow cell. A pair of bandpass filters located before (CW 490 nm ± 2 nm FWHM 10 nm ± 2 nm) and after (CW 520 nm ± 2 nm FWHM 10 nm ± 2 nm) the flow cell ensured that only light emitted by the sodium fluorescein (CW 515 nm) reached a CCD monochrome camera (Adimec 1000 m, Eindhoven, The Netherlands) attached to a monocular microscope. Images were recorded in AVI format using LabVIEW 8.0 (National Instruments, Austin, TX, USA) at a rate of 25 frames per second. Tests using solutions of different concentrations (0–100 μM) showed a linear relationship between the light intensity and the concentration of the fluorescein sodium salt solution within the flow cell.

Prior to the experiment, the flow cell was filled with deionized water. The experiment commenced with the simultaneous start of image capture and the pump containing fluorescein sodium salt solution at a predetermined flow rate (1 or 10 mL/min). Experiments were run until no change was observed between subsequent images; this took between 35 and 165 s depending on flow rate and flow cell geometry. Selected frames of the video sequence were processed using Matlab (Mathworks, Natick, MA, USA). Each pixel within the flow domain was analyzed to determine a scaled concentration, _{ratio}_{0} is the background intensity of that pixel at the start of the flow experiment and _{end}

Numerically, the response of the flow cell is studied using the time-dependant advection-diffusion equation for an incompressible flow. This allows simulation of transport of a dilute species (in this case sodium fluorescein) through a solvent (water) due to advection and diffusion:

Transport due to diffusion is controlled by the gradient in concentration at any given location and regulated by the diffusion coefficient of the analyte within the solvent. Transport due to advection is governed by the underlying flow field. This is determined through solution of a steady state Navier-Stokes Equation, subject to appropriate boundary conditions, which models the laminar fluid flow:

For this study, the underlying equations were solved using the finite element method [

A 3-dimensional geometric model was built to match the experimental apparatus. The flow domain was represented by ∼100,000 tetrahedral elements.

The steady state flow equations were then solved subject to an appropriate set of boundary conditions: a volumetric flow inlet boundary condition (to match that within the experiment), a pressure boundary condition (0 Pa) at the outlet of the flow cell and a no-slip condition applied along the solid walls. The physical properties of the fluid were assumed to be those of pure water at 20 °C (density 998 kg/m^{3} and viscosity 1 × 10^{−3} Pa·s). The independence of the solution from the problem discretization was ensured by repeatedly solving the problem using a progressively finer computational mesh until a robust solution was obtained.

The advection-diffusion equation (^{−10} m^{2}/s to match that of sodium fluorescein in water [

A flow rate range of 0.1–10 mL/min was simulated in the numerical models (

Results for the circular cell design under a flow rate of 10 mL/min demonstrate that there is very good agreement between the experimental and computational techniques employed in this study (see

The concentration ratio maps in

The variation in the flow pattern with flow cell geometry and flow velocity was investigated using the numerical model (

The impact of eddy development on the mean analyte concentration ratio within a flow cell was explicitly considered for the iCell (

As the analyte concentration in the flow cell approaches the influent concentration asymptotically, the most appropriate way to evaluate the performance of a flow cell is to compare the time and/or flow volume required to reach some pre-determined proportion of the influent concentration in the cell (the cell concentration ratio, or CCR) over a range of flow-rates appropriate to practical operation. The performance of the three channel flow cells for a CCR of 99% and a range of flow-rates is shown in

At all flow rates considered in this study some regions within any given cell will reach a given concentration of analyte quicker than others (e.g., locations aligned with the inlet respond more quickly than locations towards the edge of the cell). This is illustrated in

The performance of a commercially available impinging jet type flow cell (

There are clear advantages to operating a flow cell close to the optimum point prior to eddy development, as the cell response will be independent of the diffusion coefficient of the analyte, and relatively insensitive to slight variations in flow rate. For the circular flow cell this optimum occurred at a flow rate of 1 mL/min, when the total influent volume was 0.85 mL and the injection time was 51 s. For the iCell the optimum was at a flow rate between 1.75 and 2.5 mL/min, when the total influent volume was between 0.75 and 0.81 mL and the injection time was between 26 and 20 s. Thus the iCell performed best out of the cell geometries considered, both in terms of the smallest influent volume required (least waste produced) and shortest injection time (the period for which the biosensor is exposed to a varying analyte concentration).

The selection of an appropriate operating protocol for a flow cell will depend on a proper understanding of the biosensor kinetics. The rates of ligand-receptor association (k_{a}) and dissociation (k_{b}) must be considered relative to the flow cell response rate. Where k_{a} and k_{b} are of similar magnitude whether fast or slow relative to the flow cell response rate, e.g., [

Sensors where ligand-receptor association is fast in comparison with ligand-receptor dissociation are more problematic. The ratio k_{a}/k_{b} (equal to the distribution coefficient, K_{d}) is a measure of how the analyte partitions between the sensor surface and the solution when equilibrium is reached. A high k_{a}/k_{b} value implies more analyte association with the sensor for a given solution concentration than a low k_{a}/k_{b} value. Thus high degrees of surface association, where the sensor becomes less sensitive to differences in solution concentration, can be reached with relatively modest solution concentrations. Operating this type of sensor with modest or high solution concentrations at a high CCR will give a small dynamic range. However, with better understanding of the flow dynamics within the cell it may be possible to operate such sensors as “accumulation sensors” where the flow cell is briefly operated for achievement of a lower CCR value, flow is ceased and the sensor is allowed to equilibrate. The solution concentration can then be estimated from the sensor response using a cell factor.

The final consideration when optimizing a flow cell operating protocol will be the operating environment. Automated systems which are to be deployed remotely in the field, for example, will be constrained by the need to minimize effluent volumes (since this may have to be stored, depending on local regulations) and power usage. Additionally, whilst this article is focused upon the operation of biosensors within a flow cell unit the same principles and derived implications can be applied to other sensor types such as chemical sensors (e.g., potentiometric ion selective electrodes).

The behavior of a flow cell, measured in terms of its response to the incoming fluid, is critically dependant on both the shape of the flow cell and the flow rate of the influent. A badly designed cell or one operated above its optimum flow rate can trigger recirculation (eddies) within the flow. Once this occurs, the time and number of volume changes required to reach some predefined proportion of the influent analyte concentration (the cell concentration ratio—CCR) can be larger than that where fluid injection takes place at a lower flow rate. More importantly, outside the optimum range of flow-rates the required number of volume changes to achieve the CCR becomes more sensitive to the flow-rate used.

A range of flow cell geometries have been studied and it has been demonstrated that a flow cell with a smooth profile between the inlet and outlet (the iCell) outperformed (in terms of time to reach the CCR and total flow volume) those flow cells based on circular or square profiles or a commercial impinging jet type design, despite the iCell having the largest internal volume.

Key recommendations for the design and operation of biosensor flow cell systems are:

Select a flow cell design and operational protocol that prevents the development of flow recirculations (eddies) to minimize the volume of fluid and time to reach the CCR. This can be achieved by the combined effect of reducing the rate of channel expansion and contraction, and maintaining a flow rate below which the onset of eddies arise.

In all cases the response of a given flow cell is sensitive to flow-rate and flow domain geometry and thus good flow control is a pre-requisite for repeatable and efficient sensing.

To achieve accurate measurements using biosensors it is important for users to understand that (a) the concentration of analyte within the flow cell will differ from that within the influent, and (b) the time required to reach the CCR is a function of the cell geometry as well as the flow-rate, and thus the flow cell performance must be fully characterized before use.

We gratefully acknowledge the research project funding provided by the Nuclear Decommissioning Authority. Our thanks also extend to David Conroy for technical advice and guidance.

Schematic diagrams of common flow cell design types used with biosensors and other sensor types: (

Schematic plan view of laminar flow in an open channel with a sudden expansion in width, where eddies (a) have developed. Solid arrows indicate direction of advective transport from the inlet to the outlet. Analyte transport from within developed eddies occurs only through diffusion, as indicated by broken-line arrows. Adapted from Acrivos and Schrader [

Experimental flow cell construction (

Performance of the circular flow cell when the flow rate was 10 mL/min: (

Computational results showing (

(

Figure S1 and Videos SV1–SV4.

Supplementary Information (PDF, 151 KB)

Video SV1 (full details listed in Supplementary Information PDF document above) (AVI, 17042 KB)

Video SV2 (full details listed in Supplementary Information PDF document above) (AVI, 6720 KB)

Video SV3 (full details listed in Supplementary Information PDF document above) (AVI, 3532 KB)

Video SV4 (full details listed in Supplementary Information PDF document above) (AVI, 3385 KB)