Comprehensive Theory of the Deans' Switch As a Variable Flow

Article pubs.acs.org/ac

Comprehensive Theory of the Deans’ Switch As a Variable Flow Splitter: Fluid Mechanics, Mass Balance, and System Behavior Peter Boeker,*,# Jan Leppert,# Bodo Mysliwietz,+ and Peter Schulze Lammers# #

Institute of Agricultural Engineering, University of Bonn, Nussallee 5, D-53115 Bonn, North Rhine-Westphalia, Germany Labortechniker.de, Hellweg 217, D-45279 Essen, North Rhine-Westphalia, Germany

+

S Supporting Information *

ABSTRACT: The Deans’ switch is an effluent switching device based on controlling flows of carrier gas instead of mechanical valves in the analytical flow path. This technique offers high inertness and a wear-free operation. Recently new monolithic microfluidic devices have become available. In these devices the whole flow system is integrated into a small metal device with low thermal mass and leak-tight connections. In contrast to a mechanical valvebased system, a flow-controlled system is more difficult to calculate. Usually the Deans’ switch is used to switch one inlet to one of two outlets, by means of two auxiliary flows. However, the Deans’ switch can also be used to deliver the GC effluent with a specific split ratio to both outlets. The calculation of the split ratio of the inlet flow to the two outlets is challenging because of the asymmetries of the flow resistances. This is especially the case, if one of the outlets is a vacuum device, such as a mass spectrometer, and the other an atmospheric detector, e.g. a flame ionization detector (FID) or an olfactory (sniffing) port. The capillary flows in gas chromatography are calculated with the Hagen−Poiseuille equation of the laminar, isothermal and compressible flow in circular tubes. The flow resistances in the new microfluidic devices have to be calculated with the corresponding equation for rectangular cross-section microchannels. The Hagen−Poiseuille equation underestimates the flow to a vacuum outlet. A corrected equation originating from the theory of rarefied flows is presented. The calculation of pressures and flows of a Deans’ switch based chromatographic system is done by the solution of mass balances. A specific challenge is the consideration of the antidiffusion resistor between the two auxiliary gas lines of the Deans’ switch. A full solution for the calculation of the Deans’ switch including this restrictor is presented. Results from validation measurements are in good accordance with the developed theories. A spreadsheet-based flow calculator is part of the Supporting Information. he Deans’ switch is a device for the flow switching of GC capillary flows first described by Deans.1,2 The objective of the technique developed by Deans was to avoid mechanical valves in the analytical flow path. Flow switching is particularly challenging when the valves are in the oven at high temperatures. Some of the potential problems are of mechanical nature, material degradation, leakage, and insufficient inertness. In contrast, the valveless technique of the Deans’ switch performs the switching by setting appropriate pressure levels in a network of flow resistors. These control pressures and flows are controlled by valves outside the analytical flow path. In Figure 1 the basic setup of a Deans’ switch is depicted. A simple realization is done by three Y-type press-fit connectors.3 The two outer connectors (1 and 3) are connected to makeup lines from a 3-way solenoid valve. The carrier gas supplied here is directed to one of the two Y-connectors; the other is shut off (in Figure 1 the connector 1 is supplied with carrier gas). The additional carrier gas flow creates a pressure in the connector 1. The GC effluent therefore is directed to the connector 3 and transferred to the respective outlet, e.g. a sniffing port or a FID detector. The other detector is supplied with pure carrier gas. The small restriction 4 is a counter measure against diffusion into the closed makeup line.

T

© 2013 American Chemical Society

Figure 1. Basic setup of a Deans’ switch using press-fit connectors.3

Obviously the flows depend on the pressure levels and the various restrictions. Usually the situation is further complicated Received: May 11, 2013 Accepted: August 27, 2013 Published: August 27, 2013 9021

dx.doi.org/10.1021/ac401419j | Anal. Chem. 2013, 85, 9021−9030

Analytical Chemistry

Article

affect the splitting results. This was the reason for a more detailed calculation. For this research work we have developed the theoretical basis of the calculation of the flows and of the split ratio. In order to validate the theoretical results we have measured the split ratio over a wide range of oven temperatures by means of an n-alkane mixture (C8−C40) with varying elution temperatures ranging from 40 to 320 °C. Figure 2 shows the different operating methods of the Deans’ switch devices. On the left-hand side the operational mode is

by the fact that parts of the restrictions are exposed to the variable oven temperature and parts are constantly heated transfer lines. The classical macroscopic set up of a Deans’ switch is now integrated into microfluidic elements, e.g. used for (flow modulated) comprehensive two-dimensional GC (GC × GC) by Seeley et al.4 These metallic switches possess internal connections of very small dimensions and very low dead volumes. In a recent review by Marriott et al.5 the use of these devices for various multidimensional chromatographic modes, including heart-cut and GC × GC has been outlined. An elaborate system combining conventional, heart-cut, and GC × GC with an olfactory port has been presented by Chin et al.6 In a series of contributions Luong and co-workers7−9 discuss the benefits of microfluidic switching and splitting devices for multidimensional GC, effluent splitting, and comprehensive GC. The Deans’ switch can also be used as a variable effluent splitter. This inherent ability has been described in the contribution of Wang et al.10 They have used the classical setup of Figure 1 and have shown the dependence of the split ratio from the flow rate of the auxiliary flow. Unfortunately the split ratio with this simple setup is not linear with the flow rate. A setup similar to the Deans’ switch was used by Wetzel and Niederwieser11 for heart-cutting GC. The advantage of their construction is the exclusive use of inert GC capillaries. The reported purpose of the splitter is the switching not the splitting of the GC effluent. Nitz et al.12 especially refer to a variable splitting of a GC effluent in connection to a mass spectrometer and an olfactory port. They have modified a ‘live-T’ switching device with the insertion of an MS transfer capillary into a connecting funnel-like piece of capillary. In a recently published paper we have explained and modeled the functional principle of a glass dome splitter.13 This device consists of a central input, two outputs, and two makeup flows integrated in a common volume (the glass dome). Based on the mass balance of the flows and on assumptions according to the flow directions in the glass dome the function of the splitter has been explained. All flow values can be calculated on this theoretical basis. A main advantage of the dome splitter is the ability to ensure constant flows to the two outlets independently from the split ratio. This ability is based on two instead of one auxiliary flow. Both are delivered by mass flow controllers with different ratios. If the sum of the auxiliary flows is kept constant, the pressure in the dome and therefore the flow to the outlets is nearly constant. A constant pressure in the dome also means constant flow conditions for the GC capillary and therefore constant retention times. Unfortunately the split ratio of the dome splitter can be strongly dependent on the oven temperature. During a typical GC run the split ratio can span a huge range (e.g., a decrease from 80% to 40% of the GC effluent to the MS). The dome splitter eventually is prone to adsorption at the internal glass walls causing subsequent peak tailing and loss of sensitivity. This was the reason for us to investigate the Deans’ switch principle as an alternative, especially using the microfluidic Deans’ devices. The microfluidic Deans’ switches integrate the flow scheme into a monolithic metallic wafer with very small internal flow channels. Only five external connections ensure leak tight connections to the capillaries. We expected that the transition from the variable splitting principle of the dome splitter with its large internal volume to a device with small restrictors would

Figure 2. Operating modes of Deans’ switches as variable flow splitters (V = vacuum, A = atmospheric pressure/outlet, S1,S2 = control/ makeup lines).

similar to the variable dome splitter with two mass flow controllers. In the middle the two auxiliary flows are supplied by pressure controls. Those pressure controls can be part of the gas chromatograph or external flow regulators. The internal pressure controls of GCs can be programmed to regulate the pressure as a function of the oven temperature. Unfortunately the functional dependence is usually limited to the constant flow model of a capillary with only two boundary conditions (vacuum or atmospheric outlet pressure). The mode on the right-hand side is the classical Deans’ switch mode which can also be used (in a restricted way) as a variable splitter.

■

EXPERIMENTAL SECTION The measurements were performed using a Trace GC Ultra, (ThermoFisher Scientific, Dreieich, Germany) with a time-offlight mass spectrometer (TOF-MS) (BenchTOF-dx, ALMSCO, Llantrisant, UK) as the detector and an olfactory (sniffing) port with a 1.5 m heated transfer line (Sniffer 9000, Brechbühler, Schlieren, Switzerland). The samples were injected via the split/ splitless injector of the GC. The variable splitter used was a microfluidic Deans’ switch device (SilFlow, SGE, Ringwood, Australia). The split ratio was controlled by auxiliary flows of carrier gas supplied by two digital mass flow controllers (MFCs) (MFC 5850 S, Brooks Instruments, Hatfield, USA). The flow at the olfactory port was measured by a soap film flow meter. The readings of the soap film instrument have been corrected by a pressure, temperature, and humidity correction (eq 1). The derivation of the equation can be found in Annex A of the Supporting Information. VStd = Vmeas. ×

pamb. pStd

×

⎛ p ⎞ TStd × ⎜⎜1 − WS ⎟⎟ Tamb. ⎝ pamb. ⎠

(1)

In eq 1 pamb. and Tamb. are the actual pressure and temperature, respectively. pWS is the saturation pressure of water at Tamb.. 9022



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temperature and thus the restrictions change during a GC run. This leads to a continuous change of the split ratio. To measure the split ratio at different GC temperatures we have chosen an n-alkane test mixture (Supleco No. 49452-U, Sigma-Aldrich, USA, diluted to 9.1 mg/L in hexane) with 32 alkanes in a homologous series from C8 to C40 (see Supporting Information, Table S-1). The separation was carried out on a 15 m × 250 μm i.d. × 0.25 μm df FS-Supreme-5 ms (5% phenyl/95% mehyl silicon) capillary column (CSChromatographie, Langerwehe, Germany). Helium was used as the carrier gas with a constant flow set point of 2 mL/min. Sample volumes of 1 μL were injected manually with a 5 μL syringe (Hamilton, Bonaduz, Switzerland) with the hot empty needle injection method. The injector was operated with a split ratio of 1:30 at 280 °C. The GC oven was temperature programmed with a hold time of 3 min at 40 °C, then increased with a rate of 10 °C/min up to 320 °C, and held there for 2 min.

For the calculation of the vapor pressure of water the following equation can be used:14 1799.73

pW = 100 × 10(8.3246 −

/(ϑ+ 238.734))

in [Pa]

(2)

The temperature ϑ in eq 2 is the ambient temperature in degree Centigrade. The flow of the carrier gas helium controlled by the MFCs has to be converted from the calibration gas (here nitrogen) to helium, see eq 3 (the factor may differ between manufacturers, here the factor for the Brooks MFCs is given). Furthermore, the units of MFCs are often referenced to 0 °C and 1 atm (101.3 kPa). In the GC field the reference temperature is set to 25 °C. Therefore a temperature conversion is needed (eq 4). VHe = VN2 × 1.386

V25 ° C = V0 ° C ×

(25 + 273.15) (273.15)

(3)

■

(4)

THEORETICAL DERIVATION OF FLOW CONDITIONS 1. Isothermal, Compressible Capillary Gas Flows. For the following calculations we have used eq 5, often called the Hagen−Poiseuille equation. This form of the Hagen−Poiseuille equation is modified for the calculation of gas volume flows at standard conditions (usually 25 °C, 101.3 kPa). The derivation has recently been published in detail.8

The Deans’ switch has internal rectangular microchannels of very small dimensions (Figure 3).15 In Figure 4 the internal flow scheme and the dimensions are given.

VStd = (p12 − p2 2 ) ×

π × d 4 × TStd 256 × η × l × pStd × T

(5)

For the following calculations it is convenient to combine the constant values to a single parameter A and the dimensions of the capillary, the temperature, and the viscosity to a resistance parameter K

A=

T π × Std 256 pStd

(6)

and K= Figure 3. Scheme of the GC system with the Deans’ switch as variable effluent splitter using two MFCs for auxiliary gas flow control (the drawing is not to scale). The setup in the figure is asymmetric with regard to the pressure levels, pMS is a vacuum outlet, and pSn is an atmospheric outlet (here a sniffing port).

η(T ) × l × T d4

(7)

Therefore in the mass balances eq 8 is used: VStd = (p12 − p2 2 ) × A × 1/K

(8)

For a series of capillaries eq 9 can be derived from eq 5: VStd = (p12 − p2 2 ) × A ×

1 i ∑1 K i

(9)

All equations are calculated with SI units. In the equations the pressure has the unit Pa, the volume flow m3/s. The conversions are 1 bar = 105 Pa and 1 m3/s = 60 × 106 mL/min. The constant A is A=

Figure 4. Geometrical design of flow paths within the SilFlow Deans’ switch (SGE, Australia).

π 25 + 273.15 × K/Pa 256 1.013 × 100,000

= 3.6119 × 10−5 K/Pa

For the dynamic viscosity η of helium the formula used (T in Kelvin):

The split ratio depends on the flow resistances of the numerous restrictors inside the GC oven and in the heated transfer lines. With temperature programming the GC oven

ηT = 3.6744 × 10−7 × T 0.7 [Pa × s] 9023

(10) 16,17

was (11)



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(also known as Knudsen flows) starts with Knudsen numbers greater than 10. The self-diffusion theory of Veltzke and Thoeming22 is an analytical description of the flows from the continuum to the slip flow regime without empirical parameters. The total flow is the sum of the classical Hagen−Poiseuille flow and the additional diffusive flow. The mass flow according to Veltzke and Thoeming is

pGC is the head pressure set by the GC control algorithm. This pressure is calculated by the general equation for the capillary flow (eq 1) under the assumption of constant flow and a fixed outlet pressure (typically GC manufacturers only distinguish between vacuum or atmospheric condition considering a simple single column system). pGC =

VGC set point ×

Kcolumn + K transfer line − poutlet 2 A (12)

ṁ =

The column length in the head pressure calculation (in Kcolumn) can differ from the physical length to compensate for the inconsistent outlet pressure. 2. Flow through a Rectangular Channel. For rectangular channels, as in the microfluidic Deans’ switch with a small height h and a width w, the parameters A and K in the Hagen− Poiseuille equation are different. Zohar et al.18 have derived the mass flow rate for circular and rectangular microchannels, respectively. After some transformations to the volume flow rate at standard conditions we obtain the parameters A and K for the rectangular cross section with h as the (small) height and w as the width of the channel. T 1 × Std 24 pStd

A=

K=

VStd = ṁ ×

4

256 × h3 × w 24 × π

d3 × Δp × 6×l

2×π×M R×T

(16)

R × TStd M × pStd

(17)

We get the volume flow at standard conditions: VStd = (p12 − p2 2 ) × + (p1 − p2 ) ×

π × d 4 × TStd 256 × η × l × pStd × T d3 × 2 × π × R × TStd 6 × l × M × T × pStd

(18)

The first part of this equation accounts for convective flow (Hagen−Poiseuille term as eq 1); the second part accounts for the self-diffusion. The calculated flows for exemplary transfer lines are given in Table 1. The contribution of the self-diffusion is rising with smaller inner diameters.

(13)

(14)

One can calculate an equivalent diameter of a circular capillary to a rectangular channel with the same flow properties: d=

128 × η × R × T × l

+

With pM = (pi+po)/2 and the ideal gas law:

η(T ) × l × T h3 × w

π × d 4 × M × pM × Δp

Table 1. Calculated Flows through a Transfer Line of 0.2 m, 250 °C, Inlet Pressure 101.3 kPa, Vacuum Outlet Condition, Carrier Helium

(15)

3. Influence of Rarefaction on the Flow to the Vacuum Outlet. The flow regime through capillaries or microchannels is dependent on molecular parameters. At very low pressures the mean free path length of the molecules is high compared to the dimensions of the capillary or channel. Under these conditions the underlying assumptions of the Hagen−Poiseuille equation are no longer valid. Different fluid mechanics approaches deal with the influence of these conditions. The slip theories assume that the velocity at the walls is not zero.19 The amount of slip is calculated with the Knudsen (Kn) number (the ratio of the mean free path to the capillary dimensions). Another approach of Dongari et al.20 is based on a self-diffusion assumption. A diffusive transport mechanism is superimposed on the classical Hagen−Poiseuille flow. In a contribution of Blomberg and Brinkmann21 about the implementation of a Deans’ switch the authors postulate an anomalous behavior of the flow through the transfer line to the mass spectrometer because of the vacuum outlet conditions. We have evaluated this postulation with the available scientific literature. As a result we have found that correction factor of 2.4 stated in the contribution cannot be explained by fluid mechanics. Dongari, Sharma, and Durst20 differentiate between four flow regimes dependent on the Knudsen number. Knudsen numbers below 0.001 indicate the continuum regime. The slip flow regime ranges between Kn = 0.1 and 0.001. The transition regime between Kn = 10 and 0.1. The molecular regime

d (mm)

convection Hagen− Poiseuille (mL/min)

self-diffusion (mL/min)

sum (mL/min)

percentage self-diffusion

0.25 0.15 0.10 0.05

28.25 3.661 0.723 0.045

1.163 0.251 0.074 0.009

29.41 3.912 0.798 0.055

4.0% 6.4% 9.3% 17.1%

The effect of the self-diffusion is high near the vacuum side of the transfer lines. Figure 5 shows the contribution of the selfdiffusion on the total flow over the length of the capillary. For comparison the volume flow of the classical Hagen−Poiseuille calculation is included. To compensate for the additional self-diffusion flow for vacuum outlet conditions (p2 = 0) we calculate a factor F as the ratio of the extended equation to the classical Hagen−Poiseuille equation. F=1+

=1+

p1 × d3 × p12

2 × π × R × TStd × 256 × η(T ) × l × pStd × T

×6×l×

M ×

2 × π × R × 256 × η(T ) × p1 × 6 ×

M ×π×d

T × pStd × π × d 4 × TStd T

(19)

It is noteworthy that this factor is independent of the length of the capillary and inversely proportional to the diameter and the inlet pressure. The other parameters are dependent on the properties of the carrier gas (molecular weight and viscosity). The overall temperature dependence with T1.2 results from the 9024



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Figure 6. Schematics of the Deans’ switch with an internal restriction between the makeup lines with the inflow from the GC, the two makeup lines, and the two outlets.

Figure 5. Contribution of self-diffusion and convection to the total flow in the transfer line (0.2 m, 250 °C, inlet pressure 101.3 kPa, vacuum outlet condition).

The external rectangles are for transfer lines or restrictions at constant temperatures. A volumetric gas flow is dependent on pressure and temperature. This is the reason why a balance of the flows at actual conditions cannot be used for the calculations. In contrast, the flows at standard conditions are independent of the actual pressure and temperature and are proportional to the mass flow. The restriction between the two makeup lines is part of the usual Deans’ switch setup. The consideration of this restriction complicates the calculation to a great extent. The full solution and the solution without the consideration of the internal restriction is part of the Supporting Information. Fortunately the influence of a small restriction on the flows and pressures is negligible in most cases independent of the significance of the restriction as a counter diffusion measure. The mass balance is formulated separately in the balance volumes (the 5 dotted cycles in Figure 6). The mass balances are coupled by the respective flows. Balance I

0.7

viscosity (proportional T ) and the square root of the temperature (T0.5). In Table 2 the values of the factor F are calculated for different temperatures and diameters of the transfer line with an inlet pressure of 101.3 kPa. The fourth root of the factor F multiplied with the nominal diameter of the capillary can be used to compensate for the additional diffusive flow in the classical Hagen−Poiseuille equation (with vacuum outlet conditions). For all five diameters in Table 2 the compensated diameters given in the last column are only 3 μm greater than the real diameter. 4. Hold-up Time. The hold-up time is the time interval for the passage of the components through the uncoated transfer capillaries. Equation 20 can be derived by the integration of the medium velocities over the length of the capillaries. thold‐up =

(p13 − p2 3 ) 128 × η × l 2 × 3 × d2 (p12 − p2 2 )2

(20)

VG − V1 − V2 = 0

To calculate the hold-up time of a series of capillaries first the intermediate pressures have to be calculated with the gas flow through the capillaries. With the pairs of pressures (inlet and outlet pressure) the hold-up time for every section can be calculated. The hold-up time is especially important for GC-olfactometry setups.

(21)

Balance II

VR1 + V1 − V3 = 0

(22)

Balance III VR2 + V2 − V4 = 0

■

(23)

Balance IV

MASS BALANCE OF THE DEANS’ SWITCH The scheme of the Deans’ switch as a variable splitter is depicted in Figure 6. The dotted inner rectangle is the Deans’ switch with its internal connections and restrictions. The outer rectangle stands for the GC oven at variable temperatures.

VS1 − VR − VR1 = 0

(24)

Balance V VS2 + VR − VR2 = 0

(25)

Table 2. Compensation Factor F for Vacuum Outlet Condition temperature transfer line (vacuum outlet condition, carrier helium) 200 °C

250 °C

300 °C

350 °C

diameter d (mm)

F

F0.25

F

F0.25

F

F0.25

F

F0.25

diameter dcomp. 300 °C (mm)

0.250 0.150 0.125 0.100 0.050

1.037 1.061 1.073 1.091 1.183

1.009 1.015 1.018 1.022 1.043

1.041 1.069 1.082 1.103 1.206

1.010 1.017 1.020 1.025 1.048

1.046 1.077 1.092 1.115 1.230

1.011 1.019 1.022 1.028 1.053

1.051 1.085 1.102 1.127 1.254

1.012 1.021 1.024 1.030 1.058

0.253 0.153 0.128 0.103 0.053

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Every flow is expressed by an equation in the form VN = (p2 N1

1 − p2 N0 ) × A × KN

Table 4. Dimensions of the Internal Channels in the Microfluidic Deans’ Switcha (26)

with the index N for a section, pN1 the pressure at the inlet, pN0 the pressure at the outlet of the section, and KN the resistance factor of the section. The solution for the balance scheme with and without consideration of the restriction between the makeup lines is a rather long deduction and can be found in Annex B1 and B2 of the Supporting Information. The volumetric split ratio is now obtained from the volume flows V1 and VG. We define the split ratio R as the amount of the GC effluent flowing to the outlet with the pressure pV: R1vol =

V1 for 0 < V1 < VG VG

■

R1vol = 1 for V1 > VG

(29)

KD2

KD3

KD4

KDG

KS1

KS2

KR

5

5

2.8

2.8

4.5

9.8

9.8

20

Height: 0.075 mm; width: 0.25 mm; equivalent circular diameter: 0.1376 mm. Restriction: height: 0.05 mm; width: 0.075 mm; equivalent circular diameter: 0.0751 mm.

with a mass spectrometer as detector and a sniffing port. The pressure in the Deans’ switch must be above atmospheric pressure to generate a flow to the olfactometric port. In contrast the flow to the MS is determined by the high pressure difference between the Deans’ switch and vacuum. In many cases, one of the prerequisites of a setup for effluent splitting is that the flows to both outlets should have nearly the same value. This requires a high restriction to the vacuum outlet and a smaller restriction to the atmospheric outlet. The transfer line to the mass spectrometer usually has a short length. Therefore a short restriction with a small inner diameter has to be used. Unfortunately small deviations of the middle pressure of the Deans’ switch lead to small deviations of the flow to the vacuum outlet but to high variations to the atmospheric outlet because the relative change of the pressure difference is large to the atmospheric outlet. This behavior is represented in the calculations of the model setup. The restrictions in the oven rise with increasing oven temperature. As the mass flow controller forces a constant gas flow into the Deans’ switch the pressure level must rise correspondingly (Figure 7). The GC’s gas flow usually also rises

and (28)

KD1

a

(27)

R1vol = 0 for V1 < 0

abbrev length [mm]

RESULTS Model Predictions of the Flows and the Split Ratio. The system behavior of the Deans’ switch cannot be understood directly from the equations derived (see the Supporting Information). We have used a spreadsheet to calculate the flows, pressures, and the split ratio as a function of the respective parameters. To limit the degrees of freedom a model setup close to the validation experiments is the basis of the following calculations and figures. The lengths, dimensions, and temperature levels of the restrictions are given in Table 3. The restrictions of the Deans’ switch are in Table 4. Table 3. Parameters of the Model Setup restrictions to vacuum outlet

unit

constant heated

°C mm m °C mm m °C mm m mm mL/min

240 0.125 0.20 240 0.25 1.5 240 0.25 0.05 0.25 1.5

m

19.3

kPa

101.3

mL/min

3

mL/min mL/min

0−3 3−0

parameter

temp i.d. length to atmospheric outlet temp i.d. length GC transfer and temp column i.d. length GC flow program nominal i.d. parameters target column flow virtual column length outlet pressure MFC control flows total MFC flow MFC 1 MFC flow MFC 2 MFC flow

variable temperature in the oven 40−250 0.125 0.25 0.10 0.20 40−250 0.25 0.20 40−250 0.25 15

Figure 7. Calculation of gas flows inside the Deans’ switch and to the outlets as well as middle pressure pM and the pressure differences (delta pA and delta pV) to the outlets.

when a constant flow program of the GC is used which is parametrized with the outlet condition of atmospheric pressure. As a result we see a decrease of the flow to the MS (VV in Figure 7) and an increase to the olfactory port (VA). Please note that the flows to the MS and the sniffing port are not a direct measure for the split ratio of the GC effluent. We have to consider the auxiliary flows from the MFC’s. The fraction of the GC effluent to the MS and to the sniffing port (VGC→V and VGC→A) also show an inverse behavior with rising GC temperature. The split ratio R1 is calculated as the ratio of the GC effluent to the MS (VGC→V) to the total GC effluent (VG). Therefore, this ratio is decreasing.

The system behavior is dependent on the inherent asymmetries. This is especially the case in the configuration 9026



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In Figure 8 the ratio R1 is calculated over the oven temperature for different combinations of the auxiliary flows.

The measurement values and the model predictions after this adjustment are given in Figure 9.

Figure 8. Calculation of the effluent split ratio at different ratios of the auxiliary flows.

Figure 9. Flow measurements at different oven temperatures and the model prediction curve of the adjusted Deans’ switch model (dotted line).

Due to the temperature dependent restrictions it cannot be avoided that the split ratio varies during the GC run. If this is a reproducible behavior, then a certain amount of change is tolerable; but if the ratio falls off very strong, e.g. from 80% at 40 °C to 30% at 250 °C, this means that at the beginning of the temperature ramp only 20% of the effluent is transferred to the sniffing port; however, at the end of the temperature ramp it will be 70% respectively. Such system behavior makes regular sniffing measurements impossible. Validation Measurements of the Theoretical Predictions. The model derived in this contribution is based on basic assumptions and physical laws without any lumped parameters. Nevertheless any physical model is a selection of the effects which the authors presume to be most important. With validation measurements under controlled conditions it can be tested whether this selection was adequate and complete with respect to the problem. Therefore we have checked every parameter value with respect to the plausibility. For the validation of the theoretical approach and the proposed model three independent series of measurements have been used. 1. Measurements of the flow out of the sniffing port at different temperatures 2. Measurements of an n-alkane series for the calculation of split ratios at different temperatures 3. Confirmation measurements due to deviations of the internal diameter of the GC column between model and nominal value Validation 1. The effluent flow at the olfactory port has been measured with the soap film flow meter. The model predicts the flow using the data of the measurement method as input parameters. Some of these parameters are not welldefined; this is especially the case for the thermal behavior of the transfer line to the mass spectrometer. This independently heated line terminates within the GC oven which has an impact on the temperature distribution. Rising GC temperatures will lead to a rising temperature in this section. In the model the unaffected part at constant temperature and the variable part have to be adjusted.

Validation 2. The aim of the validation measurements was the determination of the split ratios at different temperatures during a GC run. For the second series of measurements an n-alkane mixture has been used (Figure 10). The split ratios

Figure 10. Chromatogram of the measurement of the n-alkane series from C8 to C40. The drop of the peak area (and height) is most likely partially due to an incomplete transfer of the original alkane mixture to the stem solution (loss of a fraction with higher viscosity at the glass walls).

have been determined by reference measurements with a split ratio of 100% to the MS detector. The split ratio of every compound (and its elution temperature) is calculated by the quotient of the peak area to the peak area at 100%. The measurement results show the predicted behavior of descending ratios with rising GC oven temperatures (Figure 11). The prediction with the nominal values of the transfer lines and the GC column deviates from the measurements. With some adjustments the predictions fit to the measurements, especially in the temperature range between 40 and 200 °C. The internal diameters of the GC column and of the MS transfer line had to be adjusted to 0.127 mm and 0.23 mm, respectively. The 9027



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Deans’ Switch Calculator. A spreadsheet-based calculator is part of the Supporting Information. This calculator is an implementation of the calculations of annex B. A short manual is available in annex C. For universal use three modes of carrier gas control are available: 1. constant head pressure, 2. constant flow mode, and 3. linear programmed pressure. The control flows of the Deans’ switch can either be delivered 1. by mass flow controllers or 2. by pressure controllers. All calculations are based on analytical expressions. Therefore any parameter change immediately leads to a complete recalculation of the flow scheme. For the users interested in the time shift between the two outlets the hold-up time is calculated. This is especially important for the combination of a mass spectrometer with an olfactory port. Figure 13 shows an example calculation. With the calculator the system behavior can be explored. Some findings and a strategy for balanced system behavior: 1. The inherent asymmetry of a setup with vacuum and atmospheric detector can be compensated for by the application of a high pressure level in the Deans’ switch. This strategy reduces the influence of unbalanced resistance changes in both outlets due to the changing oven temperature. 2. It is essential to use the programmed pressure mode of the GC to deliver a constant flow to the Deans’ switch. This cannot be obtained by the constant flow mode of the GC because the outlet conditions here are restricted to vacuum or atmosphere. This would lead to a pronounced change of the flow in the chromatographic column to the Deans’ switch even with a careful choice of an equivalent length for the control algorithm. The values of the initial and final temperature/pressure combinations must be determined by iteration. 3. It is essential for convenient system behavior to keep the control flows of the mass flow controllers as low as possible. If both outlets are to have the same flow, then the control flow should only be slightly higher than the column flow (e.g., 2.5 mL/min with a column flow of 2 mL/min). 4. The time shift between the outlets can be minimized by choice of the restrictions. The same flow resistance can be obtained by a short narrow bore or a long wide bore capillary. On the other hand, the hold-up time of the wide bore capillary is much greater for the same flow. By iterative adjustment a very short time shift is achievable.

Figure 11. Measurement results of different MFC settings from 30% to 80% referenced to 100% measurements. The straight lines are the model predictions with the adjusted model. The error bars reflect the error of three repeated measurements. Above 200 °C the measurements show a systematic decline of the split ratio which has not yet been explained. We assume that an additional mechanism, not accounted for in the model, may be responsible for the decline. Diffusion mixing is a potential effect that can contribute to a shift of the distribution between the two outlets. The marked increase in the diffusion coefficient with increasing temperature may be the cause of the increasing deviations.

deviation of the internal diameter of the transfer line from the nominal value of 0.125 mm is close to the value of 0.128 as derived from the theory of rarefied flows (see Table 4). The deviation of the model value of 0.23 from the nominal value of 0.25 is far from the expected tolerances of the column manufacturer. Validation 3. In order to understand this deviation an additional measurement of the exact flow properties of the GC column was performed. With a series of head pressures and the corresponding flow rates with the GC column connected directly to the soap film flow meter we have calculated an internal diameter of 0.233 mm (Figure 12). This is another proof of the validity of the physics of the model.

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DISCUSSION The setup of a GC-olfactometry system with a parallel installation of vacuum outlet condition (GC/MS) using a variable splitter has to consider many prerequisites. Such a GCO system should meet the following conditions: • Split ratios independent of the GC temperature, i.e. constant split over a GC run. • Low flow to the MS in the range of 1 to 3 mL/min, i.e. the specified optimum for the detector. • Retention times of the GC independent of the split ratio, i.e. better comparability of the results. • Constant hold-up times independent of the split ratio, i.e. no shift between the aromagram and the chromatogram. • Small difference between the hold-up time to the MS and to the sniffing port, i.e. easier synchronization of GC and sniffing results. By a careful choice of the parameters these conditions can be fulfilled. With the physical model and the calculator based on this model the influence of the numerous parameters on the system behavior is predictable. This facilitates the design of a measurement setup. Nevertheless it is advisable to make

Figure 12. Calculation of the resistance parameter K from a series of flow measurements at different head pressures. Gauge pressures converted to absolute pressures. Linear fit between the square of the absolute pressures in Pa and the (corrected) column flow. The slope is the quotient of the constant A and the resistance factor K (see eqs 5, 6, and 7). 9028



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Figure 13. Deans’ switch calculator.

Appendix A: List of Symbols

validation measurements to check if the calculated system behavior is in accordance with the measurements. Special attention is necessary because of the deviations of the nominal dimensions of the capillaries. Even small deviations have a large effect on the flow properties. The Deans’ switch as a variable splitter can be controlled either by pressure or by mass flow controllers. Both methods have their benefits. With MFCs the restrictions to the control ports of the Deans’ switch and their temperature dependence are irrelevant. This simplifies the setup and the behavior of the system. On the other hand, the control by pressures has the benefit of being more observable from a trouble shooting perspective.

Table 5 contains a list of symbols. Table 5

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CONCLUSIONS The setup of a GC-olfactometry system with a sensitive mass spectrometric detector is a complex task. Variable split ratios enable flexible GC-O methods, e.g., switching minor portions of the effluent to either side to maximize the detection via nose or detector respectively. The benefit of the Deans’ switch as a variable splitter is the characteristic that the chromatographic conditions are not affected by the split ratio in the control mode with MFC’s.10 By means of a reliable splitter also new aroma dilution setups may be possible. In a publication of Deibler et al.23 inlet splitting was used for CharmAnalysis of coffee. Instead of inlet splitting the splitting of the outlet with the variable Deans’ splitter is a potential alternative. With the model calculations presented in this contribution the construction of a ‘smart’ variable splitter is possible. This smart splitter corrects for the temperature dependence of the split ratio. For this purpose the flow rates of the auxiliary flows have to be adjusted as a function of the GC oven temperature. The mathematical derivations presented here are valid also for other chromatographic setups. With the same methods the variable mixing of two effluents to one detector is possible.

name

description

unit

p pStd pamb. pWS T TStd Tamb. ϑ t w d l V VStd η R kB M Re Kn

pressure standard pressure, 101300 Pa ambient pressure saturation pressure of water temperature standard temperature, 25 °C, 298.15 K ambient temperature temperature time velocity diameter length volume flow volume flow at standard conditions (25 °C, 101,300 Pa) dynamic viscosity universal gas constant, 8.314 J/mol*K Boltzmann constant, 1.38 × 1023 molar mass Reynolds number Knudsen number

Pa Pa Pa Pa K K K °C s m/s m m m3/s m3/s Pa*s J/mol*K J/K kg/mol -

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +49-228-732596. E-mail: [email protected]. 9029



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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the German Research Foundation DFG for the funding of the research under the Grant BO 51/1-2, especially we thank our adviser Andreas Engelke. We are grateful to our colleague Hans-Georg Schmarr, DLR Rheinpfalz, Competence Center for Wine Research, Neustadt an der Weinstraße, Germany, for the careful examination of the manuscript and the valuable advice. Many thanks to Gerhard Horner, five technologies GmbH, Munich, Germany, for his careful reading of the manuscript and the improvements to the clarity of the text. We thank SGE, Australia, for providing technical information. We also appreciate the reviewers’ comments and contributions to this revised article.

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REFERENCES

(1) Deans, D. R. J. Chromatogr. 1965, 18, 477−481. (2) Deans, D. R. J. Chromatogr. 1981, 203, 19−28. (3) Apps, P. J. Sep. Sci. 2006, 29, 2338−2349. (4) Seeley, J. V.; Micyus, N. J.; Bandurski, S. V.; Seeley, S. K.; McCurry, J. D. Anal. Chem. 2007, 79, 1840−1847. (5) Marriott, P. J.; Chin, S.-T.; Maikhunthod, B.; Schmarr, H.-G.; Bieri, S. TrAC, Trends Anal. Chem. 2012, 34, 1−21. (6) Chin, S.-T.; Eyres, G. T.; Marriott, P. J. Anal. Chem. 2012, 84, 9154−9162. (7) Luong, J.; Gras, R.; Shellie, R. A.; Cortes, H. J. J. Sep. Sci. 2013, 36, 182−191. (8) Luong, J.; Gras, R.; Hawryluk, M.; Shellie, R. A.; Cortes, H. J. J. Chromatogr., A 2013, 1288, 105−110. (9) Luong, J.; Gras, R.; Hawryluk, M.; Shellie, R. A.; Cortes, H. J. J. Chromatogr., A 2013, 1297, 231−235. (10) Wang, C.-H.; Chang, C.-C.; Wang, J.-L. J. Chromatogr., A 2007, 1163, 298−303. (11) Wetzel, E.; Niederwieser, A. HRC & CC, J. High Resolut. Chromatogr. Chromatogr. Commun 1985, 8, 357−359. (12) Nitz, S.; Drawert, F.; Gellert, U. Chromatographia 1986, 22, 51− 54. (13) Boeker, P.; Haas, T.; Schulze Lammers, P. J. Chromatogr., A 2013, 1286, 200−207. (14) Altinger, G. VDI-Waermeatlas, 7th ed.; VDI-Verl.: Duesseldorf, 1994. (15) Townsend, C. SGE Europe. personal communication, 2012 (16) Nuclear Safety Standards Commission (KTA) Germany. Calculation of the material properties of helium, KTA 3102.1 , 1978,. (17) Hinshaw, J. V.; Ettre, L. S. J. High Resolut. Chromatogr. 1997, 20, 471−481. (18) Zohar, Y.; Lee, S. Y.; Lee, W. Y.; Jiang, L. N.; Tong, P. J. Fluid Mech. 2002, 472, 125−151. (19) Vandenberg, H. R.; Tenseldam, C. A.; Vandergulik, P. S. J. Fluid Mech. 1993, 246, 1−20. (20) Dongari, N.; Sharma, A.; Durst, F. Microfluid. Nanofluid. 2009, 6, 679−692. (21) Blomberg, J.; Brinkman, U. A. J. Chromatogr., A 1999, 831, 257− 265. (22) Veltzke, T.; Thoeming, J. J. Fluid Mech. 2012, 698, 406−422. (23) Deibler, K. D.; Llesca, F. M.; Lavin, E. H.; Acree, T. E. Flavour Fragrance J. 2004, 19, 518−521.

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Comprehensive Theory of the Deans' Switch As a Variable Flow

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