Comparison of both MEMS Thermal Conductivity CO₂ Sensors

And Non-dispersive Infrared CO₂ Sensors

Xiang Zheng Tu

 

A major hazardous gas present in the atmosphere which creates various adverse effects to human is carbon dioxide (CO₂). Measurement of CO₂ gas using CO₂ sensor will help to monitor its presence and indicate us above dangerous limits to prevent adversities. In a modern ventilation system CO₂ sensors used as indoor air quality indicators help to ensure a fresh outside air supply to building occupants while simultaneously optimizing energy consumption. For such systems it has been recommended: CO₂ sensors shall be certified by the manufacturer to be accurate within plus or minus 75 ppm at a 600 and 1000 ppm concentration. Carbon dioxide air-conditioning systems have been installed in cars. In these applications the CO₂ leakage detection range is 0-50.000 ppm with a resolution of 10% while the comfort range is 0-5.000 ppm with a resolution of 200 ppm.

A non-dispersive infrared (NDIR) CO₂ sensor is shown in the above first figure. The NDIR sensor comprises an infrared source, a sample cell, an optical filter and a detector system. The infrared source directs waves of light through the cell filled with air containing CO₂ toward the filter and then detector which measures the amount of the light that hits it. As the light passes through the cell, any gas molecules that are the same size as the wavelength of the light absorb the light only, while letting other wavelengths of the light pass through. Next, the remaining light hits the filter that absorbs every wavelength of light except the exact wavelength absorbed by CO₂. Finally, the detector reads the amount of light that was not absorbed by the CO₂ molecules or the optical filter.

The difference between the amount of light radiated by the source and the amount of the light received by the detector is measured. The difference is proportional to the number of CO₂ molecules in the air inside the cell.

The advantages of the non-dispersive infrared (NDIR) CO₂ sensors are selective, sensitive, non contact and reliable. At present time this technology is accepted as a state-of-the-art. But it still has some serious problems such as inherently expensive (at least two components), large size, requiring drift compensation and complex packaging.

So many efforts have been made regarding more miniaturization and lower system costs compared to the non-dispersive infrared CO₂ sensors.

POSIFA Microsystems Company announces a MEMS thermal conductivity CO₂ sensor.

The sensor integrates all CO₂ sensing components in a single silicon microstructure with a micro-hot-bridge, which is not like the non-dispersive infrared CO₂ sensor which is assembled with at least 4 separated components. In additional the micro-hot-bridge the sensor further contains a resistor, a cavity, and a thermopile with its hot junctions near the resistor and cold junctions extending to the silicon frame along the bridge supporting beams.  

The thermal conductivity CO₂ sensor performs a measurement as follows. By applying a voltage to the resistor on the micro-hot-bridge of the sensor, the resistor is heated up and becomes a “hot source”. The cavity is open to the atmosphere and filled with air containing a certain amount of CO₂ gas or air mixture. The air mixture transfers a quantity of heat from the hot source to the cold bottom of the cavity via the air mixture. The quantity of heat is measured by the thermopile. The changes in the thermal conductivity of the air mixture can be detected by measuring the changes of the output Seebeck voltage of the thermopile. With the measured thermal conductivity of the air mixture the concentration of the CO₂ in the air can be calculated by a humidity compensation algorithm which is based on the measurement results using the same sensor operated at two different temperatures.

Compared with the non-dispersive infrared CO₂ sensors, the thermal conductivity CO₂ sensors possess many advantages such as:

• Size reduced to a single silicon chip,
• Milliwatts grade power consumption,
• Milliseconds grade response times,
• Low cost, and
• Able to identify different gases of a gas mixture.

 

It is not be surprised for the last advantage. The thermal conductivities of gases always change with temperature. As shown in the above second figure, the thermal conductivities of gases CH₄, C₂H₆, N₂ and CO₂ increase slight-non-linearly with temperature. Based on this inherent character of the gases distinguishing single components of a gas mixture can be realized by modulating operation temperature of a thermal conductivity sensor.

Hear, as a gas mixture of Air, CO₂ and humidity (water vapor) is measured as a gas mixture. The temperature modulation is conducted by applying heating voltages V₁ and V₂ with V₂ higher than V₁. The measured output signals of the thermopile are Y₁ and Y₂ respectively. Then two binary linear equations can be obtained as

Y₁ = b₀₁ + b₁₁ N_CO2 + b₁₂ N_{water vapor}       (1)

Y₂ = b₀₂ + b₂₁ N_CO2 + b₂₂ N_{water vapor}        (2)

Where Y₁ and Y₂ are the output of the thermopile, N_CO2 and N_{water vapor}  are the volume percentage of CO₂ and humidity respectively, b_01, b_02, b₁₁, b_12, b_02, b₂₁ and b₂₂ are constants determined by calibration tests. The volume N_air of Air is found by meeting the equation as

N_air + N_CO2 + N_{water vapor} = 1                   (3)

With the measured Y_1, Y₂ and the known b_01, b_02, b₁₁, b_12, b_02, b₂₁ and b₂₂, N_CO2, and N_water can be found by solving the equations (1), (2) and (3).

All these advantages offer a high potential for mass markets. The most compact thermal conductivity CO₂ sensors have been developed for human breath analysis that will focus on enabling low cost applications but without compromising on accuracy.

Advantages of Thermal Conductivity Water Flow Sensors

over Plastic Spinning Water Flow Sensors

Xiang Zheng Tu

 

Reference to the above figure, a thermal conductivity water flow sensor is made up of two thermopiles, which is used as the sensing temperature difference element and operated in conjunction with a resistive heater element for thermoelectric sensing. The fabrication of such sensors is more complicated since less conventional materials are utilized for fabrication of thermopiles but CMOS (complementary metal oxide semiconductor) compatible processing is possible. The Seebeck effect of thermopiles enables higher sensitivity and unbiased output voltages with no offset or drift.

The thermopiles are constructed with thermocouples in series and so the output voltages due to temperature difference change is summed and increased over that of a single thermocouple. Since the thermal conduction between hot and cold junctions of the thermopiles and Johnson noise increases with increasing number of thermocouples, a high thermal isolation structure is desired in order to maximize temperature difference between hot and cold junctions.

The water mass flow (m) passing through the thermal conductivity sensor is calculated on the basis of the measured temperature difference (T_hot - T_cold) between the hot and cold junctions of the thermopile, and the thermal conductivity (C_p) coefficient (k), electric heat rate (q), and specific heat (C_p) of water, as follows:

m = kq/(C_p(T_hot – T_cold)                                    (1)

The electromotive force, or emf (V) created by the thermopile is directly proportional to the differential temperature (T_hot - T_cold) between the two junctions as

Emf_AB = nS_AB (T_hot - T_cold)                                (2)

Where n is the number of thermocouples of a thermopile and S (V/K) is called the Seebeck coefficient.

Still reference to the above figure, a plastic spinning water flow sensor has a rotor, a bearing, and a shaft, which are mounted in housing. The rotor spins as water passes over it. The measured flow rate is proportional to the rotational speed of the rotor. A variety of methods are used to detect the rotor speed, including a mechanical shaft and an electronic sensor.

Plastic bearings must be lubricated, not only to reduce friction and wear, but, in the case of plain bearings, to prevent them from seizing the shaft which they support. Self-lubricating plastic bearings contain a mix of dry lubricants. In operation, movement between shaft and bearing causes microscopic abrasion of the dry lubricant, filling and smoothing the shaft surface to reduce friction. The resulted micron particles will enter the water flow which is harmful to human health.

Most plastic bearing materials expand when exposed to heat and moisture. This factor is more significant when the running clearance between the bearing and shaft is less than 0.001 in. Plastic bearings and shafts are fabricated by injection molding process which has typical accuracy within 0.005 in. As a result, excessive wear or seizing of the shaft occurs very often.

Bubbles inevitably form as air is entrained in the water during the pouring process. The formed bubbles can create many problems in plastic spinning water flow sensors, such as:

● decreasing lubricity caused by an air emulsion,
● reduction of thermal conductivity,
● higher noise emission, and
● decrease water output efficiency.

Compare with plastic spinning water flow sensors, the thermal conductivity water flow sensors have the advantages as:

1.     Thermal conductivity water flow sensors have no moving parts, in which there are no any mechanical failures to take place.

2.     Thermal conductivity water flow sensors are MEMS devices with small size, higher sensitivity, higher reliability, low power consumption, ease of fabrication, and low cost.

3.     Thermal conductivity water flow sensors calculate mass flow rather than volumetric flow and do not require temperature or pressure correction, which means there is no additional expense for the purchase and installation of additional equipment.

4.     Thermal conductivity water flow sensors provide excellent accuracy and repeatability over a wide range of flow rates using bypass flow tube design. The sensor is placed in a bypass around a restriction in the main pipe and is sized to operate in the laminar flow region over its full operating range.

It should be emphasized that the thermal conductivity water flow sensors are not influenced by the air bubbles entrained in the water. The effect of the bubbles can be added to the series conductivity by using conductivity of the air-water mixture for the water conductivity. The thermal conductivity of continuous water phase with entrapped air bubbles can be calculated using Maxwell’s model as

k_m= k_c (k_d + 2k_c – 2p_d [ k_c –k_d])/(k_d + 2kc + p_d [k_c –k_d])            (3)

Where:

K_m = conductivity of the mixture,

K_c, k_d = conductivity of continuous and disperse phases, respectively, and

P_d = volume fraction of the disperse phase.

Replacing equation (3) into equation (1), the water mass flow rate measured by the thermal conductivity water flow sensor should be

 m = {(k_d + 2k_c – 2p_d [ k_c –k_d])/(k_d + 2kc + p_d [k_c –k_d])}q/(C_p(T_hot – T_cold)     (4)                        

It can be seen that the measured water mass flow rate does not contain the air bubbles entrained in the water.

0~2000ppm Range and 232ppm Resolution

CO₂ Thermal Conductivity Sensors

Xiang Zheng Tu

 

Figure 1 shows a thermopile thermal conductivity sensor provided by POSIFA Microsystems Company. The sensor mainly comprises a silicon chip, a hot plate suspending over a cavity recessed into the silicon chip, a resistor and a thermopile both disposed on the hot plate. The resistor is heated by applying a square pulse voltage and the thermopile is used to measure the temperature difference between the hot plate and the silicon chip. The temperature difference depends upon the thermal conductivity of the gas or gas mixture filled in the cavity. Since the sensor is ultra miniature its thermal time constant is short enough to allow for heating the sensor to work with very narrow pulses of electricity. So the power consumption throughout sensor's operation is quite low.

Figure 2 shows measurement data for indoor air. The heating square pulse voltage is supplied by Agilent 8110A 150 MHz Pulse Generator. The square pulse voltage is chosen to have: period = 1s, width = 20ms and amplitude = 8.96V. The out voltage of the sensor is measured by a TDS Digitizing Oscilloscope, which is shown as 1.86mV.

Figure 3 shows measurement data for 40% carbon dioxide and 60% nitrogen.

The heating pulse voltage is maintained as the same. The out voltage of the sensor is shown as 1.924V which is higher than the out voltage measured for indoor air. 

Using the above measurement data the sensitivity of the thermopile thermal conductivity sensor for carbon dioxide in nitrogen or in indoor air can be calculated as 1.65mV/1%.

In order to determine the resolution of a practical sensor measurement system in terms of voltage, we have to make a few calculations.

·      Assume the system capable of making measurements across 0 to 5V range,

·      Using a18-bits A/D converter, and

·      Using an averaging technique for reducing the noise contribution from four counts to one count.

Therefore, the smallest theoretical change we can detect is 153μV or 232ppm carbon dioxide in nitrogen. 

Requirements for circuit design for natural gas calorific meters

Xiang Zheng Tu

The project is divided into two phases as:

·      The first phase is designing circuit for measuring the component mole fraction of a natural gas using POSIFA’s thermopile thermal conductivity sensors.  

·      The second phase is combining this circuit with an available mass flow measuring circuit. So as to obtain a complete circuit for natural gas calorific measurement.

A natural gas calorific meter comprises a MEMS thermal flow sensor and a MEMS thermopile thermal conductivity sensor which are provided by POSIFA Microsystems Company. The thermal flow sensor measures natural gas mass flow. A natural gas is a naturally occurring gas mixture, consisting of methane, ethane, propane and nitrogen. The heating value of a natural gas changes with its composition changes. The thermopile thermal conductivity sensors measure the component gas mole fraction in the natural gas flow. With the measured natural gas mass flow rate and component mole fraction the natural gas calorific flow rate and total calorific value can be calculated and displayed accordingly.

The component gas mole fraction of a natural gas can be measured based on the fact that the temperature curve of each component gas thermal conductivity coefficient is unique for each one, but highly correlated. A quaternary linear regression can be used to model the relationship between two or more explanatory variables and a response variable of a natural gas system by fitting a linear equation to observed data.

The thermopile thermal conductivity sensor is configured to have a polysilicon resistor used as heater (resistance = 250 to 350 Ω) and a thermopile used as temperature difference detector (resistance ~200 kΩ). In order to establish a quaternary linear system the heater must be driven using three square pulse voltage steps V₁, V₂, V₃.  The square pulse voltage can be shown as: 

After driving the heater a temperature difference between the hot junctions and cold junctions of the thermopile is established and a corresponding thermopile voltage is generated as:

Three square pulse voltages are used to successively heat the heater in the way as:

With resulting thermopile voltages a quaternary linear regression can be obtained as:

Y₁ =b₁₀ +b₁₁ N_Ethane +b₁₂ N_Propone +b₁₃ N_Nitrigen                     (1)

Y₂ =b₂₀ +b₂₁ N_Ethane +b₂₂ N_Propone +b₂₃ N_Nitrigen                      (2)

Y₃ =b₃₀ +b₃₁ N_Ethane +b₃₂ N_Propone +b₃₃ N_Nitrigen                      (3)

And an identity as

x_Methane +x_Ethane +x_Propone  +x_Nitrigen=1                                     (4)      

Where Y₁, Y₂ and Y₃ are the measured thermopile voltages when the heater is driven By 5, 7, and 9V square pulse voltages respectively, b₁₀ through b₃₃ are the parameters of the quaternary linear regression equation, which are determined by several experimental measurements, and N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  are the mole fraction of methane, ethane, propane, nitrogen.

With the measured values of Y₁, Y₂, Y₃, and the values obtained by fitting parameters b₀₁ through β₃₄, the values of N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  can be calculated by solving the equations (1) through (4).

A digital processing algorithm can also be build based on the equations (1) through (4). Using the obtained algorithm and the related program the component gas mole fraction of a natural gas coming from any different sources can be determined by operating a microcontroller.

                            

With the purpose of canceling the offset of the thermopile voltage of a thermopile thermal conductivity sensor a differential preamplifier is configured to have a sealed thermopile thermal conductivity sensor used as a reference input voltage. The sealed sensor may be filled with pure methane gas but not allowed to contact with natural gas to be measured. So its thermopile voltage will not change with the measured natural gas. Since the thermopile voltage of the exposed thermopile thermal conductivity sensor not only comprises natural gas signal and but also pure natural gas signal. After differential amplifying all common model signals will be canceled. That means the output of the amplifier should be no offset, no temperature drift and no noise. 

In the second phase the natural gas composition measurement circuit is incorporated with an available natural gas flow measurement circuit. The combined circuit is so called natural gas calorific measurement circuit.

Heating value of a natural gas can be calculated as:

Heating value = ( ṁ N_MethaneM_Methane/M_Mix) (HV_Methane) + ( ṁ N_EthaneM_Etane/M_Mix) (HV_Ethane)

+ ( ṁ N_PropaneM_Propane/M_Mix) (HV_Propane)                                          (5)                                                

Where: HV_n = heating value of natural gas component n, in BTU/SCF
N_n = mole or volume fraction of natural gas component n. 

ṁ = mass flow rate.

M_n = natural gas component mole quality.

M_Mix = natural gas average quality.

The following table shows the heating value of natural component gas:

Smell Liquid MEMS Vaporizers

Tu Xiang Zheng

Smell Liquid MEMS Vaporizers are used for digital smell technology which senses transmits and receives scent-enabled digital media, such as web pages, video games, movies and music. A vaporizer mainly composes: a silicon substrate, a micro-channel array, a membrane suspending over the micro-channel array and supported by the silicon substrate, a resistance heater and a resistance temperature sensor are disposed on the membrane. Since the vaporizer is a silicon-based integrated actuator which provides advantages including small size, compact structure, lower power consumption, lower cost, increased reliability, higher precision, and more environmental friendliness.

Smell consists of many different molecules, e.g.: the aroma of coffee is made up of 20 various molecules. Nonetheless our nose perceives only 15 molecules which are enough to identify the smell as coffee. The physiology of smell in humans begins in the nasal cavity. There, a huge number of receptors (over 40 million) are located in the upper roof of the cavity. When the molecules reach the receptors, an electric impulse is sent directly to the brain and establishes a direct connection between our sense of smelling and our brain.

Smell is the sense closest linked to memory. Studies have shown that people can remember a scent with 65% accuracy after 1 year while visual memory sinks to 50% after only a few months.  The smells we experience play a crucial role in how we associate with memories and places. Have you ever come across a whiff of something that instantly takes you back to an old memory? Whether it reminds you of your mother’s cooking or a childhood trip to the ocean, a distinctive scent sinks into your brain and stays there.

Smells can evoke powerful emotions. The perfume industry is built around this connection, with perfumers developing fragrances that seek to convey a vast array of emotions and feelings; from desire to power, vitality to relaxation. It is likely that much of our emotional response to smell is governed by association, something which is borne out by the fact that different people can have completely different perceptions of the same smell. Take perfume for example; one person may find a particular brand ‘powerful’, ‘aromatic’ and ‘heady’, with another describing it as ‘overpowering’, ‘sickly’ and ‘nauseating’. Despite this, however, there are certain smells that all humans find repugnant, largely because they warn us of danger; the smell of smoke, for example, or of rotten food.  

Healthcare professionals are aware of the powerful impact of scent on patient feelings of well being. Studies have shown that scent can be used in many applications to positively affect the behaviors and emotions of patients, family, caretakers, and healthcare staff.

Vanilla, lavender and neutralizing scents (“Pure”) are popular recommendations. Vanilla can reduce claustrophobia in MRI facilities, calm pre-surgery and dental patients, and can reduce patient cancellations. Neutralizing unpleasant odors for patients with a heightened sense of smell will also soothe and comfort. Citrus uplifts and helps ease anxiety.

Clearly Better Scents offers custom fragrance development developed for the unique needs of your hospital, nursing home, doctor’s office, dentist’s office, outpatient surgery facility, laboratory physical therapy or chiropractic facility.

Senses of smell can even affect productivity in office environments. Specific smells have been found to increase alertness which in turn results in higher productivity rates. One study found that when lemon oil was diffused throughout a Japanese office building, productivity among data entry operators increased by 54%. Scents can also be used to ward off mid-afternoon brain fog by revving your concentration levels.

It is may be supplied that smells can influence our perception of time. In one of the studies, 20 separate participants were exposed to a baby powder aroma, a coffee aroma, and no aroma at all. While the coffee aroma produced a reduced perception of time, the baby powder aroma produced a longer perception of time. Likewise, pleasurable fragrances have been shown to create “dwell-time” in stores, increasing the likelihood of customers making purchases.

In summary with the smell liquid MEMS vaporizers the digital smell communication will soon influence your everyday life. 

Unknown dark matter and familiar positron annihilation

Xiang Zheng Tu 

  

I must admit that I knew nothing about dark matter, but I am familiar with positron annihilation. In 1986 I utilized positron annihilation measurement to study of vacancy defects in GaAs liquid phase epitaxial layers. In the following year the research result was published in “Journal of Applied Physics” which was titled as “Positron-annihilation study of vacancy defects in GaAs liquid-phase epitaxial layers”. The paper concluded that the defects observed to trap positrons in undoped GaAs liquid phase epitaxial layers are neutral arsenic vacancies. Systematic trends of the epitaxial growth temperature on positron lifetime are observed. The setup for the measurement is shown in the above figure. Positrons are emitted from a radioactive source. The positron is the antiparticle of the electron, and when a positron enters a GaAs liquid phase epitaxial layer, it will find abundant supply of electrons with which to annihilate. The energy release by the annihilation forms two highly energetic gamma rays, and if one assumes that the momenta of the positron and electron before the annihilation, the two gamma rays photos must in opposite directions in order to conserve momentum. These coincident gamma rays at 180 degrees provide a powerful tool for eliminating all gamma events which are not coincident at 180 degrees.

It is interesting to know that positron annihilation measurement has been used to find dark matter. Despite striking evidence for the existence of dark matter from astrophysical observations, dark matter has still escaped any direct or indirect detection until today. Therefore a proof for its existence and the revelation of its nature belongs to one of the most intriguing challenges of nowadays cosmology and particle physics. A lot of work has been done to investigate the nature of dark matter through indirect signatures from dark matter annihilation into electron-positron pairs. It is thought that the dark matter particles are thermal relics, then dark matter particles and antiparticles exist in equal amounts, and they could also annihilate or decay to standard model particles that can be detected. As a two-body process, the rate of annihilation is proportional to the square of the dark matter density, whereas single-body decay process is proportional to the dark matter density. The primary products of the annihilations or decays, i.e. cosmic ray protons, antiprotons, electrons, positrons, gamma-rays and neutrinos, could in principle be observed on or around the Earth, while secondary radiation like gamma-rays, and radio or microwaves from synchrotron could be detected.

Alpha Magnetic Spectrometer (AMS-02) is a powerful state-of-the-art particle physics detector. This detector was installed on the International Space Station and operated by an international team composed of 56 institutes from 16 countries and organized under United States Department of Energy (DOE) sponsorship. It has collected the antiproton-to-proton ratio stays constant which cannot be explained by the secondary antiprotons from collisions of ordinary cosmic rays with interstellar medium.  A new source such as astrophysical accelerators and annihilating or decaying dark matter was subjected.

Samuel C. C. Ting who awarded the Nobel Prize in Physics said that more high-energy positrons than expected are buzzing around the galaxy—has not impressed the doubters. That positron excess, which a European satellite found in the mid-2000s and the AMS confirmed, has sparked hundreds of theory papers connecting it to hypothetical dark matter particles. The mutual annihilation of those particles might create a half-and-half blend of electrons and positrons in a narrow energy range. The electrons would fade into a sea of electrons from other sources, but the rarer positrons might stand out. To Ting, the best explanation for the extra positrons is a dark matter particle with a mass of 1 million megavolts —about as much energy as a flying mosquito. 

Water Flow Sensors with Wide Range of laminar Flow Rate

Xiang Zheng Tu 

The thermal flow sensors provided by POSIFA Microsystems Company are based on the linear relationship between the fluid flow rate and temperature difference dependence voltage or thermoelectric effect. The criteria for the operation of the sensors are to create and maintain laminar flow through the sensitive surface of the sensors.

Osborne Reynolds in 1883 proposed a concept relating to fluid flow properties through pipes of different diameter as well as the determination of boundary layers where the transition between laminar flow to turbulent flow occurs. The regimes where laminar or turbulent flow prevails are prescribed by a dimensionless parameter known as the Reynolds number, defined as

{\displaystyle \mathrm {Re} ={\frac {\rho uL}{\mu }}={\frac {uL}{\nu }}}

R_e = ρ u L / μ = u L / υ      (1)

Where:

ρ is the density of the fluid (SI units: kg/m³)

u is the average velocity of the fluid with respect to the object (m/s)

L is a characteristic length (m)

μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s)

ν is the kinematic viscosity of the fluid (m²/s).

The characteristic length can be calculated with the generic equation as

d_h = 4 A / p                            (2)

Where

d_h = hydraulic diameter (m)

A = area section of the duct or pipe (m2)

p = "wetted" perimeter of the duct or pipe (m)

Based on equation (2) the characteristic length of a circular duct can be expressed as:

d_h = 4 π r² / 2 π r  = 2 r                              (3)

Where

r = pipe or duct inside radius  (m)

d = pipe or duct inside diameter  (m)

As expect the hydraulic diameter of a standard circular tube or duct is the inner diameter or two times the inner radius.

Based on equation (2) the characteristic length of an annulus duct or tube with an inside duct or tube can be expressed as

dh = 4 (π r_o² - π r_i²) / (2 π r_o + 2 π r_i) = 2 (r_o - r_i)               (4)

Where

r_o = inside radius of the outside tube (m)

r_i = outside radius of the inside tube (m)

Based on equation (2) the characteristic length of a rectangular duct or pipe with very length width can be calculated as

d_h = 4 a b / 2 (a + b) = 2 a                                 (5)

Where

a = height of the duct (m)

b = width of the duct (m)

b >> a

Generally, laminar flow occurs at Reynolds numbers of less than 2,000, but in practice Reynolds numbers of less than 1,000 are used to ensure laminar flow under all conditions (e.g., viscosity and density variations with temperature).

As can be seen from the above equations:

• The laminar flow rate of the circular duct or tube is only limited by the Reynolds number.
• The laminar flow rate of the annular duct or tube can be extended by increasing the radius of inside tube and outside tube simultaneously without changing the Reynolds number.
• The laminar flow rate of the rectangular duct or tube can be extended by increasing the width of the rectangular duct or tube without changing the Reynolds number.

POSIFA Microsystems preferred rectangular duct or tube. The following water flow ranges are available:

• 0 – 10 mL / min for medical application
• 0 – 40 mL / min for medical application
• 0 – 120 mL / min for medical application
• 0 – 1000 mL / min for Coffee Makers
• 0 – 3000 mL / min for Water Dispensers
• 0 – 10 L / min for  Liquid Cooling CPU Systems