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讨论奇摄动反应扩散方程
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考虑如下用来描述浮游动物-营养物相互作用时滞微分方程模型 其中 是营养物浓度, 是浮游动物种群的度量,并且参数 为正常数. 如果 成立, 则该系统的正平衡点是全局吸引的. 也给出了正平衡点局部稳定的充分条件.
（编辑：摘要中有公式,但未能正常显示） 相似文献
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Rui Zhang Jie Huang Fei Xie Baojun Wang Ming Chu Yuedan Wang Haichao Li Wei Wang Haixia Zhang Wengang Wu Zhihong Li 《Biomicrofluidics》2014,8(3)
Nowadays, microfluidics is attracting more and more attentions in the biological society and has
provided powerful solutions for various applications. This paper reported a microfluidic strategy
for aqueous sample sterilization. A well-designed small microchannel with a high hydrodynamic
resistance was used to function as an in-chip pressure regulator. The pressure in the upstream
microchannel was thereby elevated which made it possible to maintain a boiling-free high temperature
environment for aqueous sample sterilization. A 120 °C temperature along with a pressure of 400 kPa
was successfully achieved inside the chip to sterilize aqueous samples with E. coli
and Staphylococcus aureus inside. This technique will find wide applications in
portable cell culturing, microsurgery in wild fields, and other related micro total analysis
systems.Microfluidics, which confines fluid flow at microscale, attracts more and more attentions in the
biological society.1–4 By scaling the flow
domain down to microliter level, microfluidics shows attractive merits of low sample consumption,
precise biological objective manipulation, and fast momentum/energy transportation. For example,
various cell operations, such as culturing5–7
and sorting,8–10 have already been
demonstrated with microfluidic approaches. In most biological applications, sterilization is a key
sample pre-treatment step to avoid contamination. However, as far as the author knew, this important
pre-treatment operation is generally achieved in an off-chip way, by using high temperature and high
pressure autoclave. Actually, microfluidics has already been utilized to develop new solution for
high pressure/temperature reactions. The required high pressure/temperature condition was generated
either by combining off-chip back pressure regulator and hot-oil bath,11,12 or by integrating pressure regulator, heater, and temperature
sensor into a single chip.13 This work presented a
microfluidic sterilization strategy by implementing the previously developed continuous flowing high
pressure/temperature microfluidic reactor.Figure Figure11 shows the working principle of the present
microfluidic sterilization chip. The chip consists of three zones: sample loading (a microchannel
with length of 270 mm and width of 40 μm), sterilization (length of 216 mm and
width of 100 μm), and pressure regulating (length of 42 mm and width of
5 μm). Three functional zones were separated by two thermal isolation trenches. The
sample was injected into the chip by a syringe pump and experienced two-step filtrations (feature
sizes of 20 μm and 5 μm, not shown in Figure Figure1)1) at the entrance to avoid the channel clog. All channels had the same depth of
40 μm. According to the Hagen–Poiseuille relationship,15 the pressure regulating channel had a large flow resistance (around
1.09 × 1017 Pa·s/m3, see supplementary S1 for details16) because of its small width, thereby generated a high working
pressure in the upstream sterilization channel under a given flow rate. The boiling point of the
solution will then be raised up by the elevated pressure in the sterilization zone followed by the
Antoine equation.16 By integrating
heater/temperature sensors in the pressurized zone, a high temperature environment with temperature
higher than 100 °C can thereby be realized for aqueous sample sterilization. The sample was
collected from the outlet and cultured at 37 °C for 12 h. Bacterial colony was counted to evaluate
the sterilization performance.Open in a separate windowFIG. 1.Working principle of the present microfluidic sterilization. Only microfluidic channel, heater,
and temperature sensor were schematically shown. The varied colour of the microchannel represents
the pressure and that of the halation stands for the temperature.Fabrication of this chip has been introduced elsewhere.14 The fabricated chip and the experimental system are shown in Figure Figure2.2. There were two inlets of the chip. While, in the experiment, only
one inlet used and connected to the syringe pump. The backup one was blocked manually. The sample
load zone was arranged in between of the sterilization zone and the pressure regulating zone based
on thermal management consideration. A temperature control system (heater/temperature sensor, power
source, and multi-meter) was setup to provide the required high temperature. The heater and the
temperature sensor were microfabricated Pt resistors. The temperature coefficient of resistance
(TCR) was measured as 0.00152 K−1.Open in a separate windowFIG. 2.The fabricated chip and the experimental system. (a) Two chips with a penny for comparison. The
left chip was viewed from the heater/temperature sensor side, while the right one was observed from
the microchannel side (through a glass substrate). (b) The experimental system.Thermal isolation performance of the present chip before packaging with inlet/outlet was shown in
Figure Figure3,3, to show the thermal interference issue. The results
indicated that when the sterilization zone was heated up to 140 °C, the pressure regulating zone was
about 40 °C. At this temperature, the viscosity of water decreases to 0.653 mPa·s from 1.00 mPa·s
(at 20 °C), which will make the pressure in the sterilization zone reduced from 539 kPa (calculated
at 20 °C and flow rate of 4 nl/s) to 387 kPa. The boiling point will then decrease to 142.8 °C,
which will guarantee a boiling-free sterilization. In the cases without the thermal isolation
trenches, the temperature of the pressure regulating zone reached as high as 75 °C because of the
thermal interference from the sterilization zone, as shown in Figure Figure3.3. The pressure in the sterilization zone was then reduced to 268 kPa (calculated at flow
rate of 4 nl/s) and the boiling temperature was around 130 °C, which was lower than the set
sterilization temperature. Detail calculation can be found in supplementary S2.16Open in a separate windowFIG. 3.The temperature distribution of the chips (before packaged) with and without thermal isolation
trenches (powered at 1 W). The data were extracted from the central lines of infrared images, as
shown as inserts.Bacterial sterilization performance of the present chip was tested and the experimental results
were shown in Figure Figure4.4. E. coli with initial
concentration of 106/ml was pumped into and flew through the chip with the sterilization
temperatures varied from 25 °C to 120 °C at flow rates of 2 nl/s and 4 nl/s. The outflow was
collected and inoculated onto the SS agar plate evenly with inoculation loops. The population of
bacteria in the outflow was counted based on the bacterial colonies after incubation at 37 °C for
12 h. Typical bacterial colonies were shown in Figure Figure4.4. The
low flow rate case showed a better sterilization performance because of the longer staying period in
the sterilization channel. The population of E. coli was around
1.25 × 104/ml after a 432 s-long, 70 °C sterilization (at flow rate of 2 nl/s). While at
the flow rate of 4 nl/s, the cultivation result indicated the population was around
3.8 × 104/ml because the sterilization time was shorten to 216 s. A control case, where
the solution flew through an un-heated chip at 2 nl/s, was conducted to investigate the effect of
the shear stress on the sterilization performance (see the supplementary S3 for details16). As listed in Table TableI,I, the results indicated that the shear stress did not show any noticeable effect on the
bacterial sterilization. When the chip was not heated, i.e., the case with the largest shear stress
because of the highest viscosity of fluid, the bacterial cultivation was nearly the same as the
off-chip results (no stress). The temperature has the most significant effect on the sterilization
performance. No noticeable bacteria proliferation was observed in the cases with the sterilization
temperature higher than 100 °C, as shown in Figure Figure44.
Open in a separate windowaData in the table are shear stress (Pa)/population of bacteria, where “+++” indicates a large
proliferation, “+” means small but noticeable proliferation, “−” represents no proliferation.bOff-chip control group.Open in a separate windowFIG. 4.Sterilization performance of the present chip with E. coli and S.
aureus as test bacteria. All the original population was 106/ml. Inserted images
showed the images of the culture disk after bacteria incubation.Sterilization of another commonly encountered bacterium, Staphylococcus aureus,
with initial population of 106/ml was also tested in the present chip, as shown in Figure
Figure4.4. Similarly, no noticeable S. aureus
proliferation was found when the sterilization temperature was higher than 100 °C.In short, we demonstrated a microfluidic sterilization strategy by utilizing a continuous flowing
high temperature/pressure chip. The population of E. coli or S.
aureus was reduced from 106/ml to an undetectable level when the sterilization
temperature of the chip was higher than 100 °C. The chip holds promising potential in developing
portable microsystem for biological/clinical applications. 相似文献
Table I.
The E. coli cultivation results under different flow rates and sterilization temperatures. a| 25 °C | 70 °C | 100 °C | 120 °C | 25 °C b | |
|---|---|---|---|---|---|
| 2 nl/s | 1.89/+++ | 1.38/+ | 1.16/− | 1.04/− | 0/+++ |
| 4 nl/s | 3.78/+++ | 2.76/+ | 2.32/− | 2.08/− | 0/+++ |
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