- Open Access
Advances in Valveless Piezoelectric Pump with Cone-shaped Tubes
© The Author(s) 2017
- Received: 17 December 2016
- Accepted: 27 April 2017
- Published: 23 May 2017
This paper reviews the development of valveless piezoelectric pump with cone-shaped tube chronologically, which have widely potential application in biomedicine and micro-electro-mechanical systems because of its novel principles and deduces the research direction in the future. Firstly, the history of valveless piezoelectric pumps with cone-shaped tubes is reviewed and these pumps are classified into the following types: single pump with solid structure or plane structure, and combined pump with parallel structure or series structure. Furthermore, the function of each type of cone-shaped tubes and pump structures are analyzed, and new directions of potential expansion of valveless piezoelectric pumps with cone-shaped tubes are summarized and deduced. The historical argument, which is provided by the literatures, that for a valveless piezoelectric pump with cone-shaped tubes, cone angle determines the flow resistance and the flow resistance determines the flow direction. The argument is discussed in the reviewed pumps one by one, and proved to be convincing. Finally, it is deduced that bionics is pivotal in the development of valveless piezoelectric pump with cone-shaped tubes from the perspective of evolution of biological structure. This paper summarizes the current valveless piezoelectric pumps with cone-shaped tubes and points out the future development, which may provide guidance for the research of piezoelectric actuators.
- Piezoelectric pump
- Cone-shaped tube
In 1993, Swedish scientists Stemme et al , published the paper entitled “A valveless diffuse/nozzle-based fluid pump”. It marked the birth of the first non-rotary pump without any movable valve body driven by piezo-vibrators, which is invented based on the dynamic passive valve presented by Smith . The proposed pump consists of a diffuser, a nozzle and a piezoelectric vibrator, where the diffuser and the nozzle are mounted below the pump chamber as inlet and outlet of pump, and the piezoelectric vibrators are used as driving source to generate reciprocating change of volume in pump chamber. Along flow direction, the tube whose cross-section broadens is defined as the diffuser tube, while the one whose cross-section tapers off is defined as the nozzle tube. The two aforementioned flow tubes are collectively named cone-shaped tubes by their shape. Hence, the valveless piezoelectric pump encompassing these tubes is known as valveless piezoelectric pump with cone-shaped tubes.
The appearance of the valveless piezoelectric pump with cone-shaped tubes influences directly the classification of pumps. The conventional volume-type reciprocating pump is divided into the pumps using valve, but the cone-shaped tube pump does not have any valve from a common sense perspective. And in the definition of non-rotary pump, the valveless concept was thus generated. The emergence of the valveless piezoelectric pump with cone-shaped tubes also manifests the discovery of a novel driving source, piezoelectric vibrator, which can convert electric energy into mechanical strain energy of piezoelectric ceramic, and then transfer the mechanical strain into kinetic or potential energy of fluid through pump chamber and cone-shaped tube. This pump breaks through the banal definition of conventional pump and driving source, and eliminates the maladjustment between conventional pump and new driving source, as well as between new function and old principle . It is like a spring breeze blowing into the traditional industry of pump. Unlike the situation in a conventional pump with valve(s) and vibrator(s), no compromise should be made in the valveless piezoelectric pump with cone-shaped tubes because the cone-shaped tube with dynamic unidirectional character matches the driving source, piezoelectric vibrator, surprisingly well. Thanks to the facts that the driving source matches channel and the pump structure adapts its function, the valveless piezoelectric pump with cone-shaped tubes becomes competitive in the fields of bio-engineering, micro/nano manufacturing and micro/nano driving [4–9], thus attracting much attention of researchers. According to our retrieve data using “piezoelectric pump” as a key word, there are nearly 1400 papers available, of which the papers about the valveless pump with cone-shaped tubes accounts for nearly one-third of the total.
Hence, this paper will review the structural evolvement of the valveless piezoelectric pump with cone-shaped tubes over the past 25 years and pinpoint those milestones in its developing history. After the classification of various valveless piezoelectric pumps with cone-shaped tubes and the functional analysis of each type, researchers will also endeavor to shape the future development and implications.
2.1 Three-dimensional structure
The resonant frequency of pump depended on the structure of pump, fluid density and piezoelectric parameter of vibrator, etc.
The amplitude of vibrator was linear with driving voltage.
The pressure output of the valveless piezoelectric pump with tapered angle of 5.3° (Type A) was higher than that with tapered angle of 10.7° (Type B), but the volume flow rate of Type A was smaller than that of Type B. The pressure loss coefficient of the nozzle tube was always larger than that of the diffuser tube.
The performance of the diffuse was related to the element geometry of flow channel, while that of the nozzle was independent of the element geometry.
The flow channel of the diffuser/nozzle element can be divided into three regions, i.e., the inlet region, the outlet region, and the diffuser/nozzle region in the middle (Fig. 2).
Although their results seem to be a little out-dated and some are even not quite right, Stemme E. and Stemme G. are still two pioneers in the field. They created a new era of piezoelectric pump with their unique piece of work. With the presentation of valveless pump, the match between the old valve body and novel driving source, like an intermarriage of traditional European aristocrats and American newly rich, is no longer worrisome. Eventually, the cone-shaped tube perfectly adapts to the piezoelectric vibrator dynamically.
Since then, piezoelectric pumps have entered a new period of development and stepped onto a broader arena. The research and development of valveless piezoelectric pumps, led by the investigation on the valveless pump with cone-shaped tubes have drawn increasing attention and achieved fruitful results. Therefore, we subsequently survey the progresses in the development of valveless piezoelectric pump with cone-shaped tubes.
Suppose that the piezoelectric oscillator is bounded on the pump chamber.
Suppose that pump chamber is connected to transfer flow through at least one cone-shaped tube.
Suppose that using macroscopic flow direction define the different types of cone-shaped tubes, with the macroscopic flow direction becoming wider gradually defined diffuser and on the contrary, defined nozzle.
The definition is that no matter how figure shows in papers, flow channel sectional area flowing into pump chamber from the left of center line of piezoelectric pump is larger than that from the right of center line.
On the wafer of the single-crystal silicon, trapezoidal cone flow channel was etched, whose shape could be imagined as a hollow topless pyramid. Etching was processed along lattice angle formed naturally. The angle between the bottom surface and any side face is 54.74°, and the angle between either opposite couple of side faces is 70.52°, that is, the angle of square cone is 70.52°, as shown in Fig. 4. By using the equivalent circuit method, it can be concluded that the pump mechanism cannot be in effect until the Reynolds number of the micro-conical flow tube is larger than 100.
All these aforementioned pumps are valveless piezoelectric pumps with cone-shaped tubes in the form of solid structure. Here, the “solid structure” refers to a three-dimensional structure that the cone-shaped tube, as a flow-resistance-type non-movable valve, retains, such as cone, square cone and so on. For fluid delivery, the solid structure has the advantages of good symmetry, little disturbance, easy to control and high efficiency. However, it also has some disadvantages with respect to the structure itself, such as big duty cycle and difficulty in processing. Probably influenced a lot by the research from Stemme  and Gerlach , early valveless piezoelectric pumps with cone-shaped tubes were mostly in the form of solid.
2.2 Plane structure
All those above are valveless piezoelectric pumps with cone-shaped tubes in the form of plane structure. The so-called “plane structure” refers to two-dimensional or two-and-a-half dimensional in-plane structure that the cone-shaped tube has, as the flow-resistance-type non-movable valve. When cutting this structure in the longitudinal direction by using the tapered plane up and down, we will always obtain new tapered planes in the same shape. (That is to say, for a cone-shaped tube in the form of plane, the new tapered shapes generated in the longitudinal direction are all the same). The advantages of the plane structure include, with respect to the structure itself, small duty cycle, easy implementation of internal structure design and optimization for the cone-shaped tube, easy processing, easy realization of miniaturization. But there also exists some disadvantages with respect to fluid delivery, such as bad symmetry, large system disturbance, low efficiency, and necessary consideration of the on-way flow resistance.
What is worth mentioning in particular is that the valveless piezoelectric pump with a single raindrop-shaped tube developed by Huang, Wang and Yang [29, 30]. This pump can be used in structural design to realize the special fluid delivery or energy transfer. It can match the energy consumption between diffuser and nozzle, which may become a design direction for the valveless piezoelectric pumps with cone-shaped tubes in the future. But this structure may be not suitable to be called “cone-shaped tube” if it goes into a far more complicated form, same as the evolution of mankind itself from the ape.
2.3 Brief summary
In the past twenty years, a considerable amount of research and development has been conducted by researchers from all over the world on the topic of single-type valveless piezoelectric pumps with cone-shaped tubes, which reveals in depth the structural characteristics of the pumps (e.g., piezoelectric vibrator, diffuser/nozzles, pump chamber). Whether the pump is in the form of plane or solid structure, it always contains those characteristics.
Relationship between cone angle and flow direction
Cone angle θ / (°)
Flow direction deduced in Ref. 
After reviewing the above history of technology, the research on cone-shaped tube of single-type pump can be retrieved to the papers studying fire sprinklers one hundred years ago, or even earlier. In this sense, the valveless piezoelectric pumps with cone-shaped tubes can be regarded as the innovative applications of a traditional structure. From a wider-dimensional perspective, we can learn from the organism itself to develop the applications of the cone-shaped tubes.
In 1999, Owerkowicz, et al reported that the gullet of a varanid had a function similar to that of a car’s turbocharger, thus assisting lung ventilation and providing sufficient supply of oxygen . As the gullet plays a role of inlet channel and realizes pressure boosting, it’s necessary for it to equip with the ability of fluid resistance control. It can be observed that the structure of the varanid’s gullet is a kind of cone-shaped tube.
To pursue scientific discovery and technology advance, scientists create continuous innovation by inventing novel structures of valveless piezoelectric pumps with new principles. In this sense, the valveless piezoelectric pumps with cone-shaped tubes have been significantly improved. But in the sense of learning from the structures and principles of the organism itself, the improvement of the valveless piezoelectric pump with cone-shaped tubes is far from significant. A new challenge for scientists is to think about human being itself, as well as to imitate and optimize it.
3.1 Parallel structure
The combined valveless piezoelectric pump with cone-shaped tubes was fabricated on a brass substrate with thickness of 1 mm. The diameter of single piezoelectric vibrator was 13 mm. The cross-sections of both diffuser and nozzle were square, where the narrowest size was 0.3 mm × 0.3 mm. When the two pump chambers were working in reversed phase, the maximum flow rate was 16 ml/min at the driving frequency of 540 Hz and the maximum pump pressure was 1.7 m. Compared with the performance of the two pump chambers working in a same phase, the pump flow increased by 2 times and the pressure increased by 3 times.
Pump dimensions and measured pump performance 
W1 / μm
L / μm
α / (°)
d 1 / μm
Q 1 / (μL·min−1)
H 1 / mH2O
d 2 / μm
Q 2 / (μL·min−1)
H 2 / mH2O
3.2 Series structure
3.3 Brief summary
The combined valveless piezoelectric pump with cone-shaped tubes was invented soon after the invention of single valveless piezoelectric pump with cone-shaped tubes. So, we would like to thank Olsson and Stemme et al. for their great contribution to the valveless piezoelectric pump with cone-shaped tubes, who let once again demonstrated the logic of technological progress. Since the efficiency of fluid transfer for a single valveless piezoelectric pump with cone-shaped tubes was low, the idea of making a combined valveless piezoelectric pump with cone-shaped tubes naturally came into being.
The macroscopic fluid converge refers to the fluid flow of the system during a complete cycle. At the micro level, fluid converge is the process of the diffuser and the nozzles transforming between each other during suction stage and discharge stage in a single cycle. The conversion of the diffuser and the nozzles results in the shunting and impact of the fluid at the above-mentioned concentration junction, which will cause the trend of the shunting and the impact of the fluid within the pump chamber.
This is the case of the parallel structure and synchronous phase as driving signal only. It is also necessary to discuss the case of the parallel structure and asynchronous phase as driving signal. Here, valveless piezoelectric pump with a phase difference of 180° and small cone angle (about 10°) is taken as an example. In the case of the parallel structure and asynchronous phase as driving signal, the inner and outer circulations of the flow path are generated. The inner circulation means that two independent piezoelectric pumps are driven asynchronously, and therefore, one pump is in the suction period (the pump volume becomes larger) and the other is in the discharge period (the pump volume becomes smaller). The flow between the two pumps is called inner circulation. The outer circulation means that the flow between each pump and the flow path of the external system.
Under the aforementioned complex condition, it is difficult to determine which differential pressure (flow rate) is better, the one generated by synchronous phase or the one by asynchronous phase, are better. Nevertheless, the following factors need to be discussed in detail: driving force output by piezoelectric vibrator, driving frequency which forms vibration and frequentness of inner and outer circulation, boundary condition of cone angle, boundary condition of pipe tee of confluence and diffluence, boundary condition of pump chamber, etc. In further research, researchers are trying their best to clarify the impact of these factors.
It is worthwhile to mention that the pumps shown in Fig. 30 are synchronously driven in a parallel structure. They share a same pump chamber and a same driving source. The analysis of this pump is different from other valveless piezoelectric pumps with cone-shaped tubes of synchronous phase mentioned above. In this paper, the authors think its structure over and hypothesize that this pump may have the problems of vibration, shock, and inner and outer circulation, thus can be a preferred and suggested option for micro- mixer and agitator.
Up to now, few papers solely about series-connected valveless piezoelectric pump with cone-shaped tubes have been found in our retrieve data, and their research is also superficial. Series structure is a type of array to connect one pump’s pump chamber and piezoelectric vibrator with another one’s by connecting their cone-shaped tubes in turns. A separate unit of series-connected structure, including a group of flow tubes, piezoelectric vibrator and pump chamber, still exhibits phenomenon of vibration, and the flow in the lower level of separate unit vibrates and shocks more severely than that in the upper level. At the same time, turbulence and eddy in the lower separate unit are also severer than that in the upper level. Here, this phenomenon is defined as amplification and carrying in the series-connected valveless piezoelectric pump with cone-shaped tubes.
Amplification and carrying phenomena may bring a relevant increase of energy into the unit of the lower level. Therefore, it is necessary to consider the energy offering when designing the series-connected valveless piezoelectric pump with cone-shaped tubes. In the pump, the piezoelectric vibrators should not be designed in a series connection of exactly same vibrators, but of the vibrators with input driving energy increasing by levels. At the same time, carrying phenomenon brings the related increase of turbulence and eddy energy to the lower level of unit cone-shaped tube. So it is required to design cone-shaped tubes with Reynolds number increasing level by level, not just the simple series of the same cone-shaped tubes.
The above content is just a review of the technique history. The research of cone-shaped tubes of combined pumps can be retrieved to the papers of studying fire sprinklers connected in series at the beginning of last century. Viewed from this angle, cone-shaped tubes of combined pumps were not an innovative structure. If further consideration is given to more ancient and wider dimensions, maybe we can learn from organism itself to develop the applications of the cone-shaped tubes in the combined forms.
The history of valveless piezoelectric pumps with cone-shaped tubes in the past two decades has been reviewed. The valveless piezoelectric pumps with cone-shaped tubes have been classified into the following categories: single valveless piezoelectric pump with cone-shaped tubes (solid structure and plane structure) and combined valveless piezoelectric pump with cone-shaped tubes (parallel structure and series structure).
The functions of various types of cone-shaped tubes and pump structures have been analyzed, and future research directions of valveless piezoelectric pumps with cone-shaped tubes have been summarized and identified.
The historical theory, provided by the literature, highlighted that for a valveless piezoelectric pump with cone-shaped tubes, cone angle determines the flow resistance and the flow resistance determines the flow direction. The theory has been discussed and verified by each valveless piezoelectric pump with cone-shaped tubes presented in this study.
The bionics deduced from the evolution of biological structure may play an important role in the future development of valveless piezoelectric pump with cone-shaped tubes.
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