Abstract Flow and Its Presence in Problems

by Igor Polkovnikov (AKA Igor Polk). Started 2014-02-22, this version 2014-02-27, www.virtuar.com/triz/2014/flows.htm

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An intuitive idea of a flow between systems is formalized to include changes in distance, area and volume. It is possible that the generalized "flows" participate in 2/3 of TRIZ problem formulations and solutions. A table of problems taken from the Altshuller's book "Creativity as an exact science" shows participating flows and their functions. It is proposed that the notion of abstract flows may help in general definition of interaction and expand TRIZ application to new areas.

Keywords: TRIZ, flow, system, interaction, automatic problem solving, flow of distance, flow of area, flow of volume, boundary.


Despite any definition one gives to a word "system", if there is a system, there is surrounding of this system. It may be another system, systems, or the "environment". If there is a system and surrounding, there is a boundary between them.

Contrary to an abstract boundary which is a line, surface, etc., i.e. a product of human's mental considerations, a boundary between a system and its surrounding is real. And again, contrary to abstract boundaries a real boundary is not precise. It has some vagueness in its existence. In TRIZ terms, it combines, may be on a micro- or a micro-micro- level properties of the system and its immediate surrounding. As such it may attract attention of TRIZ developers as an area combining contradictory properties. For now, let us take that a boundary is abstract, ideal, ignore the effects in the boundary.

When subsystems Subs of a system S1 pass the boundary B it is called a flow. From where Subs are coming is irrelevant for now. They can be passed from internals of the system or be formed right on the boundary. The concept of flow implies the abstract movement and time. Regarding where the flow goes, there are three cases possible. First, when Subs pass to the environment. Second, when Subs pass to another system. Both of them will be called S2. Or third, when Subs become a part of system S1 right after passing the boundary B.

Systems posses a property of stability. It relates to flows too. Water flow is a system itself, traffic flow is a system on a road.

There should be a mechanism providing the flow. Speaking generally, borrowing from physics, it can be called a difference of potentials or dP. Subs being responsive to a certain potential PS1 are moving in the direction of lower potential PS2. Another constraint of flow existence is the passing property of the boundary, is it able to pass the flow.

A boundary may have two regions. One may be able to pass Subs, BP. Another one, BI, not. It insulates S1 from S2 in relation to the Subs flow.

Subs are systems themselves. They may possess other subsystems or/and properties. Let us call them all E. In particularly, an E may be a subject of dP, move over the B and curry the whole Sub with it. Example, the charged dust particles moving in electrical field. On the other hand, in this case, instead of talking about a flow of Subs, one may abstract, ignore Subs, and talk about a flow of E.

A system issuing a flow of Subs directly affects the environment or the neighboring system by injecting Subs into it.

If there is a system S1 and a system S2 ( it may be an environment, for briefness I will use "system" from now for both), and there is a third system SC which conducts the flow of Subs from S1 to S2, the SC is called a conductor. It conducts the flow from S1 to S2. The conductor may have three regions of its boundary. First with S1, second with S2, and the third one with some other system, systems, or environment. The third one may be absent. In a case when the conductor has insulation with the third systems, it is called a pipe SP.

Within a single system, there can be a field of potentials inducing a field of flows. In relation to flows, systems posses such properties like capacity, resistance.

Examples of Flows

Here are some examples of basic physical flows:

Flow Potential E  
Flow of liquids Pressure Particles of liquid with mass  
Flow of mass Gravity Everything which has mass  
Electrical flow Electric potential Electrical charge, electrons, protons  
Heat Temperature Heat  
Flux of momentum Velocity Momentum  
Diffusion Concentration Molecules  

Abstraction 1

If many Subs are moving, it is a flow. When only one Sub is moving it is a flow too. For example, two boys through a ball at each other.

Abstraction 2

When two flows exist or may exist, it is called a contra flow. The actual flow may be absent because a system is in rest, but there is a cause for both flows. The flows balance each other.

Example 1. If two vessels with the same level of liquid in gravitational field are interconnected with a pipe, there is no flow through the pipe, or one can say there is a contra flow. Liquids from one vessel diffuse to another, but this is not a flow caused by gravity. If one vessel is moved, the flow caused by gravity will appear in one direction or another.

Example 2. Let a weight be put on a spring in gravitational field. Movement of the weight is a flow. In some time the system will come to a balance when the spring is compressed and there is no movement. The flow of the weight down initiated by the gravity is balanced with the flow of weight movement up initiated by the spring. If the gravitational field is suddenly switched off, the spring will push the weight up.

Contra flows may not necessary balance each other. When a contra flow exists, one flow may be compensated by another flow partially or completely. Also, contra flows are not the same as two different flows between S1 to S2. In the case with two different flows as well as with contra flows, one might say that the systems interact.

Abstraction 3

Example 1. Let us look at a small water flow in desert. With the rain, water comes out of a small pond and starts flowing down the dry stream bed. At the front of it, a boundary between water and dry bed exist. With every drop of water flowing into it from upstream, the water spreads down. Water flows out of the stream, but it stays as a part of the water stream.

Example 2. The gas confined in a cylinder S sealed with a movable piston is heated. The gas expands, the piston moves. The gas obtained a larger volume as if there was a flow of volume from the environment E into the gas. If the piston is pressed, decreasing the volume of the gas, one might say, there is a flow if volume from the gas to the environment.

Here we came to the abstract flow of volume. A Sub here is an elementary volume of gas, but one may say there is a flow of volume.

Similarly, in two dimensions, one may say that there is a flow of area, if, for example, in a triangle ABC a side BC inflects. A flow of dS from S to E.



Similarly, in one dimension, one may say that there is a flow of distance. For example, here, if a point S is moving along a line BA, there is a flow of distance dX from the segment AS to SB.




Flow Functions

- Generation
- Formation of a flow
- Insulation
- Changing parameters, controlling (with potentials, resistance)
- Capacity
- Moving contrary to potential


- Reflection
- Filtration
- Accelleration ( + accompanying effects)
- Termination
- Detection ( + in the past)


- Effects of gradient in flows
- Effects of origination of a penpendicular flow
- Effects of uneven flow (page 157, Principle 15)
- Impuls and periodic flows (Pr.21, 24, St 7, Pr 25, 48)
- Creating flows of what can not flow
- etc., etc.


System Effects

- Charge-Discharge (when the second system is large);
- Exchange between systems;
In a single conductor:
- When the transferred system contains two elementary properties, charges, the difference of the second potential appears;
- Concentration effect, etc. When a difference of one potential creates a difference of another potential;


- When one system is captured and carried by another one;
- When one flow is regulated by another one;
In a couple of conductors:
- Effect of contact potential difference;
- Effects when charges of a flow overcome contact potential difference (may be of another kind);
- Effects of thermocouples and other couples.

Transformation of Flows:
Physical Effects

1. Potential - Elementary property (electric potential-electical charge);
2. Potential - Flow
- Potential - flow of the same kind (temperature-heat)
- Potential - flow of another kind (temperature-deformation);
3. Change of capacity => Change of potential (area of geometrical, math effects);
4. Changing fileds geometry (area of math effects);
5. Change of elementary transfer parameters (resistance);
6. Etc.


All actions and interactions are flows



1) Flows belong to the domain of Systems Theory (TRIZ).
With abstract flows which expand flows concept to all movements, system theory obtains a new passage to mathematics and physics.
2) Cross-disciplinary abstraction of actions through flows may be valuable for artificial intelligence, particularly in automatic inventive problem solving.
3) With TRIZ problems being 2/3 about abstract flows, open application of flows theory may lead to new achievements.


Everything flows, nothing stays still

Heraclitis of Ephesus (535-475 BC)


Web reference to the presentation


In particularly,


Potential and "Charge"

Gravity Gravitational potential Mass
Electricity Electrical potential El. charges
Diffusion Concentration Moleculus
PΔV Pressure Volume



Flows in TRIZ

How often flows are encountered in inventive problems? To make a rough estimate I took the famous Altshuller's book and went through all problems given there. Out of 143 problems, in 100 problems flows where part of the problem formulation or a solution. In 43 problems I was not able to find references to flows.

Here is the table where I wrote a problem name, what flows are there, and what functions related to flows are in those problems. On the left, for convenience, there are page numbers of the two editions of Altshuller's book, in Russian and in English. The Russian edition is "Творчество как точная наука", Г.С.Альтшуллер, Москва, "Советское радио", 1979. The English edition is "Creativity as an exact science", by Al'tshuller, G.S., Gordon and Breach Science Publishers, 1984, ISBN 0-677-21230-5.

Name Flow of Functions
  17 Problem 1, conveying liquid oxygen into the furnace liquid oxygen, heat providing, insulation
  18 Problem 2, lighting of welding place light reflection
  21 Problem 3, wood and bark chips -  
  29 Problem 4, polishing lenses water replace, generate
  45 Problem 5, killing Bolton bullet from a gun indication of past flow
  46 Problem 6, plough testing ground plough through the ground resistance, conductivity
  46 Problem 7, measuring depth of river from aircraft water geometrical
  47 Problem 8, measure an abrasive disk wear area of circle geometrical
  48 Problem 9, find leaks in refrigerators liquid indication now
  48 Problem 10, measure degree of polymer hardness ?  
  48 Problem 11, intensity of movement in pseudo-liquification chaotic solid particles measure waves
  48 Problem 12, extractable wedge heat create, enable phase transitions in the conductor
  59 Problem 13, filtering air from dust air and dust filtration
  64 Problem 14, paper electrifying paper along plexiglas insulation
41 67 Problem 15, drilling shaft jamming deformation of solid body effect accompanying the flow ( de-magnetization)
42 69 Problem 16, floating solid moving in magnetic liquid solid in 2D liquid enhancing controllability
42 70 Problem 17, (Ac 304356) pneumoflow of solid balls solid balls protecting the pipe (conductor)
43 70 Problem 18, close-fitting testing with paint -  
43 71 Problem 19, mixing rotating flow of something generate
43 71 Problem 20, orientation of micro diamonds -  
43 71 Problem 21, cavitation on hydrofoils hydrofoils through water effect accompanying the flow (generation of "bubbles" in the flow)
43 71 Problem 22, measure stress on reinforcement micro deformation measure
45 76 Problem 23, pre-stressed reinforced concrete deformation, heat generate
52 89 A "weevil" problem ( dolgonosik ). It seems does not have a flow, but Altshuller used an analogy with "temperature of a single droplet if it is raining and one can gather a glassful of rainwater", or with flow of water... Glass is a capacity. particles capacity
- 287 Problem 24, polishing spoons chaotic particles effect accompanying the flow (polishing)
- 287 Problem 25, radio-telescope radio waves from stars, lightning, electrical current in conductors shielding
57 98 Problem 26, about heated catalyst -  
58 100 Problem 27, inclination gauge -  
58 101 Problem 28, checking cones -  
58 102 Problem 29, animations -  
59 102 Problem 30, greenhouse ( transformation of temperature into linear movement) -  
59 103 Problem 31, metal cubes and aggressive liquid -  
59 103 Problem 32, a moment of boiling find a flow detection
66 117 Problem 33, a speed boat -  
75 134 Problem 34 cylinder painting aerosol  
78 139 Problem 35, ions ions reflection
81 144 Problem 36, pulp in a pipeline water-solid mix  
81 145 Problem 37, sealing ampoules heat insulation
81 146 Problem 38, rate of acceleration -  
81 146 Problem 39, chemical deposition atoms termination of the flow, activation
82 147 Problem 40, measure density with Archimedean force solid in water controlling with potential
82 148 Problem 41, alcohol in tank alcohol extracting from flow
84 151 Ex. to Principle 1, -  
84 152 Ex. to Principle 2, removal noise, vibrations insulation
84 152 Ex. to Principle 3, local quality liquid, drops insulation, making a pipe
85   Ex. to Principle 4, -  
85   Ex. to Principle 5, -  
85   Ex. to Principle 6, -  
85   Ex. to Principle 7, -  
85 154 Ex. to Principle 8, counterweight air, wing perpendicular flow
86 155 Ex. to Principle 9, preliminary counter-action vibrations controlling with potential, suppression
86   Ex. to Principle 10, the same like Problem 41  
86   Ex 1. to Principle 11, cushion chemicals diffusion boundary effect
86 156 Ex 2. to Principle 11, tree branch nutrition chemicals in water creating capacity
87 156 Ex. to Principle 12, equipotentiality material bodies flow equipotentially (in crossing direction to potential gradient)
87 156 Ex. to Principle 13, -  
87 157 Ex. to Principle 14, -  
87 157 Ex. to Principle 15, strip electrode metal strip with width varying effects of uneven flow
88   Ex. to Principle 16, the same like Problem 34  
88   Ex. to Principle 17, -  
88 159 Ex. to Principle 18, cutting timber without a saw solid in solid decreasing resistance
89 159 Ex. to Principle 19, welding and measuring thermo-electric motive force (emf) electrical current effects on junctions
89 160 Ex. to Principle 20, drilling solid in solid flow and contra-flow, constant flow
89 160 Ex. to Principle 21, veneer heating heat impulse flow
89 160 Ex. to Principle 22, restore flowing of loose dry disperse particles generation of flowing particles
90 161 Ex. to Principle 23, feedback principle heat, solid particles, gas  
90 161 Ex. to Principle 24, tension measurement device calibration deformation interruption
90 161 Ex. to Principle 25, welding rod feed metal wire generation
90 162 Ex. to Principle 26, -  
91 162 Ex. to Principle 27, mouse-trap a mouse "Maxwell's daemon" flow generator
91 162 Ex. to Principle 28, metallization of plastic surface "diffusion" intensification
91 163 Ex. 1 to Principle 29, "air bag" on a drive shaft momentum turning on-off or switching
92 164 Ex. to Principle 30, gas-concrete gas insulation, generation
92 165 Ex. to Principle 31, porous steel machine elements head, liquid a flow intensified by another flow
92 165 Ex. to Principle 32, transparent bandage liquid, light filter
93 165 Ex. to Principle 33, cast mould deformation contraflow to eliminate the flow
93 166 Ex. to Principle 34, melting light-conductor light, solid flow of flow conductor
93 166 Ex. to Principle 35, breaking zone of landing stripes aircraft increasing resistance, stopping
93 166 Ex. to Principle 36, sealing with cold metal heat, deformation  
93 167 Ex. to Principle 37, greenhouse head, deformation, movement transformation of flows
94 167 Ex. to Principle 38, chemical gas transporting reaction molecules increase stopping
94 168 Ex. to Principle 39, cotton transportation cotton, gas prevention of the effects
94 168 Ex. to Principle 40, cooling heat stabilization
97 172 Problem 42, paraffin deposits oil, paraffin deposition
97 172 Problem 43, sprinkler machine water, momentum, weight  
97 173 Problem 44, vacuum bag -  
97 173 Problem 45, Mobius tape -  
101 182 Problem 46, pressed ball ball impulse generation
103 184 Ac 259949, -  
103 185 Ac 282342, power plant circle heat, two reacting chemicals circle with two different flows
103 185 Ac 152842 -  
103 185 Ac 247159 -  
104 186 Ac 465502 -  
105 188 Ac 247064, electromagnetic pump as a ship propulsion engine ionized water propulsion
105 188 Ac 489862 - next, micro movement displacement  
107 193 Ac 518591 Maltese cross mechanism magnetization -  
107 193 Problem 47, improve a spring -  
108 194 Problem 48, ferrite warmers -  
108 195 Ac 452055, effect "Hopkinson Peak" heat, electromagnetic energy stabilization of one flow to achieve the maximum of another.
109 196 Ac 504944, effect similar to Barkhausen effect deformation, electromagnetic energy (force is potential)
    Barkhausen effect heat, electromagnetic, orientation of domains transformation of continuous flows into discrete
110 198 Problem 49, measure high voltages electromagnetic  
111 200 Problem 50, tomato sorting There are ;)  
111 201 Problem 51, weigh railcars with scrap metal -  
112 202 Problem 52, precise control of the flow between vessels gas, displacement perpendicular flows, flow control: "valve"
112 202 Problem 53, heat centrifuge angle of rotation perpendicular flows, effect on a flow
112 203 Problem 54, brilliant cut in pieces -  
112 204 Problem 55, stabilizing transmission angle of rotation  
118 214 a problem about a drum furnace cement, heat  
129 234 Standard 1, Ac 415516, diamond changes with heat heat, light, displacement  
129 234 Standard 2, Ac 350219, yellow, blue, green.. light of different color multiple flows, combination of flows
129 235 Standard 3, Ac 412062, protection of hydrofoils water deposition, "inversed pipe"( solid inside the flow)
129 235 Standard 4, magnetism magnetic liquid, magnets controllability, change of flow-not flow
130 236 Standard 5, system->subsystem -  
130 236 Standard 6, -  
130 236 Standard 7, combination of mutually exclusive actions any flows in pauses of each other
130 237 Standard 8, trigger and measure vibrations (any parameters of response) any, vibrations, waves  
132 241 Problem 56, pack fruits peaches  
133 242 Application 1 of morphological analysis liquid, magnetic field, electrical current perpendicular flows
135 245 Ac 499912, non-die drawing of steel wire through a ferromagnetic mass steel wire, deformation narrowing the flow
135 246 Ac 165651, rotating magnetic field - rotating part metal inversion of the pair system-flow
135 247 Ac 397289, -  
136 247 Problem 57, -  
136 248 Problem 58, obtain polymer miniscule spheres compressed air, liquid polymer, solid spheres process within a flow
136 249 Problem 59, are the lids tight? air in liquid detection of conductors
137 249 Problem 60 -  
137 250 Problem about heat-resistant insulation of a converter -  
138 251 Problem about hydraulic extrusion wave of pressure  
139 254 Ac 270209, swamping concrete gravel  
139 254 Problem 61, metal-plating lubricants molecules decomposition, deposition
141 258 Problem with Antonov's aircraft aircraft-air stabilization
142 260 Problem with"armed" machine flows through measuring
149 275 Problem with coiling wires metal wire, liquid metal transforming
150 277 Paradox of traveling of hydrogen atoms off metal molecules, hydrogen forming
151 279 Problem 62, turn rubber on a lathe -  
152 280 Problem 63, Toms effect liquid decrease friction
152 280 Problem 64, measure critical level sound indication, a flow through everything
152 281 Problem 65, melting beryllium -  
152 282 Problem 66, breaking-in of engines there are..  
153 283 Problem 67, -  
153 283 Problem 68, -  
153 284 Problem 69, soldering capillaries hot solder  
153 284 Problem 70, -  


With the formalization proposed, it is assumable that the majority of TRIZ problems have, operate with the "flows". As one can see from the right table column, there are numerous functions, situations associated with flows. All of them are systematic, they are general and applicable to any flow. Such properties of the "flow" system domain as "potential", "capacity", "conductivity" are not researched in general TRIZ, but they are abundant in scientific research and technology. The inventive problems might be restated in terms of flows and all phenomena related to them, which might lead to a better solution path. Bringing "flows" into TRIZ may expand its application, and may enable automatic solution of inventive problems. In future, the proposed formalization unifying "movements" in Euclidean space with flows may support "mathematization" of TRIZ. The proposed formalization is an idea, but it seems to have merits for more research.