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Pumping Speed vs Conductance

Vacuum technology novices, and even some veterans, have a tough time distinguishing between pumping speed and conductance. They seem to describe similar things and use identical units. This article attempts to make the distinction clear.

Formal Definitions of Pumping Speed

  • the volumetric rate at which gas is transported across a plane.
  • the ratio of the throughput of a given gas to the partial pressure of that gas at a specific point near the inlet port of the pump.

The first definition makes clear its dependence on volumetric rate, emphasizing that pumping speed is not about the quantity of gas measured by: “pressure x volume per unit time” or “number of molecules per unit time.”

Formal Definition of Conductance

  • the ratio of throughput, under steady-state conservation conditions, to the pressure differential between two specified isobaric sections inside the pumping system.

None of the definitions is easy to interpret. So I offer some informal interpretations and a thought-experiment involving molecule watching. Perhaps these will make pumping speed and conductance more understandable.

Practical Interpretation of Pumping Speed

You often hear talk about a pump sucking gas from a chamber. This is nonsense! If gas molecules are (magically) removed from one section of an enclosed volume, molecules in the remaining sections (in their normal high-speed flight) randomly collide and bounce off walls to fill the total volume at a lower pressure. For pumps this means until a gas-phase molecule propelled by collisions enters the pump's mechanism, that molecule cannot be removed from the chamber. A pump is more like a one-way valve into which gas molecules may enter but do not leave.

Suction

It is a common mistake to think a vacuum pump sucks gas from a chamber. There is no such force as suction. If gas molecules in one “section” of an enclosed volume are (for this paragraph, mysteriously) removed, then molecules from the remaining volume, in their normal random, high-speed flight, collide and bounce off walls until they fill the total space at a lower pressure.

Expressing it differently, until a molecule (propelled by random collisions) enters the pumping mechanism of a pump, it cannot be removed from the chamber. The pump does not reach out, grab a molecule from the chamber, and suck it in. Grasping that basic fact makes all other aspects of vacuum easy to understand. So, the first principle of vacuum technology is: Vacuum Doesn't Suck!

Pumping speed measures the pump's ability to remove gas from its inlet in some stated time period. But the measurement uses the gas volume, not the amount of gas. It might also be called a measure of the pump's quality. With any one type of pump, the higher this quality, the more expensive it is.

At any fixed pressure at the pump's inlet, there is a direct relationship between the volume pumped and the number of molecules entering the “one-way valve” in unit time. The table shows a pump with a 1000 L/sec pumping speed throughout its usable range. (For simplicity, atoms and molecules are lumped together and called “atoms.”)

Pumping Speed Inlet
Pressure
Number of
Atoms/cc
Total Volume
Pumped/sec
Total Number of
Atoms Pumped/sec
1000 L/sec 1 x 10-4 torr 3.3 x 1016 1000 L/sec 3.3 x 1022
1 x 10-6 torr 3.3 x 1014 1000 L/sec 3.3 x 1020
1 x 10-8 torr 3.3 x 1012 1000 L/sec 3.3 x 1018

If we could watch the molecules at an ideal pump's entrance, the movement would be in one direction only - into the one-way valve. As the inlet pressure reduced, the number entering would reduce, but the (volumetric) pumping speed remains constant.

While pumping speed is fundamental to determining a chamber's pump-down time, it is a common mistake to accept the manufacturer's quoted pumping speed as if it were the effective pumping speed of gas from the chamber. This is never true. The manufacturer measures pumping speed according to AVS or Pneurop procedures using a tiny chamber that blanks the pump's entrance. These ideal measurement conditions are never duplicated in practical vacuum systems. When the effective pumping speed is measured or calculated, it is always lower than the manufacturer's quoted value.

Practical Interpretation of Conductance

Imagine a chamber connected by a straight tube to a pump and the whole shebang is at a fixed pressure. If we did a “molecule watch” near the chamber-tube intersection, we could count the molecules/sec entering the tube and the molecules/sec returning from the tube. We would expect more to enter than return — after all, there is a pump at the other end that “disappears” some of the molecules.

Replace the pump with a blank flange and assume the chamber's pressure is still constant. In our new watch, we expect the molecule/sec entering to equal the molecules/sec returning. There's nothing about the tube and flange that can cause a 'disappearance'.

Now, replace the flange with another chamber — call it chamber 2 — at the same pressure as chamber 1. From our molecule-watching position in chamber 1, the molecules/sec entering the tube is the same as before. But what about the number returning? Since chamber 2 is at the same pressure as chamber 1, if we did a chamber 2 molecular watch the molecules/sec entering that end of the tube will be the same as the chamber 1 molecule-watch. And since pressure can't build up in the tube, the molecules/sec returning to both chambers is the same as molecules/sec entering. That is, replacing the blank flange with a chamber at identical pressure does nothing to the molecules/sec entering and returning.

The molecules/sec value is a measure of the tube's conductance — its ability to allow molecules to pass from one end to the other. But since we stated the pressure is fixed (like pumping speed), conductance is quoted as a volumetric flow.

What if we connect these two chambers with two tubes, one narrow bore and one wide bore? During our molecule watch now, we would expect the narrow tube to accept and return fewer molecules/sec than the wide tube. In simple terms, the wide tube has a bigger opening for molecules to “hit” during their random flights in the chamber. And, obviously, a molecule must enter the tube at chamber 1 or there can be no chance of its transmission to chamber 2.

If a molecule is to pass from one chamber to the other without hitting a tube wall, then its acceptance angle (the cone around the tube's axis) is smaller for the narrow tube than the large tube. Since we don't control the trajectory of molecules, we should expect that any molecule, traveling from one chamber to the other, has a greater chance of hitting the wall of the narrower tube than the wider tube.

Hitting the wall in any tube is undesirable since gas molecules are not reflected like light (with angle of incidence equal to angle of reflection). They hit, stick, and desorb with cosine distribution giving them equal chance of heading to either end of the tube and a maximum probability leaving the surface in a direction perpendicular to the surface.

The simple interpretation of these possible events is: the passage of molecules between chambers in the wide tube is “easier” than the passage in the narrow tube. That is, for tubes of equal length, wider tubes have a greater conductance than narrower tubes. For tubes of equal diameter, short tubes have a greater conductance than long tubes. The clear message for vacuum design - use short, wide bore tubes.

Units of Measure

Although both are measured in the same units of volume per unit time (for example, liter/sec, cubic meters/hr, cubic feet/min, etc.), the terms conductance and pumping speed should not be used interchangeably. Pumping speed applies to active devices that permanently remove gas molecules from a system (i.e., pumps or traps). Conductance applies to passive devices that simply transmit the gas from end to end (e.g., tubes, elbows, valves, non-cooled baffles). However, it is very relevant to ask how the pump's pumping speed is affected by the conductances of ports, valves between pump and chamber. We examine numerical combinations in Calculating Conductances.

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