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How many diavolumes until the buffer is exchanged?

UF/DF concentration factor and diavolume calculator

Works out how many times ultrafiltration (UF) concentrates the product, how much of the original salts remain after buffer exchange by diafiltration (DF), and how many diavolumes it takes to reach your target.

When to use itUse it at the end of purification, in the UF/DF step that moves an antibody into its formulation buffer, to estimate buffer volume and processing time.

Prefilled with an example: concentrating 10 L down to 2 L, then exchanging 5 diavolumes of buffer. Change any value and the result updates.

L

The volume on the feed side of the membrane (retentate) when concentration, or diafiltration, starts.

L

The volume you want to end up with. Same unit as V0.

DV

Total buffer added divided by the volume at the start of diafiltration. 1 means you exchanged as much buffer as the liquid volume.

%

Enter 99 to remove 99% (leaving 1%). Use a value from 0 up to, but not including, 100.

Concentration factor (CF)5 ×
Original component remaining0.6738 %
Diavolumes needed for the target4.605 DV

Going from 10 L to 2 L concentrates large components such as the antibody about 5 times. After 5 diavolumes, the calculated share of the original salts left is 0.6738%, and removing 99% takes about 4.605 diavolumes. Decide the end point by measuring conductivity and pH, not by the count.

Guide to the number of diavolumes (DV)

The row that matches your result is marked.

  • Fewer than 3Still in progress (over 5% left)By the guide in our related article, about 37% remains after 1 diavolume and about 5% after 3. Much of the original buffer is still there, and you are not at the end point.
  • 3 to under 5Well along (about 0.7 to 5% left)Removal is exponential, but exchange above 99% usually takes 5 to 7 diavolumes, so this range falls short.
  • 5 to under 7Your resultUsual completion range (about 0.09 to 0.7% left)Small components such as salts are usually more than 99% exchanged within 5 to 7 diavolumes. About 0.7% remains after 5 and about 0.09% after 7. These are calculated expectations, though.
  • 7 or moreExpected to be fully exchanged (about 0.09% or less)Beyond this, removal continues by orders of magnitude, but buffer species can lag behind the calculation because of charge effects (the Donnan effect) or incomplete passage through the membrane (sieving coefficient below 1).
  • Deciding the end pointDiavolumes are a guide; measure to decide the endThe main point of our related article: use the number of diavolumes only to estimate the work, and decide the end point by measuring conductivity, pH and osmolality in the retentate. In practice, the end is when they nearly match the target buffer. The count alone does not decide it.

How it is calculated

The concentration factor is the volume ratio, assuming the protein, which does not pass the membrane, is almost entirely retained. The fraction remaining is an ideal value that assumes small components such as salts pass the membrane freely (sieving coefficient = 1) and the liquid is well mixed. Each diavolume cuts what remains to about 37% (1/e).

concentration factor CF = V0 ÷ Vf fraction remaining = exp(−DV) DV needed = −ln(1 − target removal)

Source: Concentration factor CF = V0 ÷ Vf, and the fraction remaining after diafiltration is exp(−DV). This is standard UF/DF (TFF) theory (see, for example, the Millipore and Cytiva UF/DF handbooks).

With your numbers

  1. CF = initial volume V0 ÷ final volume Vf = 10 ÷ 2 = 5×
  2. remaining = exp(−DV) × 100 = exp(−5) × 100 = 0.6738 %
  3. DV needed = −ln(1 − target removal % ÷ 100) = −ln(1 − 99 ÷ 100) = 4.605 DV

Limits of this calculation

  • The fraction remaining, exp(−DV), is an expected value assuming small components pass the membrane freely (sieving coefficient = 1) and ideal mixing. It is not the end point itself.
  • In real solutions the sieving coefficient may be below 1, and charged buffer species may be unevenly distributed by the Donnan effect, so exchange can lag the calculation. Buffer species often exchange more slowly than salts.
  • In high-concentration formulations, the volume taken up by the protein (excluded volume effect) shifts the actual buffer concentration. Conductivity and pH can appear to reach the target while the composition still does not match.
  • The concentration factor V0 ÷ Vf is a volume ratio that assumes the protein is fully retained by the membrane (sieving coefficient ≈ 0). The concentration actually reached is affected by losses through the membrane and by liquid held up in the system (hold-up volume).
  • The end point is normally decided by measuring several values, such as conductivity, pH and osmolality, never by the number of diavolumes alone (a consistent recommendation in our related article).

Primary sources

Every calculator gives an estimate for learning, built on published information and primary sources. Real decisions follow the applicable guidance and expert judgment.