A common question we get is: **how many cells can one of your microbubbles lift?**

For many users, the most important questions around microbubble-based separation will have to do with how many microbubbles to add to a sample. To answer this question, it requires getting into what is the total ‘lifting capacity’ of a microbubble.

Part of the answer derives from how a microbubble engaging cells or clumps of cells or even larger structures such as spheroids or mammospheres. Any of these will rise as long as the combined density of the bubble and its passenger cells remains less than the density of the surrounding fluid.

That’s the good news. The unavoidable flip side is that as more and more cells load onto a bubble, the slower and slower it will rise, and so separation times can grow longer.

When isolating fully dispersed cells (such as in a Ficoll or leukopheresis PBMC prep), we have seen microbubbles carrying as many as 4 cells. Cells may also serve as a bridge between two microbubbles, significantly increasing the lifting capacity of the overall structure (see fluorescence microscopy example at left, where the microbubbles are blue).

Estimating the number of cells that can be lifted by a microbubble requires considering two features, one difficult and one pretty easy.

The difficult one first. The absolute limit on how many cells can be lifted is set by how many cells can be simultaneously attached to the surface of a sphere. This is a variant of what is know as the *kissing sphere* problem which has an extensive history in theoretical geometry. Fortunately, in real life it is highly unlikely that a microbubble would spontaneously load with the absolute number of cells geometrically possible, so only the easy problem remains.

The simpler question is how many cells are required to drive the effective buoyancy of the microbubble and its cargo to a value greater than the density of the surrounding fluid. This ‘break even’ point at which *F _{B} *in Stokes’ Law changes sign (i.e., goes from a floating force to a settling one) is a function of the density of the cells loading onto the bubble.

To find this threshold, you can begin by knowing the individual densities and radii of the microbubble and all of its cargo cells and calculating a total density (which we’ll call *ρ _{T}*) and an effective radius of the extended cell-bubble assembly.

Note here that the total density will determine will determine whether the bubble complex sinks or floats, and the effective radius will largely determine the rate at which it does so. The total density is just a volume-weighted average of the densities of the microbubble and its captured cells. There are many options for estimating an effective radius – I’ll leave that decision to you, but would suggest that you could proceed from looking at microbubble-cell complexes under fluorescence microscopy to gauge their overall architecture. Once you have, you can arrive at terminal velocity.

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