How to separate bacteria from eukariotic grinded tissue in liquid medium?

Any specific organelles you want separated? Recall bacteria don't have organelles. I'm sure you've heard of differential centrifugation? The following exert is from wiki

Differential centrifugation is a common procedure in microbiology and cytology used to separate certain organelles from whole cells for further analysis of specific parts of cells. In the process, a tissue sample is first homogenised to break the cell membranes and mix up the cell contents. The homogenate is then subjected to repeated centrifugations, each time removing the pellet and increasing the centrifugal force. Finally, purification may be done through equilibrium sedimentation, and the desired layer is extracted for further analysis.

Separation is based on size and density, with larger and denser particles pelleting at lower centrifugal forces. As an example, unbroken whole cells will pellet at low speeds and short intervals such as 1,000g for 5 minutes. Smaller cell fragments and organelles remain in the supernatant and require more force and greater times to pellet. In general, one can enrich for the following cell components, in the separating order in actual application:

• Whole cells and nuclei;
• Mitochondria, lysosomes and peroxisomes;
• Microsomes (vesicles of disrupted endoplasmic reticulum); and
• Ribosomes and cytosol.

No, I only want the bacteria. I've already thought about differential centrifugation, the problem is that 20% of the bacteria will be lost and it's extremelly inconvenient to do, as I need to extract the DNA from 50 mL of medium

True

Why are the two types of organisms submerged to begin with? This might result in a big issue later on

The bacteria were inside the animal. I want to study this population so I need to sequence the genomes from the microbiota. The DNA from the animal could spoil my sequencing.

Swab the bacteria on a petri dish and grow it individually, otherwise it's bad practice. Do you have the luxury to do this?

I have the resources, but not the time. On top of that, I thing I might lose some diversity by doing that

It would take a day to grow. You'll increase diversity, don't you think? Even bacteria you thought didn't exist would begin to form colonies. Otherwise, i wouldn't know who to do to separate the two organisms

Howzit

I have found that either Qiagen stool, M-N soil, or ISOLATE 2 tissue genomic exaction kits work well for the extraction of all genomic material from gut samples.  I advice dissecting the gut and flash freezing with liquid nitrogen.  To process the sample, grind it in liquid nitrogen and the use 25mg of the frozen powder for the DNA extraction by inserting it into appropriate buffer and then following protocol.  This way you are extracting all the genomic DNA in the sample and are not getting any culture bias.  The PCR is a crucial step which will require optimization.  A good primer set that selects for the 16S gene will specifically amplify your bacterial DNA. It would be worth your effort to compare try a nested PCR as well.  To get quick ideas of your diversity and community structure one could use DGGE as a tool because individual bands can be excised and sequenced but the most informative data will some from a meta-genomic sample.

I hope that helps