what is the best way to make ceramic foams is it by impregnation or by emerssion and what is the time and the procedure in order to incorporate the suspension over the sponge template
There are mainly two ways of making ceramic foams, by preparing a mixture that includes the foaming agent and the rest of the ingredients to form a polymeric foam (bubble processing) or inmersing a polymer foam in a ceramic slurry (replication), and in both cases submitting the mixture to thermal treatment in order to decompose the polymer in a controlled way, leaving the ceramic you require. Some examples are described in J. Eur. Ceram. Soc. 18 (1998) 1339. I hope this is of help.
From what I understand from your question, you're mainly interested in producing a ceramic foam from a polymer template. In order to get a good foam in the end, you need to achieve an uniform coverage of the template with ceramic slurry. Whether you can achieve this better by immersion or by impregnation depends a lot on the viscosity of your ceramics precursor slurry, the pore structure and mechanical properties of the foam and its wetting properties for the slurry. Generally speaking, things will become increasingly tricky the thicker the foam is and the finer its pore structure is. In certain cases you might be able to achieve a better coating of the foam template with ceramics when doing a subsequent immersion in two reactive components that lead to the formation of a coating on the surface. In this case, the viscosities of the individual immersion baths might be smaller and it's easier to remove the rest of the precursor bath from the foam.