The primary goal of relational databases is to provide efficient query processing on sets of tuples and thereafter, query evaluation and optimization strategies are a key issue in database implementation. Producing universally fast execu- tion plans remains a challenging task since the underlying relational model has a significant impact on algebraic definition of the operators, thereby on their implementation in terms of space and time complexity. At least, it should pre- vent a quadratic behavior in order to consider scaling-up towards the processing of large datasets. The main purpose of this paper is to show that there is no trivial relational modeling for managing collections of partitions (i.e. sets of sets). In the withheld case, we show that one could not express all the operators of the partition lattice and set-theoretic operations of the algebra of sets (viewing blocks as elements) within FO, and consequently as queries of the relational algebra (RA). We also show multiple evidence of inefficiency of RA-expressible operators and an alternative which warrant another computational model. Further, we present some experimental results that enforce this evidence and conclude that R-DBMS are inadequate for partition querying. Hence, we claim that there is a strong requirement for the design of an ad hoc system to manage partitions or at least to supplement an existing system on which both data persistence and transaction management could be delegated.