The invention generally provides a sieve valve including: a substrate defining a channel; a flexible membrane adapted and configured for deployment at an intersection with the channel; and one or more protrusions extending into the channel from the substrate or the flexible membrane. The one or more protrusions define a plurality of recesses extending beyond the intersection between the channel and the flexible membrane;A microfluidic circuit including one or more sieve valves. In particular embodiments, the circuit comprises one or more input/output valves. The one or one or more input/output valves can include one or more input valves and one or more output valves.The microfluidic circuit can further include a mixing circuit. At least one of the sieve valves can be positioned between the one or more input/output valves and the mixing circuit.The invention further provides methods of using the device for the analysis of samples comprising cells.