The present disclosure is drawn to inertial pumps. An inertial pump can include a microfluidic channel, a fluid actuator located in the microfluidic channel, and a check valve located in the microfluidic channel. The check valve can include a moveable valve element, a narrowed channel segment located upstream of the moveable valve element, and a blocking element formed in the microfluidic channel downstream of the moveable valve element. The narrowed channel segment can have a width less than a width of the moveable valve element so that the moveable valve element can block fluid flow through the check valve when the moveable valve element is positioned in the narrowed channel segment. The blocking element can be configured such that the blocking element constrains the moveable valve element within the check valve while also allowing fluid flow when the moveable valve element is positioned against the blocking element.

Embodiments disclosed herein are directed to microfluidic devices that allow for scalable on-chip screening of combinatorial libraries and methods of use thereof. Droplets comprising individual molecular species to be screened are loaded onto the microfluidic device. The droplets are labeled by methods known in the art, including but not limited to barcoding, such that the molecular species in each droplet can be uniquely identified. The device randomly sorts the droplets into individual microwells of an array of microwells designed to hold a certain number of individual droplets in order to derive combinations of the various molecular species. The paired droplets are then merged in parallel to form merged droplets in each microwell, thereby avoiding issues associated with single stream merging. Each microwell is then scanned, e.g., using microscopy, such as high content imaging microscopy, to detect the optical labels, thereby identifying the combination of molecular species in each microwell.