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We present experiments on the motion of swimming microbes in a laminar, hyperbolic flow. We test a theory that predicts the existence of swimming invariant manifolds (SwIMs) that act as invisible, one-way barriers that block the motion of the microbes. The flow is generated in a cross-channel in a PDMS cell, driven by syringe pumps. The swimming microbes are euglena and tetraselmis, both single-celled, eukaryotic algae. The algae are not ideal smooth-swimmers: there is significant rocking in their motion with occasional tumbles and a swimming speed that can vary. The experiments show that the swimming algae are bound very effectively by the predicted SwIMs. The different shapes and swimming behavior of the euglena and tetraselmis affect the distribution of swimming angles, with the elongated euglena having a larger probability of swimming in a direction parallel to the outflow directions. The differences in swimming orientation affect the ability of the microbes to penetrate the manifolds that act as barriers to passive tracers. The differing shapes of the euglena and tetraselmis also affect probabilities for the microbes to escape in one direction or the other along the outflow.