We propose a method for classifying Wi-Fi enabled mobile handheld devices (smartphones) and non-handheld devices (laptops) in a completely passive way, that is resorting neither to traffic probes on network edge devices nor to deep packet inspection techniques to read application layer information. Instead, classification is performed starting from probe requests Wi-Fi frames, which can be sniffed with inexpensive commercial hardware. We extract distinctive features from probe request frames (how many probe requests are transmitted by each device, how frequently, etc.) and take a machine learning approach, training four different classifiers to recognize the two types of devices. We compare the performance of the different classifiers and identify a solution based on a Random Decision Forest that correctly classify devices 95% of the times. The classification method is then used as a pre-processing stage to analyze network traffic traces from the wireless network of a university building, with interesting considerations on the way different types of devices uses the network (amount of data exchanged, duration of connections, etc.). The proposed methodology finds application in many scenarios related to Wi-Fi network management/optimization and Wi-Fi based services
