Introducing surface inclination in the case of droplet impact on solid substrates results in complicated dynamics post impact. The present work investigates the dynamics involved in the spreading phase of the droplet on inclined substrates. Experiments are conducted with water droplets impinging on inclined dry solid substrates with varying wettability values. The results reveal the presence of three phases in the droplet spread behavior. In the first phase, the droplet is observed to depict a close radial symmetry and is dominated by inertia forces. Phase 1 ends when the upstream droplet lamella post impact gets pinned to the surface or starts retracting as a consequence of surface forces becoming dominant. A scaling analysis developed to predict the pinning time of the droplet shows that the pinning time is independent of impact velocity, which is also observed during experiments. The asymmetries in the radial evolution of the droplet appear in phase 2 and become dominant in phase 3. Phase 2 terminates when the droplet attains the maximum lateral spread, which is established as a function of the normal component of the Weber number. Phase 3 is initiated when the droplet starts retracting in the lateral direction while the longitudinal expansion continues. Using an energy-based model constructed to predict the maximum spread, we show that the impact inertia of the droplet controls the longitudinal droplet spread in phases 1 and 2, while the gravity forces are primarily responsible for the droplet spread in phase 3. The model results were validated with the experiments conducted in-house and were found to be in good agreement.

The generation of monodispersed droplets in T-junction microchannels has wide range applications in biochemical analysis and material synthesis. While the generation of these monodispersed droplets was previously considered to be a balance between forces acting from continuous phase and interfacial force, it is shown here that the inertial force from the dispersed phase also plays an important role in determining the size of the generated droplets. A theoretical analysis for the size of monodisperse droplets generated in a microfluidic T-junction device is developed, and it is validated with a large set of experimental observations. The theoretical analysis accounts for the inertial forces from the dispersed phase along with the forces from the continuous phase and the interfacial forces to define the non-dimensional numbers that govern the droplet breakup in the T-junction microchannel.

In a T-junction microchannel, channel geometry plays a major role that affects the physics behind droplet generation. The effect of channel width on droplet size and frequency in a T-junction microchannel is investigated in the present study. The current work is an extension of our previous work, where a model was developed to predict the size of the droplets generated in a T-junction microchannel when both the continuous and dispersed phase channels have equal widths. In the present work, we extended the model to account for the varying width ratio between the dispersed and continuous phase channels. We performed the in-house experiments by varying the channel width and viscosity ratios between the fluids to study the size of the droplets generated and to validate the proposed scaling law. We further investigated the effect of channel geometry on the frequency of droplet generation in the T-junction microchannels. Experimental results show that the droplet length increases with an increase in the width of the continuous phase channel. On the other hand, droplet production frequency decreases with an increase in the width of the continuous phase channel. With variations in the width of the dispersed phase channel, similar behavior in droplet sizes and frequency of droplet production is observed. The analysis of this study provides new insights into the effect of channelwidth on droplet length and frequency. Overall, this research intends to provide a thorough understanding of the design of microchannels based on the geometry and manipulation of droplets with varying widths.

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