Processing of concentrated lignocellulosic biomass suspensions typically involves the conversion of the cellulose into sugars and sugars into ethanol. Biomass is usually pretreated via methods like comminution or steam explosion to form fine cellulosic fibers to be dispersed into an aqueous phase for further treatment. The resulting cellulose suspensions need to be pressurized and pumped into and out of various processing vessels without allowing the development of flow instabilities that are typically associated with "demixing", that is, the segregation of the cellulosic biomass from the aqueous phase via the formation of mats of cellulosic fibers and the filtration of the aqueous phase. Such demixing can prevent continuous processing at high rates. Here, the development of flow instabilities via the demixing effect for cellulose suspensions is demonstrated using capillary and compressive squeeze flows. It is shown that the use of a gelation agent, hydroxypropyl guar gum, at the critical concentration of 0.5 wt% or higher significantly affects the viscoelastic material functions of cellulosic suspensions, improves the dispersive mixing of the fibers within the aqueous phase, and results in the elimination of the flow instabilities and associated demixing effects that are ubiquitously observed during the pressurization and processing of cellulosic suspensions.