In practical applications, the chemical and physical adsorption of a polymer solution greatly affects its action mode and effect. Understanding the adsorption mechanism and its influencing factors can help to optimize the application mode and ensure application efficiency. Three types of polymer solutions—partially hydrolyzed polyacrylamide (HPAM), hydrophobically associating polymer (AP-P4), and dendrimer hydrophobically associating polymer (DHAP), which are viscoelastic liquids—were used as sorbates to study their adsorption by a sorbent such as quartz sand. The effects of the solution concentration, contact time, particle size of quartz sand, solid–liquid ratio, and fluid movement on the adsorption capacity of the polymer solutions were examined. The results showed that HPAM presents a typical Langmuir monolayer adsorption characteristic, and its adsorption capacity (per unit area) is 1.17–1.62 μg/cm2. The association enhances the interactions of the AP-P4 and DHAP solutions, and they present multilayer characteristics of first-order chemical adsorption and secondary physical molecule adsorption. Moreover, the dendrite structure further increases the adsorption thickness of DHAP. Hence, the adsorption thicknesses of AP-P4 and DHAP are four and six times that of HPAM, respectively. The adsorption of the three polymers is consistent with the influence of fluid motion and decreases with increasing fluid velocity. However, the larger the thickness of the adsorption layer, the clearer the influence of the flow, and the higher the decrease in adsorption capacity. Optimizing the injection rate is an effective method to control the applications of a polymer in porous media.